Alternatives to general relativity

16703:, ghost poles and higher order poles, and those that have problems with behaviour at infinity. Among metric theories, self-consistency is best illustrated by describing several theories that fail this test. The classic example is the spin-two field theory of Fierz and Pauli; the field equations imply that gravitating bodies move in straight lines, whereas the equations of motion insist that gravity deflects bodies away from straight line motion. Yilmaz (1971) contains a tensor gravitational field used to construct a metric; it is mathematically inconsistent because the functional dependence of the metric on the tensor field is not well defined. 19820:

general relativity as a special case, but only agree with the Parametric post-Newtonian values of general relativity when they are equal to general relativity to within experimental error. As experimental tests get more accurate, the deviation of the scalar–tensor theories from general relativity is being squashed to zero. The same is true of vector–tensor theories, the deviation of the vector–tensor theories from general relativity is being squashed to zero. Further, vector–tensor theories are semi-conservative; they have a nonzero value for

16930:

The incorporation of Maxwell's equations is incomplete unless it is assumed that they are imposed on the flat background space-time, and when that is done they are inconsistent, because they predict zero gravitational redshift when the wave version of light (Maxwell theory) is used, and nonzero redshift when the particle version (photon) is used. Another more obvious example is Newtonian gravity with Maxwell's equations; light as photons is deflected by gravitational fields (by half that of general relativity) but light as waves is not.

15989: 13208: 10904:

light was higher in the early universe. The discovery of unexpected rotation curves for galaxies took everyone by surprise. Could there be more mass in the universe than we are aware of, or is the theory of gravity itself wrong? The consensus now is that the missing mass is "cold dark matter", but that consensus was only reached after trying alternatives to general relativity, and some physicists still believe that alternative models of gravity may hold the answer.

4816: 14133:. This is not a metric theory. It was first claimed that it does not contain a black hole horizon, but Burko and Ori have found that nonsymmetric gravitational theory can contain black holes. Later, Moffat claimed that it has also been applied to explain rotation curves of galaxies without invoking "dark matter". Damour, Deser & MaCarthy have criticised nonsymmetric gravitational theory, saying that it has unacceptable asymptotic behaviour. 17035:'s conjecture states that any complete, self-consistent theory of gravity that embodies the Weak Equivalence Principle necessarily embodies Einstein's Equivalence Principle. This is likely to be true if the theory has full energy conservation. Metric theories satisfy the Einstein Equivalence Principle. Extremely few non-metric theories satisfy this. For example, the non-metric theory of Belinfante & Swihart is eliminated by the 15648: 3470: 12662: 10539: 6681: 10874:, which replaces the metric in its field equations with a pair of gauge fields in flat spacetime. On the one hand, the theory is quite conservative because it is substantially equivalent to Einstein–Cartan theory (or general relativity in the limit of vanishing spin), differing mostly in the nature of its global solutions. On the other hand, it is radical because it replaces differential geometry with 10296:

criteria for testing non-metric theories against Einstein's Equivalence Principle. Misner et al. claims that Cartan's theory is the only non-metric theory to survive all experimental tests up to that date and Turyshev lists Cartan's theory among the few that have survived all experimental tests up to that date. The following is a quick sketch of Cartan's theory as restated by Trautman.

5061: 4589: 13971: 15984:{\displaystyle S_{S}=-\int d^{4}x\,{\sqrt {-g}}{\frac {1}{G^{3}}}\left({\frac {1}{2}}g^{\mu \nu }\,\nabla _{\mu }G\,\nabla _{\nu }G-V(G)\right)+{\frac {1}{G}}\left({\frac {1}{2}}g^{\mu \nu }\,\nabla _{\mu }\omega \,\nabla _{\nu }\omega -V(\omega )\right)+{1 \over \mu ^{2}G}\left({\frac {1}{2}}g^{\mu \nu }\,\nabla _{\mu }\mu \,\nabla _{\nu }\mu -V(\mu )\right).} 13203:{\displaystyle {\begin{aligned}S_{s}&=-{\frac {1}{2}}\int \left{\sqrt {-g}}\,d^{4}x\\S_{v}&=-{\frac {K}{32\pi G}}\int \left}U_{}-{\frac {2\lambda }{K}}\left(g^{\mu \nu }U_{\mu }U_{\nu }+1\right)\right]{\sqrt {-g}}\,d^{4}x\\S_{m}&=\int L\left({\tilde {g}}_{\mu \nu },f^{\alpha },f_{|\mu }^{\alpha },\ldots \right){\sqrt {-g}}\,d^{4}x\end{aligned}}} 3239: 4558: 10911:. This led to the rapid reinstatement of Einstein's cosmological constant, and quintessence arrived as an alternative to the cosmological constant. At least one new alternative to general relativity attempted to explain the supernova surveys' results in a completely different way. The measurement of the speed of gravity with the gravitational wave event 8477: 10310: 5256: 15640: 6351: 17416:

existence of a black hole horizon can be used as tests of alternative to general relativity. General relativity predicts that gravitational waves travel at the speed of light. Many alternatives to general relativity say that gravitational waves travel faster than light, possibly breaking causality. After the multi-messaging detection of the

5721: 10855: 8800: 4841: 4811:{\displaystyle L_{\varphi }=e^{{\frac {1}{2}}(3\varphi +\chi )}\left(-{\tfrac {1}{2}}e^{-\varphi }\,\partial _{\alpha }\varphi \,\partial _{\alpha }\varphi -e^{-\varphi }\,\partial _{\alpha }\varphi \,\partial _{\chi }\varphi +{\tfrac {3}{2}}e^{-\chi }\,\partial _{0}\varphi \,\partial _{0}\varphi \right)\,} 17016:

10. The third is local position invariance, which includes spatial and temporal invariance. The outcome of any local non-gravitational experiment is independent of where and when it is performed. Spatial local position invariance is tested using gravitational redshift measurements. The test parameter

16929:

is set to -1, in which case they match the theory of Brans–Dicke and so are worthy of further consideration. Milne is incomplete because it makes no gravitational red-shift prediction. The theories of Whitrow and Morduch, Kustaanheimo and Kustaanheimo and Nuotio are either incomplete or inconsistent.

12078:

According to Occam's razor, Farnes' theory is a simpler alternative to the conventional LambdaCDM model, as both dark energy and dark matter (two hypotheses) are solved using a single negative mass fluid (one hypothesis). The theory will be directly testable using the world's largest radio telescope,

11915:

for only negative mass particles. In this way, the negative mass particles surround galaxies and apply a pressure onto them, thereby resembling dark matter. As these hypothesised particles mutually repel one another, they push apart the Universe, thereby resembling dark energy. The creation of matter

85:

Experimental tests improved along with the theories. Many of the different strategies that were developed soon after general relativity were abandoned, and there was a push to develop more general forms of the theories that survived, so that a theory would be ready when any test showed a disagreement

19819:

The stratified theories of Ni, Lee Lightman and Ni are non-starters because they all fail to explain the perihelion advance of Mercury. The bimetric theories of Lightman and Lee, Rosen, Rastall all fail some of the tests associated with strong gravitational fields. The scalar–tensor theories include

17456:

is the strictest test. For those theories that incorporate or aim to replace dark energy, the supernova brightness results and the age of the universe can be used as tests. Another test is the flatness of the universe. With general relativity, the combination of baryonic matter, dark matter and dark

17068:

Work on developing a standardized rather than ad hoc set of tests for evaluating alternative gravitation models began with Eddington in 1922 and resulted in a standard set of Parametric post-Newtonian numbers in Nordtvedt and Will and Will and Nordtvedt. Each parameter measures a different aspect of

15001: 10886:

This section includes alternatives to general relativity published after the observations of galaxy rotation that led to the hypothesis of "dark matter". There is no known reliable list of comparison of these theories. Those considered here include: Bekenstein, Moffat, Moffat, Moffat. These theories

10299:

Cartan suggested a simple generalization of Einstein's theory of gravitation. He proposed a model of space time with a metric tensor and a linear "connection" compatible with the metric but not necessarily symmetric. The torsion tensor of the connection is related to the density of intrinsic angular

9653:

Before we start, Will (2001) has said: "Many alternative metric theories developed during the 1970s and 1980s could be viewed as "straw-man" theories, invented to prove that such theories exist or to illustrate particular properties. Few of these could be regarded as well-motivated theories from the

81:

After general relativity, attempts were made either to improve on theories developed before general relativity, or to improve general relativity itself. Many different strategies were attempted, for example the addition of spin to general relativity, combining a general relativity-like metric with a

19847:

which can have a measurable effect on the Earth's tides. Non-metric theories, such as Belinfante and Swihart, usually fail to agree with experimental tests of Einstein's equivalence principle. And that leaves, as a likely valid alternative to general relativity, nothing except possibly Cartan. That

19776:

All experimental tests agree with general relativity so far, and so Parametric post-Newtonian analysis immediately eliminates all the scalar field theories in the table. A full list of Parametric post-Newtonian parameters is not available for Whitehead, Deser-Laurent, Bollini–Giambiagi–Tiomino, but

10903:

and the observation that at early times when quarks were first forming there was not enough space on the universe to contain even one quark. Inflation theory was developed to overcome these difficulties. Another alternative was constructing an alternative to general relativity in which the speed of

1572: 16352:

The model was proposed in a series of articles, the first dating from 2003. The basic point is that since within General Relativity, gravitational fields couple to each other, this can effectively increase the gravitational interaction between massive objects. The additional gravitational strength

2997: 89:

By the 1980s, the increasing accuracy of experimental tests had all confirmed general relativity; no competitors were left except for those that included general relativity as a special case. Further, shortly after that, theorists switched to string theory which was starting to look promising, but

45:

These attempts can be split into four broad categories based on their scope. In this article, straightforward alternatives to general relativity are discussed, which do not involve quantum mechanics or force unification. Other theories which do attempt to construct a theory using the principles of

10303:

The original description is in terms of differential forms, but for the present article that is replaced by the more familiar language of tensors (risking loss of accuracy). As in general relativity, the Lagrangian is made up of a massless and a mass part. The Lagrangian for the massless part is:

10295:

Cartan's theory is particularly interesting both because it is a non-metric theory and because it is so old. The status of Cartan's theory is uncertain. Will claims that all non-metric theories are eliminated by Einstein's Equivalence Principle. Will (2001) tempers that by explaining experimental

8153: 14668:

Haugan and Kauffmann used polarization measurements of the light emitted by galaxies to impose sharp constraints on the magnitude of some of nonsymmetric gravitational theory's parameters. They also used Hughes-Drever experiments to constrain the remaining degrees of freedom. Their constraint is

12105:

The original theory of MOND by Milgrom was developed in 1983 as an alternative to "dark matter". Departures from Newton's law of gravitation are governed by an acceleration scale, not a distance scale. MOND successfully explains the Tully–Fisher observation that the luminosity of a galaxy should

10895:

Motivations for the more recent alternatives to general relativity are almost all cosmological, associated with or replacing such constructs as "inflation", "dark matter" and "dark energy". The basic idea is that gravity agrees with general relativity at the present epoch but may have been quite

9637:

So long as general relativity is confirmed by experiment, general Scalar–Tensor theories (including Brans–Dicke) can never be ruled out entirely, but as experiments continue to confirm general relativity more precisely and the parameters have to be fine-tuned so that the predictions more closely

1019:

General relativity is a tensor theory, the equations all contain tensors. Nordström's theories, on the other hand, are scalar theories because the gravitational field is a scalar. Other proposed alternatives include scalar–tensor theories that contain a scalar field in addition to the tensors of

16711:

To be complete, a theory of gravity must be capable of analysing the outcome of every experiment of interest. It must therefore mesh with electromagnetism and all other physics. For instance, any theory that cannot predict from first principles the movement of planets or the behaviour of atomic

1243:

Almost every theory described in this article has an action. It is the most efficient known way to guarantee that the necessary conservation laws of energy, momentum and angular momentum are incorporated automatically; although it is easy to construct an action where those conservation laws are

12501:

is the MOND length scale. By 1988, a second scalar field (PCC) fixed problems with the earlier scalar–tensor version but is in conflict with the perihelion precession of Mercury and gravitational lensing by galaxies and clusters. By 1997, MOND had been successfully incorporated in a stratified

17415:

Parametric post-Newtonian is only a measure of weak field effects. Strong gravity effects can be seen in compact objects such as white dwarfs, neutron stars, and black holes. Experimental tests such as the stability of white dwarfs, spin-down rate of pulsars, orbits of binary pulsars and the

3523:

Ni summarized some theories and also created two more. In the first, a pre-existing special relativity space-time and universal time coordinate acts with matter and non-gravitational fields to generate a scalar field. This scalar field acts together with all the rest to generate the metric.

13709: 3519:

is constant. Given that variable c and zero deflection of light are both in conflict with experiment, the prospect for a successful scalar theory of gravity looks very unlikely. Further, if the parameters of a scalar theory are adjusted so that the deflection of light is correct then the

3465:{\displaystyle f\left({\frac {\varphi }{c^{2}}}\right)={\frac {\varphi }{c^{2}}}+\alpha \left({\frac {\varphi }{c^{2}}}\right)^{2},\qquad {\frac {c_{\infty }^{2}}{c^{2}}}=1+4\left({\frac {\varphi }{c_{\infty }^{2}}}\right)+(15+2\alpha )\left({\frac {\varphi }{c_{\infty }^{2}}}\right)^{2}} 12391: 4407: 3228: 10534:{\displaystyle {\begin{aligned}L&={1 \over 32\pi G}\Omega _{\nu }^{\mu }g^{\nu \xi }x^{\eta }x^{\zeta }\varepsilon _{\xi \mu \eta \zeta }\\\Omega _{\nu }^{\mu }&=d\omega _{\nu }^{\mu }+\omega _{\xi }^{\eta }\\\nabla x^{\mu }&=-\omega _{\nu }^{\mu }x^{\nu }\end{aligned}}} 12073: 8265: 69:, remaining consistent with all observations so far. In contrast, many of the early alternatives have been definitively disproven. However, some of the alternative theories of gravity are supported by a minority of physicists, and the topic remains the subject of intense study in 16123: 5548: 5069: 6676:{\displaystyle {\begin{aligned}(y^{\mu })^{-}&=x^{\mu }-(x^{\mu })^{-},\qquad (y^{\mu })^{-}(y_{\mu })^{-}=0,\\w^{-}&=(y^{\mu })^{-}(u_{\mu })^{-},\qquad (u_{\mu })={\frac {dx^{\mu }}{d\sigma }},\\d\sigma ^{2}&=\eta _{\mu \nu }\,dx^{\mu }\,dx^{\nu }\end{aligned}}} 90:

has since lost popularity. In the mid-1980s a few experiments were suggesting that gravity was being modified by the addition of a fifth force (or, in one case, of a fifth, sixth and seventh force) acting in the range of a few meters. Subsequent experiments eliminated these.

6291: 15449: 16968:

As an example of disagreement with Newtonian experiments, Birkhoff theory predicts relativistic effects fairly reliably but demands that sound waves travel at the speed of light. This was the consequence of an assumption made to simplify handling the collision of masses.

12251: 16690:

Any putative alternative to general relativity would need to meet a variety of tests for it to become accepted. For in-depth coverage of these tests, see Misner et al. Ch.39, Will Table 2.1, and Ni. Most such tests can be categorized as in the following subsections.

8993: 11565: 17196: 5559: 1956:

is appropriate because a few of these theories rely on Mach's principle (e.g. Whitehead), and many mention it in passing (e.g. Einstein–Grossmann, Brans–Dicke). Mach's principle can be thought of a half-way-house between Newton and Einstein. It goes this way:

13396: 15107: 9645:, the most general Lagrangian constructed out of the metric tensor and a scalar field leading to second order equations of motion in 4-dimensional space. Viable theories beyond Horndeski (with higher order equations of motion) have been shown to exist. 2572:

These theories are presented here without a cosmological constant or added scalar or vector potential unless specifically noted, for the simple reason that the need for one or both of these was not recognized before the supernova observations by the

642: 82:

spacetime that is static with respect to the expansion of the universe, getting extra freedom by adding another parameter. At least one theory was motivated by the desire to develop an alternative to general relativity that is free of singularities.

762: 9502: 3704: 11436: 4225: 3096: 10697: 5056:{\displaystyle S={1 \over 64\pi G}\int d^{4}x\,{\sqrt {-\eta }}\eta ^{\mu \nu }g^{\alpha \beta }g^{\gamma \delta }(g_{\alpha \gamma |\mu }g_{\alpha \delta |\nu }-\textstyle {\frac {1}{2}}g_{\alpha \beta |\mu }g_{\gamma \delta |\nu })+S_{m}} 7086:

associated with this partial gauge invariance is wrong. Linear Fixed Gauge theories seek to remedy this by breaking the gauge invariance of the gravitational action through the introduction of auxiliary gravitational fields that couple to

5852: 16952:(generally tested around the Sun), and anomalous perihelion advance of the planets. Each theory should reproduce the observed results in these areas, which have to date always aligned with the predictions of general relativity. In 1964, 8682: 15198: 14422: 16263: 6689:

Deser and Laurent and Bollini–Giambiagi–Tiomno are Linear Fixed Gauge theories. Taking an approach from quantum field theory, combine a Minkowski spacetime with the gauge invariant action of a spin-two tensor field (i.e. graviton)

14847: 17428:

Useful cosmological scale tests are just beginning to become available. Given the limited astronomical data and the complexity of the theories, comparisons involve complex parameters. For example, Reyes et al., analyzed 70,205

1434: 11326: 2857: 11776: 8000: 24146:

Reyes, Reinabelle; Mandelbaum, Rachel; Seljak, Uros; Baldauf, Tobias; Gunn, James E.; Lombriser, Lucas; Smith, Robert E. (2010). "Confirmation of general relativity on large scales from weak lensing and galaxy velocities".

13966:{\displaystyle {\begin{aligned}\alpha _{1}&={\frac {4G}{K}}\left((2K-1)e^{-4\varphi _{0}}-e^{4\varphi _{0}}+8\right)-8\\\alpha _{2}&={\frac {6G}{2-K}}-{\frac {2G(K+4)e^{4\varphi _{0}}}{(2-K)^{2}}}-1\end{aligned}}} 11127: 8674: 17069:

how much a theory departs from Newtonian gravity. Because we are talking about deviation from Newtonian theory here, these only measure weak-field effects. The effects of strong gravitational fields are examined later.

16675:

Finally, the model made a prediction that the amount of missing mass (i.e., the dark mass in dark matter approaches) in elliptical galaxies correlates with the ellipticity of the galaxies. This was tested and verified.

3618: 2846: 7077: 18975: 2669: 13670: 13283: 866: 12262: 9919: 17398: 11219: 4553:{\displaystyle L_{\varphi }=e^{\varphi }\left({\tfrac {1}{2}}e^{-\varphi }\,\partial _{\alpha }\varphi \,\partial _{\alpha }\varphi +{\tfrac {3}{2}}e^{\varphi }\,\partial _{0}\varphi \,\partial _{0}\varphi \right)} 14676:(MSTG) theory is able to predict rotation curves for galaxies without either dark matter or MOND, and claims that it can also explain gravitational lensing of galaxy clusters without dark matter. It has variable 8472:{\displaystyle {\mathcal {L}}={\sqrt {-g}}\ (\alpha _{0}+\alpha _{1}R+\alpha _{2}\left(R^{2}+R_{\alpha \beta \mu \nu }R^{\alpha \beta \mu \nu }-4R_{\mu \nu }R^{\mu \nu }\right)+\alpha _{3}{\mathcal {O}}(R^{3})),} 9572: 4138: 3107: 16983:

Einstein's Equivalence Principle has three components. The first is the uniqueness of free fall, also known as the Weak Equivalence Principle. This is satisfied if inertial mass is equal to gravitational mass.

22318:

Achour, Jibril Ben; Crisostomi, Marco; Koyama, Kazuya; Langlois, David; Noui, Karim; Tasinato, Gianmassimo (December 2016). "Degenerate higher order scalar–tensor theories beyond Horndeski up to cubic order".

17477:. The following table lists Parametric post-Newtonian values for a large number of theories. If the value in a cell matches that in the column heading then the full formula is too complicated to include here. 11926: 1378: 12667: 10315: 6356: 16000: 10690:

is the metric tensor as usual. By assuming that the linear connection is metric, it is possible to remove the unwanted freedom inherent in the non-metric theory. The stress–energy tensor is calculated from:

5390: 5251:{\displaystyle \Box _{\eta }g_{\mu \nu }-g^{\alpha \beta }\eta ^{\gamma \delta }g_{\mu \alpha |\gamma }g_{\nu \beta |\delta }=-16\pi G{\sqrt {g/\eta }}(T_{\mu \nu }-\textstyle {\frac {1}{2}}g_{\mu \nu }T)\,} 11811:

is an arbitrary function of the scalar field rather than a constant, it can be set to give an acceleration that is large in the early universe and small at the present epoch. This is known as quintessence.

10216: 7440:

where the coefficients of the extra terms are chosen so that the action reduces to general relativity in 4 spacetime dimensions and the extra terms are only non-trivial when more dimensions are introduced.

528: 15635:{\displaystyle S_{K}=-\int d^{4}x\,{\sqrt {-g}}\omega \left({\frac {1}{4}}B_{\mu \nu }B^{\mu \nu }+V(K)\right),\qquad {\text{where }}\quad B_{\mu \nu }=\partial _{\mu }K_{\nu }-\partial _{\nu }K_{\mu }.} 8879: 6785: 14116: 13714: 12130:). A relativistic version of this based on scalar–tensor theory was rejected because it allowed waves in the scalar field to propagate faster than light. The Lagrangian of the non-relativistic form is: 6096: 4396: 18026: 17930: 17831: 10034: 17473:

General Relativity is now more than 100 years old, during which one alternative theory of gravity after another has failed to agree with ever more accurate observations. One illustrative example is

10152: 2599:

The scalar field theories of Nordström have already been discussed. Those of Littlewood, Bergman, Yilmaz, Whitrow and Morduch and Page and Tupper follow the general formula give by Page and Tupper.

1158: 12136: 17400:

measure the extent and nature of breakdowns in global conservation laws. A theory of gravity possesses 4 conservation laws for energy-momentum and 6 for angular momentum only if all five are zero.

16858: 10612: 3917: 17317: 15238: 8887: 16809: 11044: 10657: 7989: 7616: 7435: 1677: 22188:

Zumalacárregui, Miguel; García-Bellido, Juan (2014-03-19). "Transforming gravity: from derivative couplings to matter to second-order scalar–tensor theories beyond the Horndeski Lagrangian".

14664: 11447: 7258: 5968: 5340: 1244:

violated. Canonical methods provide another way to construct systems that have the required conservation laws, but this approach is more cumbersome to implement. The original 1983 version of

10263: 7676: 5716:{\displaystyle a\Box _{\eta }B^{\mu \nu }+f\eta ^{\mu \nu }\Box _{\eta }B=-4\pi G{\sqrt {g/\eta }}\,T^{\alpha \beta }\left({\frac {\partial g_{\alpha \beta }}{\partial B_{\mu }\nu }}\right)} 17420:

coalescence of neutron stars, where light and gravitational waves were measured to travel at the same speed with an error of 1/10, many of those modified theories of gravity were excluded.

16988:

is a parameter used to test the maximum allowable violation of the Weak Equivalence Principle. The first tests of the Weak Equivalence Principle were done by Eötvös before 1900 and limited

11867: 19803:, which is in strong conflict with general relativity and experimental results. In particular, these theories predict incorrect amplitudes for the Earth's tides. (A minor modification of 15244:. The skew field coupling is a Pauli coupling and is gauge invariant for any source current. The source current looks like a matter fermion field associated with baryon and lepton number. 10915:

ruled out many alternative theories of gravity as explanations for the accelerated expansion. Another observation that sparked recent interest in alternatives to General Relativity is the

9960: 17075: 14836: 13526: 9632: 9306: 298: 19716: 19451: 19369: 15332: 13289: 12651: 8158:

in order to make sure that only massless spin −2 and spin −0 components propagate in the graviton propagator around Minkowski background. The action becomes non-local beyond the scale

10221:

These vector–tensor theories are semi-conservative, which means that they satisfy the laws of conservation of momentum and angular momentum but can have preferred frame effects. When

2713: 364: 15009: 10575: 9162:

was thought to be zero at the time anyway, this would not have been considered a significant difference. The role of the cosmological constant in more modern work is discussed under

3925:

is the universal time coordinate. This theory is self-consistent and complete. But the motion of the solar system through the universe leads to serious disagreement with experiment.

5911: 982: 11809: 11652: 11601: 9056: 932: 12499: 9605: 9026: 16426:

have the same form. The validity of the GRSI model then simply hinges on whether the coupling of the gravitational fields is large enough so that the same effects that occur in

10989:

led to the general acceptance that it is zero, but the use of a non-zero value came back when data from supernovae indicated that the expansion of the universe is accelerating.

536: 448: 395: 329: 218: 14041: 653: 14215: 9335: 3626: 16566: 16463: 15394: 14729: 14572: 14165: 11680: 10688: 8580: 7116: 6719: 6002: 5290: 1637: 1606: 1291: 1227: 253: 18310: 6343: 19010: 18726: 18562: 14673: 12443: 10987: 10919:. It was quickly discovered that alternatives to general relativity could explain this anomaly. This is now believed to be accounted for by non-uniform thermal radiation. 10064: 9138: 3510: 19845: 19801: 19248: 19212: 18816: 18788: 18660: 18632: 18491: 18463: 18370: 18224: 18164: 18136: 17628: 17600: 17572: 12576: 11337: 10850:{\displaystyle T^{\mu \nu }={1 \over 16\pi G}(g^{\mu \nu }\eta _{\eta }^{\xi }-g^{\xi \mu }\eta _{\eta }^{\nu }-g^{\xi \nu }\eta _{\eta }^{\mu })\Omega _{\xi }^{\eta }\;} 3984: 3955: 2001:

This section includes alternatives to general relativity published after general relativity but before the observations of galaxy rotation that led to the hypothesis of "

19771: 19572: 19310: 19279: 17740: 17712: 17684: 17656: 14757: 14600: 14504: 14476: 13572: 11622: 10960: 10899:

In the 1980s, there was a slowly dawning realisation in the physics world that there were several problems inherent in the then-current big-bang scenario, including the

8245: 6030: 15362: 12549: 10094: 9685: 9188: 4146: 3730: 3008: 18930: 16295: 13483: 12528: 9160: 8795:{\displaystyle L_{\varphi }=\varphi R-{\omega (\varphi ) \over \varphi }g^{\mu \nu }\,\partial _{\mu }\varphi \,\partial _{\nu }\varphi +2\varphi \lambda (\varphi )\;} 4248: 2740: 24545: 19156: 18411: 18084: 17502: 17218: 16927: 16902: 14246: 9084: 6315: 6088: 5732: 1010: 19177: 18757: 18583: 18432: 18105: 17951: 17852: 17523: 17240: 14541: 14455: 13699: 4832:

Bimetric theories contain both the normal tensor metric and the Minkowski metric (or a metric of constant curvature), and may contain other scalar or vector fields.

1192: 17262: 16733: 15421: 8210: 8183: 4581: 4268: 3757: 18604: 17544: 17319:

measure the extent and nature of "preferred-frame effects". Any theory of gravity in which at least one of the three is nonzero is called a preferred-frame theory.

15118: 13463: 7708: 1421: 1401: 19634: 19530: 14695: 14254: 13424: 9327: 9233: 9212: 9105: 8552: 6063: 5382: 5361: 1100: 1079: 890: 170: 145: 19686: 19607: 19503: 19421: 19339: 16419:

emerging from the strong force. In both cases, the phenomenological formulas describing these observations are similar, albeit with different numerical factors.

17039:

formalism for testing Einstein's Equivalence Principle. Gauge theory gravity is a notable exception, where the strong equivalence principle is essentially the

16878: 16753: 16527: 16507: 16483: 16176: 16146: 15441: 12414: 11815:

A similar method can be used in alternatives to general relativity that use vector fields, including Rastall and vector–tensor theories. A term proportional to

7285: 1793: 20227:

Ni, Wei-Tou (1972). "Theoretical Frameworks for Testing Relativistic Gravity.IV. a Compendium of Metric Theories of Gravity and Their POST Newtonian Limits".

14996:{\displaystyle S_{F}=\int d^{4}x\,{\sqrt {-g}}\left({\frac {1}{12}}F_{\mu \nu \rho }F^{\mu \nu \rho }-{\frac {1}{4}}\mu ^{2}A_{\mu \nu }A^{\mu \nu }\right)\;} 10300:

momentum. Independently of Cartan, similar ideas were put forward by Sciama, by Kibble in the years 1958 to 1966, culminating in a 1976 review by Hehl et al.

13703:

The Parametric post-Newtonian parameters of this theory are calculated in, which shows that all its parameters are equal to general relativity's, except for

1567:{\displaystyle 0=\nabla _{\nu }T^{\mu \nu }={T^{\mu \nu }}_{,\nu }+\Gamma _{\sigma \nu }^{\mu }T^{\sigma \nu }+\Gamma _{\sigma \nu }^{\nu }T^{\mu \sigma }\,} 14841:

Both the gravity and mass terms match those of general relativity with cosmological constant. The skew field action and the skew field matter coupling are:

2992:{\displaystyle f\left({\frac {\varphi }{c^{2}}}\right)=\exp \left(-{\frac {\varphi }{c^{2}}}-{\frac {(c/\varphi ^{2})^{2}}{2}}\right)\qquad c=c_{\infty }\,} 8148:{\displaystyle 2f_{1}\left({\frac {\Box }{M_{s}^{2}}}\right)+f_{2}\left({\frac {\Box }{M_{s}^{2}}}\right)+2f_{3}\left({\frac {\Box }{M_{s}^{2}}}\right)=0,} 8523:

reduces to a 4 by 4 metric and a single scalar. So if the 5th element is treated as a scalar gravitational field instead of an electromagnetic field then

5261:

Lightman–Lee developed a metric theory based on the non-metric theory of Belinfante and Swihart. The result is known as BSLL theory. Given a tensor field

11230: 8247:, the gravitational interaction weakens enough to resolve point-like singularity, which means Schwarzschild's singularity can be potentially resolved in 2267: 23355:

Deur, Alexandre (2019). "An explanation for dark matter and dark energy consistent with the Standard Model of particle physics and General Relativity".

11688: 10265:

they reduce to general relativity so, so long as general relativity is confirmed by experiment, general vector–tensor theories can never be ruled out.

17433:

with a cross-correlation involving galaxy velocity estimates and gravitational potentials estimated from lensing and yet results are still tentative.

24380: 23736:

Barker, W. E. V.; Hobson, M. P.; Lasenby, A. N. (2023). "Does gravitational confinement sustain flat galactic rotation curves without dark matter?".

16598: 16944:

There are three "classical" tests (dating back to the 1910s or earlier) of the ability of gravity theories to handle relativistic effects; they are

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Lombriser, Lucas; Lima, Nelson (2017). "Challenges to Self-Acceleration in Modified Gravity from Gravitational Waves and Large-Scale Structure".

12386:{\displaystyle L=-{a_{0}^{2} \over 8\pi G}{\tilde {f}}\left(\ell _{0}^{2}g^{\mu \nu }\,\partial _{\mu }\varphi \,\partial _{\nu }\varphi \right)} 9657:

Hellings and Nordtvedt and Will and Nordtvedt are both vector–tensor theories. In addition to the metric tensor there is a timelike vector field

6796: 21932:

Field, J. H. (2007). "Retarded electric and magnetic fields of a moving charge: Feynman's derivation of Liénard-Wiechert potentials revisited".

18936: 2608: 2602:

According to Page and Tupper, who discuss all these except Nordström, the general scalar field theory comes from the principle of least action:

24682: 22781:

Farnes, J.S. (2018). "A Unifying Theory of Dark Energy and Dark Matter: Negative Masses and Matter Creation within a Modified ΛCDM Framework".

13584: 13219: 777: 16533:, a background-field model. or the coincidental phenomenologies in galactic or hadronic dynamics mentioned in the previous paragraph, is that 16301:. This avoids a black hole singularity near the origin, while recovering the 1/r fall of the general relativity potential at large distances. 9693: 17324: 17000:

10. The second is Lorentz invariance. In the absence of gravitational effects the speed of light is constant. The test parameter for this is

11138: 3223:{\displaystyle f\left({\frac {\varphi }{c^{2}}}\right)=\exp \left(-{\frac {\varphi }{c^{2}}}\right),\qquad c^{2}=c_{\infty }^{2}-2\varphi \,} 12068:{\displaystyle R_{\mu \nu }-{\frac {1}{2}}Rg_{\mu \nu }={\frac {8\pi G}{c^{4}}}\left(T_{\mu \nu }^{+}+T_{\mu \nu }^{-}+C_{\mu \nu }\right)} 10860:

The space curvature is not Riemannian, but on a Riemannian space-time the Lagrangian would reduce to the Lagrangian of general relativity.

9654:

point of view, say, of field theory or particle physics. Examples are the vector–tensor theories studied by Will, Nordtvedt and Hellings."

1990:

was the most accurate theory of gravity. Since then, a number of alternatives were proposed. The theories which predate the formulation of

9513: 3992: 16411:(analogous to the repulsion of dark energy that balances gravitational attraction at large scales.) Two other parallel phenomena are the 16118:{\displaystyle V(K)=-{\frac {1}{2}}\mu ^{2}\varphi ^{\mu }\varphi _{\mu }-{\frac {1}{4}}g\left(\varphi ^{\mu }\varphi _{\mu }\right)^{2}} 5543:{\displaystyle S={1 \over 16\pi G}\int d^{4}x{\sqrt {-\eta }}(aB^{\mu \nu |\alpha }B_{\mu \nu |\alpha }+fB_{,\alpha }B^{,\alpha })+S_{m}} 23128:

Biswas, Tirthabir; Conroy, Aindriú; Koshelev, Alexey S.; Mazumdar, Anupam (2013). "Generalized ghost-free quadratic curvature gravity".

12106:

scale as the fourth power of the rotation speed. It also explains why the rotation discrepancy in dwarf galaxies is particularly large.

1303: 24488: 22015:

Biswas, Tirthabir; Gerwick, Erik; Koivisto, Tomi; Mazumdar, Anupam (2012). "Towards Singularity- and Ghost-Free Theories of Gravity".

23181:

Biswas, Tirthabir; Gerwick, Erik; Koivisto, Tomi; Mazumdar, Anupam (2011). "Towards singularity and ghost free theories of gravity".

10163: 20261: 16667:, that is the fact that at present time, the purported repulsion of dark energy nearly exactly cancels the action of gravity in the 7141:

Einstein's general relativity is the simplest plausible theory of gravity that can be based on just one symmetric tensor field (the

6286:{\displaystyle g_{\mu \nu }(x^{\alpha })=\eta _{\mu \nu }-2\int _{\Sigma ^{-}}{y_{\mu }^{-}y_{\nu }^{-} \over (w^{-})^{3}}\left^{-}} 24410: 17470:(See Will and Ni for more details. Misner et al. gives a table for translating parameters from the notation of Ni to that of Will) 1987: 1254:

A theory of gravity is a "metric theory" if and only if it can be given a mathematical representation in which two conditions hold:

456: 93:

Motivations for the more recent alternative theories are almost all cosmological, associated with or replacing such constructs as "

14136:

The mathematics is not difficult but is intertwined so the following is only a brief sketch. Starting with a non-symmetric tensor

11603:

can be added to scalar tensor theories. This can be done in every alternative the general relativity that contains a scalar field

8808: 6727: 58:. Finally, the most ambitious theories attempt to both put gravity in quantum mechanical terms and unify forces; these are called 24986: 24806: 14049: 24659: 22754: 4276: 1731: 24965: 24914: 24473: 23781:

Deur, A. (2022). "Effect of the field self-interaction of General Relativity on the cosmic microwave background anisotropies".

20272:

Although an important source for this article, the presentations of Turyshev (2006) and Lang (2002) contain many errors of fact

17986: 17890: 17791: 17474: 17056: 16602: 16373: 12246:{\displaystyle L=-{a_{0}^{2} \over 8\pi G}f\left\lbrack {\frac {|\nabla \varphi |^{2}}{a_{0}^{2}}}\right\rbrack -\rho \varphi } 9968: 1251:

A few theories have an action but not a Lagrangian density. A good example is Whitehead, the action there is termed non-local.

1297:(−, +, +, +), which governs proper-length and proper-time measurements in the usual manner of special and general relativity: 24991: 24458: 24373: 23242:

Lousto, Carlos O; Mazzitelli, Francisco D (1997). "Exact self-consistent gravitational shock wave in semiclassical gravity".

20077: 17453: 10106: 1108: 8988:{\displaystyle T^{\mu \nu }\ {\stackrel {\mathrm {def} }{=}}\ {2 \over {\sqrt {g}}}{\delta S_{m} \over \delta g_{\mu \nu }}} 24736: 24667: 24643: 24616: 23757:

Deur, A. (2023). "Comment on "Does gravitational confinement sustain flat galactic rotation curves without dark matter?"".

20358:

Fierz, M.; Pauli, W. (1939). "On relativistic wave equations for particles of arbitrary spin in an electromagnetic field".

19804: 15259: 15253: 12507: 12096: 8530:

Scalar–Tensor theories include Thiry, Jordan, Brans and Dicke, Bergman, Nordtveldt (1970), Wagoner, Bekenstein and Barker.

2036: 22865:

Sagi, Eva (July 2009). "Preferred frame parameters in the tensor–vector–scalar theory of gravity and its generalization".

20023: 16814: 15262:

contains a tensor, vector and three scalar fields. But the equations are quite straightforward. The action is split into:

10580: 7681:

and is a family of theories, each defined by a different function of the Ricci scalar. Starobinsky gravity is actually an

3765: 24790: 22249:

Gleyzes, Jérôme; Langlois, David; Piazza, Federico; Vernizzi, Filippo (2015-05-27). "Healthy theories beyond Horndeski".

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allows the density of the exotic negative mass particles to remain constant as a function of time, and so appears like a

11560:{\displaystyle T^{\mu \nu }={1 \over 8\pi G}\left(R^{\mu \nu }-{\frac {1}{2}}g^{\mu \nu }R+g^{\mu \nu }\Lambda \right)\;} 20063:

Einstein, A. (1917) Über die Spezielle und die Allgemeinen Relativatätstheorie, Gemeinverständlich, Vieweg, Braunschweig

16758: 16576:

The main observations that appear to require dark matter and/or dark energy can be explained within this model. Namely,

10998: 10621: 24971: 24443: 7727: 7455: 7301: 7142: 1646: 256: 21796: 14605: 7181: 6686:

Nevertheless, the metric construction (from a non-metric theory) using the "length contraction" ansatz is criticised.

5916: 5295: 24624: 24453: 23014:

Haugan, Mark; Kauffmann, Thierry (1996). "New test of the Einstein equivalence principle and the isotropy of space".

21668:

Bekenstein, Jacob (1977). "Are particle rest masses variable? Theory and constraints from solar system experiments".

19867:

Clifton, Timothy; Pedro G. Ferreira; Antonio Padilla; Constantinos Skordis (2012). "Modified Gravity and Cosmology".

17191:{\displaystyle \gamma ,\beta ,\eta ,\alpha _{1},\alpha _{2},\alpha _{3},\zeta _{1},\zeta _{2},\zeta _{3},\zeta _{4}.} 14130: 10224: 9634:

in the current epoch. However, there could be significant differences from general relativity in the early universe.

7632: 7133:, as suggested by G. Temple in 1923. Temple's suggestions on how to do this were criticized by C. B. Rayner in 1955. 118: 54:. Thirdly, there are theories which attempt to explain gravity and other forces at the same time; these are known as 21626:

Lee, D.; Lightman, A.; Ni, W. (1974). "Conservation laws and variational principles in metric theories of gravity".

11821: 65:

None of these alternatives to general relativity have gained wide acceptance. General relativity has withstood many

24366: 21256:"Post-Newtonian metric for a general class of scalar–tensor gravitational theories with observational consequences" 9927: 1773: 1028:

Theories of gravity can be classified, loosely, into several categories. Most of the theories described here have:

55: 22076:

Horndeski, Gregory Walter (1974-09-01). "Second-order scalar–tensor field equations in a four-dimensional space".

14765: 13492: 13391:{\displaystyle {\tilde {g}}^{\alpha \beta }=e^{2\varphi }g^{\alpha \beta }+2U^{\alpha }U^{\beta }\sinh(2\varphi )} 11896:. The theory may help to better understand the considerable amounts of unknown dark matter and dark energy in the 9610: 24425: 24345:. Video lecture discussion on the possibilities and constraints to revision of the General Theory of Relativity. 22441:

Trautman, A. (1972) On the Einstein–Cartan equations I, Bulletin de l'Academie Polonaise des Sciences 20, 185-190

9238: 1995: 1981: 15102:{\displaystyle S_{FM}=\int d^{4}x\,\epsilon ^{\alpha \beta \mu \nu }A_{\alpha \beta }\partial _{\mu }J_{\nu }\;} 10962:

is a very old idea, going back to Einstein in 1917. The success of the Friedmann model of the universe in which

10907:

In the 1990s, supernova surveys discovered the accelerated expansion of the universe, now usually attributed to

10863:

Some equations of the non-metric theory of Belinfante and Swihart have already been discussed in the section on

272: 24731: 24653: 24420: 19692: 19427: 19345: 15265: 12584: 2594: 8516:

These all contain at least one free parameter, as opposed to general relativity which has no free parameters.

7125:

can be introduced into a quasilinear theory by the simple expedient of changing the Minkowski background to a

2680: 338: 24924: 24448: 23075:

Biswas, Tirthabir; Mazumdar, Anupam; Siegel, Warren (2006). "Bouncing Universes in String-inspired Gravity".

16422:

These parallels are expected from a theoretical point of view: General Relativity and the Strong Interaction

10547: 5863: 5726:

In Rastall, the metric is an algebraic function of the Minkowski metric and a Vector field. The Action is:

941: 25038: 12100: 2578: 2213: 1839:(the most well-known alternative to general relativity, intended to be better at applying Mach's principle) 1749: 637:{\displaystyle R_{\mu \nu }={\frac {8\pi G}{c^{4}}}\left(T_{\mu \nu }-{\frac {1}{2}}g_{\mu \nu }T\right)\,} 11784: 11627: 11576: 10992:

In Newtonian gravity, the addition of the cosmological constant changes the Newton–Poisson equation from:

9031: 895: 25043: 24709: 24603: 24593: 24468: 17410: 17062: 16939: 16685: 16588: 16388:, a weakening of gravitational attraction outside said galaxy. This mimics the repulsion of dark energy. 16157: 12448: 12092: 10932: 9580: 9001: 8248: 7718: 2574: 1245: 1195: 768: 757:{\displaystyle T^{\mu \nu }={c^{4} \over 8\pi G}\left(R^{\mu \nu }-{\frac {1}{2}}g^{\mu \nu }R\right)\,.} 66: 22002: 21955:

Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics

16305:

and Mazzitelli (1997) found an exact solution to this theories representing a gravitational shock-wave.

11570:

In alternative theories of gravity, a cosmological constant can be added to the action in the same way.

9497:{\displaystyle \omega (\varphi )=-\textstyle {\frac {3}{2}}-\textstyle {\frac {1}{4}}f(\varphi )^{-2}\;} 3699:{\displaystyle L_{\varphi }=\varphi R-2g^{\mu \nu }\,\partial _{\mu }\varphi \,\partial _{\nu }\varphi } 417: 369: 303: 192: 24909: 24551: 24463: 24415: 24352: 22005:. Applied Process Metaphysics Summer Institute Memorandum, Louvain-la-Neuve, Éditions Chromatika, 2010. 17044: 16162:

In order to remove ghosts in the modified propagator, as well as to obtain asymptotic freedom, Biswas,

13983: 11892:

theory, related to notions of gravitationally repulsive negative masses that were presented earlier by

10286: 7154: 2056: 1932: 1810: 22430: 1020:

general relativity, and other variants containing vector fields as well have been developed recently.

24703: 24698: 22385:

Bekenstein, J. D. (2004). "Revised gravitation theory for the modified Newtonian dynamics paradigm".

17441: 16668: 14173: 8527:

can be considered the progenitor of Scalar–Tensor theories of gravity. This was recognized by Thiry.

1037: 332: 22838: 20807:

Belinfante, F. J.; Swihart, J. C. (1957b). "Phenomenological linear theory of gravitation Part II".

16536: 16433: 15367: 14703: 14546: 14139: 11657: 11431:{\displaystyle T^{\mu \nu }={1 \over 8\pi G}\left(R^{\mu \nu }-{\frac {1}{2}}g^{\mu \nu }R\right)\;} 10662: 8557: 7090: 6693: 5976: 5264: 1615: 1580: 1265: 1204: 227: 24919: 24800: 24629: 20763:

Belinfante, F. J.; Swihart, J. C. (1957a). "Phenomenological linear theory of gravitation Part I".

18267: 17430: 8491: 7449:

Stelle's 4th derivative gravity, which is a generalization of Gauss–Bonnet gravity, has the action

7146: 7130: 6320: 1805: 1609: 22725: 18983: 18686: 18522: 17004:. The first tests of Lorentz invariance were done by Michelson and Morley before 1890 and limited 16634:

Additionally, the model explains observations that are currently challenging to understand within

12419: 10965: 10039: 9116: 4220:{\displaystyle \eta ^{\mu \nu }\partial _{\mu }\partial _{\nu }\varphi =4\pi \rho ^{*}k(\varphi )} 3478: 3091:{\displaystyle f\left({\frac {\varphi }{c^{2}}}\right)=1,\qquad c^{2}=c_{\infty }^{2}-2\varphi \,} 1697:(includes conformally flat theories & Stratified theories with conformally flat space slices) 1428:: Stressed matter and fields being acted upon by gravity respond in accordance with the equation: 24834: 24767: 23409: 22563:

Moffat (2005). "Gravitational Theory, Galaxy Rotation Curves and Cosmology without Dark Matter".

19823: 19780: 19221: 19185: 18794: 18766: 18638: 18610: 18469: 18441: 18348: 18202: 18142: 18114: 17606: 17578: 17550: 17242:

is a measure of nonlinearity in the addition of gravitational fields, one for general relativity.

17220:

is a measure of space curvature, being zero for Newtonian gravity and one for general relativity.

12554: 12445:

are arbitrary functions selected to give Newtonian and MOND behaviour in the correct limits, and

8524: 8520: 3960: 3931: 1962: 23834:

Deur, A. (2021). "Effect of gravitational field self-interaction on large structure formation".

22507:

Moffat (2003). "Bimetric Gravity Theory, Varying Speed of Light and the Dimming of Supernovae".

19848:

was the situation until cosmological discoveries pushed the development of modern alternatives.

19749: 19550: 19288: 19257: 17718: 17690: 17662: 17634: 16657: 16407:

on the one hand (analogous to the need of stronger gravity to explain away dark matter) and the

14734: 14577: 14481: 14460: 13535: 11606: 10944: 8215: 6007: 5847:{\displaystyle S={1 \over 16\pi G}\int d^{4}x\,{\sqrt {-g}}F(N)K^{\mu ;\nu }K_{\mu ;\nu }+S_{m}} 24751: 24635: 23952:

Sargent, C.; Deur, A.; Terzic, B. (2024). "Hubble tension and gravitational self-interaction".

20320: 16945: 16486: 16353:

then avoid the need for dark matter. This field coupling is the origin of General Relativity's

16334: 16298: 15337: 13675:

is given as an example with the right asymptotic behaviour; note how it becomes undefined when

12533: 12080: 10936: 10069: 9660: 9172: 8495: 6041: 3712: 2234: 2031: 1836: 173: 20926:; Morduch, G. E. (1960). "General relativity and Lorentz-invariant theories of gravitations". 18915: 16271: 14602:

is a connection, and is a bit difficult to explain because it's defined recursively. However,

13468: 12513: 9145: 4233: 2725: 1813:(allows the Lagrangian to depend on higher-order contractions of the Riemann curvature tensor) 1796:(allows the Lagrangian to depend on second-order contractions of the Riemann curvature tensor) 24883: 24862: 24855: 24795: 23991: 23932: 23502: 22839:"Bringing balance to the universe: New theory could explain missing 95 percent of the cosmos" 20137:

Brans, C.; Dicke, R. H. (1961). "Mach's principle and a relativistic theory of gravitation".

19141: 18396: 18069: 17487: 17437: 17203: 16978: 16949: 16911: 16887: 16643: 16616: 16581: 16412: 16338: 15193:{\displaystyle F_{\mu \nu \rho }=\partial _{\mu }A_{\nu \rho }+\partial _{\rho }A_{\mu \nu }} 14457:

is a curvature term analogous to but not equal to the Ricci curvature in general relativity,

14223: 11917: 10928: 9642: 9061: 8511: 8185:, and recovers to general relativity in the infrared, for energies below the non-local scale 7721:

is a covariant theory of gravity, quadratic in curvature, torsion free and parity invariant,

7264: 7166: 7122: 6299: 6072: 2089: 1041: 987: 24056:"Updated analysis of an unexpected correlation between dark matter and galactic ellipticity" 23627:

Deur, Alexandre (2021). "Relativistic corrections to the rotation curves of disk galaxies".

22804: 19162: 18732: 18568: 18417: 18090: 17936: 17837: 17508: 17225: 16529:

is a characteristic length of the system. The claim of the GRSI proponents, based either on

14509: 14430: 14417:{\displaystyle L_{R}={\sqrt {-g}}\left}\right]-{\frac {1}{6}}g^{\mu \nu }W_{\mu }W_{\nu }\;} 13678: 9028:

is a different dimensionless function for each different scalar–tensor theory. The function

1167: 24950: 24869: 24848: 24841: 24716: 24571: 24529: 24313: 24274: 24232: 24166: 24118: 24077: 23971: 23910: 23853: 23800: 23702: 23646: 23588: 23480: 23431: 23374: 23308: 23261: 23200: 23147: 23094: 23033: 22996: 22937: 22884: 22834: 22800: 22691: 22638: 22582: 22526: 22473: 22404: 22338: 22268: 22207: 22146: 22085: 22034: 21972: 21889: 21870:

Misner, C. W., Thorne, K. S. and Wheeler, J. A. (1973) Gravitation, W. H. Freeman & Co.

21836: 21761: 21717: 21677: 21635: 21577: 21568:

Lightman, Alan; Lee, David (1973). "New Two-Metric Theory of Gravity with Prior Geometry".

21535: 21487: 21439: 21391: 21351: 21311: 21267: 21171: 21127: 21077: 21025: 20987: 20935: 20923: 20888: 20850: 20772: 20728: 20656: 20524: 20417: 20367: 20236: 20146: 20072:

Bojowald, Canonical Gravity and Applications, Cambridge University Press, 2001, chapter 3,

20035: 19944: 19882: 19866: 17247: 16718: 16530: 16423: 15399: 11885: 10871: 8188: 8161: 4566: 4253: 3735: 2445: 2272: 2249: 2149: 2108: 1946: 1876: 1640: 59: 23297:"Review of latest advances on dark matter from the viewpoint of the Occam razor principle" 21922:

Will (1981) lists this as bimetric but I don't see why it isn't just a vector field theory

20485: 20291: 18589: 17529: 16258:{\displaystyle S=\int \mathrm {d} ^{4}x{\sqrt {-g}}\left({\frac {R}{2}}+RF(\Box )R\right)} 13429: 7684: 1406: 1386: 8: 20602: 20571: 20512: 19613: 19509: 16609: 16385: 14679: 13403: 9311: 9217: 9196: 9089: 8536: 8519:

Although not normally considered a Scalar–Tensor theory of gravity, the 5 by 5 metric of

6047: 5366: 5345: 2195: 2132: 2103: 1953: 1084: 1063: 874: 154: 129: 70: 24317: 24278: 24236: 24170: 24122: 24081: 23975: 23914: 23857: 23804: 23706: 23650: 23592: 23569:

Deur, Alexandre (2009). "Implications of Graviton-Graviton Interaction to Dark Matter".

23484: 23435: 23378: 23312: 23265: 23204: 23159: 23151: 23106: 23098: 23037: 23000: 22941: 22918:

Burko, L.M.; Ori, A. (1995). "On the Formation of Black Holes in Nonsymmetric Gravity".

22888: 22695: 22650: 22642: 22594: 22586: 22530: 22477: 22408: 22342: 22272: 22211: 22150: 22089: 22038: 21976: 21893: 21840: 21792: 21765: 21721: 21681: 21639: 21581: 21539: 21491: 21443: 21395: 21355: 21315: 21271: 21175: 21131: 21081: 21029: 20991: 20939: 20892: 20854: 20776: 20732: 20660: 20528: 20421: 20371: 20240: 20150: 20039: 19948: 19886: 19668: 19589: 19485: 19403: 19321: 16148:

is a coupling constant. The functions assumed for the scalar potentials are not stated.

25012: 24478: 24435: 24198: 24156: 24067: 24024: 23961: 23900: 23869: 23843: 23816: 23790: 23758: 23737: 23718: 23692: 23662: 23636: 23604: 23578: 23523: 23470: 23421: 23390: 23364: 23332: 23277: 23251: 23224: 23190: 23163: 23137: 23110: 23084: 23057: 23023: 22986: 22961: 22927: 22900: 22874: 22816: 22790: 22707: 22681: 22654: 22628: 22598: 22572: 22542: 22516: 22489: 22463: 22394: 22362: 22328: 22300: 22258: 22231: 22197: 22170: 22136: 22109: 22058: 22024: 21988: 21962: 21933: 21905: 21603: 21523: 21407: 21231: 21187: 20951: 20680: 20548: 20440: 20405: 20383: 19999: 19975: 19934: 19922: 19898: 19872: 17445: 16863: 16738: 16664: 16512: 16492: 16468: 16392: 16330: 16131: 15426: 15241: 12399: 10615: 8503: 7270: 7172: 6066: 1991: 1853: 1777: 1680: 1048: 406: 266: 35: 23658: 21953:

Gary Gibbons; Will (2008). "On the Multiple Deaths of Whitehead's Theory of Gravity".

24996: 24904: 24648: 24576: 24302:"Die Nordströmsche Gravitationstheorie vom Standpunkt des absoluten Differentkalküls" 24202: 24190: 24182: 23873: 23820: 23722: 23714: 23666: 23608: 23394: 23386: 23336: 23324: 23216: 23167: 23049: 22953: 22904: 22711: 22485: 22354: 22304: 22292: 22284: 22235: 22223: 22174: 22162: 22113: 22101: 22050: 21909: 21607: 21411: 21235: 21191: 21089: 21037: 20999: 20900: 20820: 20784: 20684: 20672: 20622: 20591: 20552: 20540: 20445: 20387: 20292:"Sur une généralisation de la notion de courbure de Riemann et les espaces à torsion" 20073: 19980: 19962: 19902: 17032: 16404: 16362: 10875: 10290: 2467: 2449: 2365: 1880: 1871: 1845: 184: 47: 23061: 22965: 22820: 22658: 22546: 22493: 22366: 21992: 17448:

due to galactic clusters act as constraints. For those theories that aim to replace

16908:. The theories of Thirry (1948) and Jordan are incomplete unless Jordan's parameter 12119:

It was inconsistent in that it gives different galactic orbits for gas and for stars

24978: 24672: 24566: 24321: 24282: 24240: 24174: 24126: 24085: 24034: 23979: 23918: 23865: 23861: 23808: 23710: 23654: 23600: 23596: 23488: 23443: 23439: 23382: 23316: 23281: 23269: 23228: 23212: 23208: 23155: 23114: 23102: 23041: 22945: 22892: 22808: 22703: 22699: 22646: 22590: 22534: 22481: 22412: 22346: 22280: 22276: 22215: 22154: 22093: 22062: 22046: 22042: 21980: 21897: 21844: 21769: 21725: 21685: 21643: 21593: 21585: 21543: 21495: 21447: 21399: 21359: 21319: 21275: 21223: 21179: 21135: 21085: 21033: 20995: 20955: 20943: 20896: 20858: 20816: 20780: 20736: 20664: 20614: 20583: 20532: 20435: 20425: 20375: 20335: 20244: 20154: 20043: 19970: 19952: 19890: 19808: 17883: 17449: 17040: 16953: 16354: 16326: 11321:{\displaystyle S={1 \over 16\pi G}\int (R-2\Lambda ){\sqrt {-g}}\,d^{4}x\,+S_{m}\;} 10274: 7083: 6090:

and matter variables, so it doesn't even have a scalar field. The construction is:

2585:

to a theory is discussed under Modern Theories (see also Einstein–Hilbert action).

2527: 1828: 1684: 1294: 1237: 1033: 1013: 260: 94: 22812: 22602: 22127:

Deffayet, C.; Esposito-Farese, G.; Vikman, A. (2009-04-03). "Covariant Galileon".

20647:

Littlewood, D. E. (1953). "Conformal transformations and kinematical relativity".

19894: 16699:

Self-consistency among non-metric theories includes eliminating theories allowing

11771:{\displaystyle S={1 \over 16\pi G}\int d^{4}x\,{\sqrt {-g}}\,L_{\varphi }+S_{m}\;} 24677: 24598: 24558: 24524: 24342: 24258: 24216: 23296: 22980: 21752:

Rastall, P (1979). "The Newtonian theory of gravitation and its generalization".

21708:

Barker, B. M. (1978). "General scalar–tensor theory of gravity with constant G".

16905: 16623: 16163: 14697:, increasing to a final constant value about a million years after the big bang. 13977: 12503: 11912: 11893: 10916: 10900: 8212:. In the ultraviolet regime, at distances and time scales below non-local scale, 7126: 4827: 2229: 1941: 935: 221: 106: 51: 31: 23: 23320: 22949: 22350: 21984: 21211: 21053:

Kustaanheimo, P. E. and Nuotio, V. S. (1967) Publ. Astron. Obs. Helsinki No. 128

20321:"Sur les variétés à connexion affine et la théorie de la relativité généralisée" 10887:

are presented with a cosmological constant or added scalar or vector potential.

1968:

Mach: The reference frame comes from the distribution of matter in the universe.

24877: 23983: 23923: 23889:"Significance of Gravitational Nonlinearities on the Dynamics of Disk Galaxies" 23888: 23812: 23493: 23459:"Significance of Gravitational Nonlinearities on the Dynamics of Disk Galaxies" 23458: 22896: 22416: 22219: 22158: 20978:

Whitrow, G. J.; Morduch, G. E. (1965). "Relativistic theories of gravitation".

20172: 17465: 16627: 16381: 2333: 2166: 2075: 1753: 148: 122: 24346: 22538: 20668: 20316: 20287: 11122:{\displaystyle \nabla ^{2}\varphi +{\frac {1}{2}}\Lambda c^{2}=4\pi \rho \ G;} 9086:

is a dimensionless normalization constant that fixes the present-day value of

8669:{\displaystyle S={1 \over 16\pi G}\int d^{4}x{\sqrt {-g}}L_{\varphi }+S_{m}\;} 2051: 25032: 24814: 24483: 24325: 24286: 24244: 24186: 24090: 24055: 23328: 23273: 23045: 22358: 22288: 22227: 22166: 22105: 21848: 21689: 21647: 21140: 21115: 20862: 20676: 20626: 20618: 20595: 20587: 20544: 20047: 19966: 16957: 16881: 16715:

Many early theories are incomplete in that it is unclear whether the density

16408: 16366: 16317:

is an attempt to explain astrophysical and cosmological observations without

16302: 16167: 12122:

It did not state how to calculate gravitational lensing from galaxy clusters.

11904: 2509: 2484: 2300: 2225: 1892: 1716: 1260: 1054: 177: 38:. There have been many different attempts at constructing an ideal theory of 24039: 24012: 21598: 21589: 21547: 21451: 21363: 21323: 20171:

this isn't exactly the way Mach originally stated it, see other variants in

20158: 16963: 16170:(2005) considered a string-inspired infinite set of higher derivative terms 9607:

allows Scalar Tensor Theories to tend to general relativity in the limit of

3613:{\displaystyle S={1 \over 16\pi G}\int d^{4}x{\sqrt {-g}}L_{\varphi }+S_{m}} 2841:{\displaystyle f(\varphi /c^{2})=\exp(-\varphi /c^{2}),\qquad c=c_{\infty }} 24772: 24581: 24194: 23220: 23053: 22957: 22759: 22296: 22054: 21998: 21302:

Wagoner, Robert V. (1970). "Scalar–Tensor Theory and Gravitational Waves".

20449: 20379: 19984: 16591: 16416: 14126: 11881: 7150: 7072:{\displaystyle S={1 \over 16\pi G}\int d^{4}x{\sqrt {-\eta }}\left+S_{m}\;} 2505: 2488: 2411: 2394: 2071: 1896: 1799: 1712: 24358: 21068:

Deser, S.; Laurent, B. E. (1968). "Gravitation without self-interaction".

21016:

Kustaanheimo, P (1966). "Route dependence of the gravitational redshift".

20430: 18970:{\displaystyle \textstyle {\frac {3}{4}}+\textstyle {\frac {\lambda }{4}}} 17436:

For those theories that aim to replace dark matter, observations like the

16430:

also occur in very massive systems. This coupling is effectively given by

2664:{\displaystyle \delta \int f\left({\tfrac {\varphi }{c^{2}}}\right)\,ds=0} 411:

For comparison with alternatives, the formulas of General Relativity are:

109:

has caused renewed public interest in alternatives to general relativity.

24741: 24013:"A relation between the dark mass of elliptical galaxies and their shape" 23528: 22843: 22577: 22399: 16377: 16322: 16318: 13665:{\displaystyle F(\mu )={\frac {3}{4}}{\mu ^{2}(\mu -2)^{2} \over 1-\mu }} 13278:{\displaystyle h^{\alpha \beta }=g^{\alpha \beta }-U^{\alpha }U^{\beta }} 10908: 2002: 861:{\displaystyle S={c^{4} \over 16\pi G}\int R{\sqrt {-g}}\ d^{4}x+S_{m}\,} 102: 98: 27: 24178: 19957: 16403:

dramatically strengthens quark-quark interaction, ultimately leading to

12578:. The action is split into parts for gravity, scalars, vector and mass. 9914:{\displaystyle S={\frac {1}{16\pi G}}\int d^{4}x{\sqrt {-g}}\left+S_{m}} 9110:

The full version is retained in Bergman and Wagoner. Special cases are:

9058:

plays the same role as the cosmological constant in general relativity.

6296:

where the superscript (−) indicates quantities evaluated along the past

24955: 23683:

Deur, A. (2017). "Self-interacting scalar fields at high-temperature".

23089: 22097: 21901: 21403: 21227: 21183: 20536: 20340: 17393:{\displaystyle \zeta _{1},\zeta _{2},\zeta _{3},\zeta _{4},\alpha _{3}} 16635: 16346: 12126:

By 1984, problems 2 and 3 had been solved by introducing a Lagrangian (

11908: 11889: 11214:{\displaystyle S={1 \over 16\pi G}\int R{\sqrt {-g}}\,d^{4}x\,+S_{m}\;} 2513: 2428: 1720: 1194:

at spatial infinity when using Cartesian coordinates. For example, the

23256: 23028: 22991: 22932: 22633: 22521: 22468: 21967: 20740: 20515:(1954). "Eine Theorie des Gravitationsfeldes mit einer Feldfunktion". 16735:

used by the theory should be calculated from the stress–energy tensor

1802:(allows the Lagrangian to depend on higher powers of the Ricci scalar) 24960: 24942: 24746: 24723: 21825:"Zur Theorie der Gravitation vom Standpunkt des Relativitätsprinzips" 20947: 20719:

Bergman, O (1956). "Scalar field theory as a theory of gravitation".

20004: 16358: 12116:

It violated the conservation of energy, momentum and angular momentum

11872:

is added to the Lagrangian for the gravitational part of the action.

8507: 1858: 24301: 24262: 24220: 21824: 21773: 11654:

inside the Lagrangian for the gravitational part of the action, the

9567:{\displaystyle \omega (\varphi )={\frac {4-3\varphi }{2\varphi -2}}} 4133:{\displaystyle ds^{2}=e^{-2f(\varphi )}dt^{2}-e^{2f(\varphi )}\left} 25017: 24827: 24820: 24131: 24107:"Conservation laws and preferred frames in relativistic gravity II" 24106: 24072: 23966: 23905: 23848: 23795: 23763: 23742: 23697: 23641: 23475: 23369: 22795: 22730: 22686: 22431:

http://star-www.st-and.ac.uk/~hz4/workshop/workshopppt/turyshev.pdf

22333: 21729: 21500: 21475: 21280: 21255: 20248: 17417: 16345:, observations that are currently challenging to understand within 11897: 11132:

In general relativity, it changes the Einstein–Hilbert action from

10912: 24161: 24029: 23583: 23426: 23195: 23142: 22879: 22263: 22202: 22141: 22029: 21938: 21476:"Conservation laws and preferred frames in relativistic gravity I" 19939: 19877: 1373:{\displaystyle {d\tau }^{2}=-g_{\mu \nu }\,dx^{\mu }\,dx^{\nu }\,} 24389: 23951: 23886: 23456: 19773:

can take one of two values. The value closest to zero is listed.

16700: 16568:

is indeed sufficiently large for large systems such as galaxies.

16427: 8499: 8482:

and can be thought of as a generalization of general relativity.

39: 22726:"Quest to settle riddle over Einstein's theory may soon be over" 21162:

Bergmann, P. G. (1968). "Comments on the scalar–tensor theory".

20879:

Yilmaz, H (1973). "New approach to relativity and gravitation".

17021:. Upper limits on this found by Pound and Rebka in 1960 limited 16679: 16395:, where a comparable phenomenon occurs. The interaction between 183:

Latin indices go from 1 to 3, Greek indices go from 0 to 3. The

21116:"Scalar gravitational theories with variable velocity of light" 20702:

Jordan, P. (1955) Schwerkraft und Weltall, Vieweg, Braunschweig

20649:

Mathematical Proceedings of the Cambridge Philosophical Society

19998:

Asmodelle, E. (2017). "Tests of General Relativity: A Review".

17025:

to less than 0.1. Modern tests have reduced this to less than 1

16400: 16396: 13489:

is a Lagrangian translated from flat spacetime onto the metric

10211:{\displaystyle \tau =0;\quad \epsilon =1;\quad \eta =-2\omega } 23522:

Deur, Alexandre (2003). "Non-Abelian Effects in Gravitation".

23410:"Implications of graviton–graviton interaction to dark matter" 22317: 20262:

Lang, R. (2002) Experimental foundations of general relativity

16372:

A natural implication of this model is its explanation of the

1935:(intended to handle spin-orbital angular momentum interchange) 24609: 23180: 22248: 22126: 22014: 19923:"The Confrontation between General Relativity and Experiment" 19807:

avoids this problem. However, the modification predicts the

16308: 15994:

The potential function for the vector field is chosen to be:

12127: 3928:

In the second theory of Ni there are two arbitrary functions

3475:

Page and Tupper matches Yilmaz's theory to second order when

523:{\displaystyle {ds}^{2}=g_{\mu \nu }\,dx^{\mu }\,dx^{\nu }\,} 24145: 23127: 22429:

Turyshev, S. G. (2006) Testing gravity in the solar system,

22187: 20196:

Will, C. M. (originally published 1981/revise edition 1993)

17466:

Parametric post-Newtonian parameters for a range of theories

8874:{\displaystyle S_{m}=\int d^{4}x\,{\sqrt {g}}\,G_{N}L_{m}\;} 6780:{\displaystyle g_{\mu \nu }=\eta _{\mu \nu }+h_{\mu \nu }\;} 1164:

In this equation it is usual, though not essential, to have

14669:

eight orders of magnitude sharper than previous estimates.

14111:{\displaystyle G^{-1}={\frac {2}{2-K}}+{\frac {k}{4\pi }}.} 12506:

theory it has problems of its own. Bekenstein introduced a

9163: 4401:

In Papapetrou the gravitational part of the Lagrangian is:

2582: 24155:(7286). Springer Science and Business Media LLC: 256–258. 4391:{\displaystyle ds^{2}=\varphi ^{2}\,dt^{2}-\psi ^{2}\left} 3515:

The gravitational deflection of light has to be zero when

18021:{\displaystyle \textstyle {\frac {1+\omega }{2+\omega }}} 17925:{\displaystyle \textstyle {\frac {1+\omega }{2+\omega }}} 17826:{\displaystyle \textstyle {\frac {1+\omega }{2+\omega }}} 17404: 16964:

Agreement with Newtonian mechanics and special relativity

16357:

behavior. It can be understood, in particle language, as

10922: 10029:{\displaystyle F_{\mu \nu }=K_{\nu ;\mu }-K_{\mu ;\nu }.} 9193:

Bekenstein variable mass theory Starting with parameters

1690:

Metric theories include (from simplest to most complex):

24221:"Lichtgeschwindigkeit und Statik des Gravitationsfeldes" 24053: 22982:

Nonsymmetric Gravity has Unacceptable Global Asymptotics

21382:

Rosen, N (1975). "A bimetric theory of gravitation II".

20841:

Yilmaz, H (1958). "New approach to general relativity".

20605:(1954). "Eine neue Theorie des Gravitationsfeldes. II". 20406:"Matter, electricity and gravitation in flat space-time" 16960:. It is usually regarded as a "classical" test as well. 12109:

There were several problems with MOND in the beginning.

20574:(1954). "Eine neue Theorie des Gravitationsfeldes. I". 20523:(5). Springer Science and Business Media LLC: 518–532. 16409:

suppression of the Strong Nuclear Force outside hadrons

12656:

The gravity part is the same as in general relativity.

10147:{\displaystyle \omega =\eta =\epsilon =0;\quad \tau =1} 7263:

and has been used to explain inflation, in the form of

1612:

for all matter and non-gravitational fields, and where

1153:{\displaystyle S=\int L{\sqrt {-g}}\,\mathrm {d} ^{4}x} 22755:"Theoretical battle: Dark energy vs. modified gravity" 22619:

Moffat (2006). "Scalar–Tensor–Vector Gravity Theory".

21209: 19696: 19431: 19349: 18954: 18940: 17990: 17894: 17795: 17444:, the faster rotation rate of dwarf galaxies, and the 17050: 16571: 9371: 9357: 9107:. An arbitrary potential can be added for the scalar. 5216: 4983: 4750: 4650: 4496: 4440: 2626: 1060:

If a theory has a Lagrangian density for gravity, say

21880:

Rosen, N (1973). "A bimetric theory of gravitation".

21210:

Bollini, C. G.; Giambiagi, J. J.; Tiomno, J. (1970).

19826: 19783: 19752: 19695: 19671: 19616: 19592: 19553: 19512: 19488: 19430: 19406: 19348: 19324: 19291: 19260: 19224: 19188: 19165: 19144: 18986: 18939: 18918: 18797: 18769: 18735: 18689: 18641: 18613: 18592: 18571: 18525: 18472: 18444: 18420: 18399: 18351: 18270: 18205: 18145: 18117: 18093: 18072: 17989: 17939: 17893: 17840: 17794: 17721: 17693: 17665: 17637: 17609: 17581: 17553: 17532: 17511: 17490: 17327: 17272: 17250: 17228: 17206: 17078: 16972: 16914: 16890: 16866: 16817: 16761: 16741: 16721: 16539: 16515: 16495: 16471: 16436: 16274: 16179: 16134: 16003: 15651: 15452: 15429: 15423:

is the standard gravity term with the exception that

15402: 15370: 15340: 15268: 15209: 15121: 15012: 14850: 14768: 14737: 14706: 14682: 14608: 14580: 14549: 14512: 14484: 14463: 14433: 14257: 14226: 14176: 14142: 14052: 13986: 13712: 13681: 13587: 13538: 13495: 13485:

is a Lagrange multiplier (calculated elsewhere), and

13471: 13432: 13406: 13292: 13222: 12665: 12587: 12557: 12536: 12516: 12451: 12422: 12402: 12265: 12139: 11929: 11824: 11787: 11691: 11660: 11630: 11609: 11579: 11450: 11340: 11233: 11141: 11058: 11001: 10968: 10947: 10700: 10665: 10624: 10583: 10550: 10313: 10227: 10166: 10109: 10072: 10042: 9971: 9930: 9696: 9663: 9613: 9583: 9516: 9338: 9314: 9241: 9220: 9199: 9175: 9148: 9119: 9092: 9064: 9034: 9004: 8890: 8811: 8685: 8591: 8560: 8539: 8268: 8218: 8191: 8164: 8003: 7730: 7687: 7635: 7458: 7304: 7273: 7184: 7093: 6799: 6730: 6696: 6354: 6323: 6302: 6099: 6075: 6050: 6010: 5979: 5919: 5866: 5735: 5562: 5393: 5369: 5348: 5298: 5267: 5072: 4844: 4592: 4569: 4410: 4279: 4256: 4236: 4149: 3995: 3963: 3934: 3768: 3738: 3715: 3629: 3536: 3481: 3242: 3110: 3011: 2860: 2754: 2728: 2683: 2611: 1916: 1649: 1618: 1583: 1437: 1409: 1389: 1306: 1268: 1207: 1170: 1111: 1087: 1066: 990: 944: 898: 877: 780: 656: 539: 459: 420: 372: 341: 306: 275: 230: 195: 157: 132: 23074: 22833: 22454:

Moffat (1995). "Nonsymmetric Gravitational Theory".

16853:{\displaystyle \rho =T_{\mu \nu }\delta ^{\mu \nu }} 16329:

terms when calculating the gravitational effects in

10607:{\displaystyle \varepsilon _{\xi \mu \eta \zeta }\;} 3912:{\displaystyle \Box \varphi =4\pi T^{\mu \nu }\left} 23735: 22978: 21049: 21047: 21011: 21009: 20328:

Annales Scientifiques de l'École Normale Supérieure

20024:"Die Grundlage der allgemeinen Relativitätstheorie" 17312:{\displaystyle \alpha _{1},\alpha _{2},\alpha _{3}} 15233:{\displaystyle \epsilon ^{\alpha \beta \mu \nu }\;} 13532:need not equal the observed gravitational constant 10881: 10273:Others metric theories have been proposed; that of 4583:. The gravitational part of the Lagrangian is now: 20806: 20802: 20800: 20798: 20796: 20794: 20762: 20758: 20756: 20754: 20752: 20750: 20566: 20564: 20562: 20507: 20505: 20503: 20490:Comptes Rendus de l'Académie des Sciences de Paris 20296:Comptes Rendus de l'Académie des Sciences de Paris 19839: 19795: 19765: 19710: 19680: 19628: 19601: 19566: 19524: 19497: 19445: 19415: 19363: 19333: 19304: 19273: 19242: 19206: 19171: 19150: 19004: 18969: 18924: 18810: 18782: 18751: 18720: 18654: 18626: 18598: 18577: 18556: 18485: 18457: 18426: 18405: 18364: 18304: 18218: 18158: 18130: 18099: 18078: 18020: 17945: 17924: 17846: 17825: 17734: 17706: 17678: 17650: 17622: 17594: 17566: 17538: 17517: 17496: 17392: 17311: 17256: 17234: 17212: 17190: 16921: 16896: 16872: 16852: 16804:{\displaystyle \rho =T_{\mu \nu }u^{\mu }u^{\nu }} 16803: 16747: 16727: 16560: 16521: 16501: 16477: 16457: 16289: 16257: 16140: 16117: 15983: 15634: 15435: 15415: 15388: 15356: 15326: 15232: 15192: 15101: 14995: 14830: 14751: 14723: 14689: 14658: 14594: 14566: 14535: 14498: 14470: 14449: 14416: 14240: 14209: 14159: 14110: 14035: 13965: 13693: 13664: 13566: 13520: 13477: 13457: 13418: 13390: 13277: 13202: 12645: 12570: 12543: 12522: 12493: 12437: 12408: 12385: 12245: 12067: 11861: 11803: 11770: 11674: 11646: 11616: 11595: 11559: 11430: 11320: 11213: 11121: 11039:{\displaystyle \nabla ^{2}\varphi =4\pi \rho \ G;} 11038: 10981: 10954: 10849: 10682: 10652:{\displaystyle \varepsilon _{0123}={\sqrt {-g}}\;} 10651: 10606: 10569: 10533: 10257: 10210: 10146: 10088: 10058: 10028: 9954: 9913: 9679: 9626: 9599: 9566: 9496: 9321: 9300: 9227: 9206: 9182: 9154: 9132: 9099: 9078: 9050: 9020: 8987: 8873: 8794: 8668: 8574: 8546: 8471: 8239: 8204: 8177: 8147: 7983: 7702: 7670: 7610: 7444: 7429: 7279: 7252: 7110: 7071: 6779: 6713: 6675: 6337: 6309: 6285: 6082: 6057: 6024: 5996: 5962: 5905: 5846: 5715: 5542: 5376: 5355: 5334: 5284: 5250: 5055: 4810: 4575: 4552: 4390: 4262: 4242: 4219: 4132: 3978: 3949: 3911: 3751: 3724: 3698: 3612: 3504: 3464: 3222: 3090: 2991: 2840: 2734: 2707: 2663: 2005:". Those considered here include (see Will Lang): 1986:At the time it was published in the 17th century, 1975: 1683:. The stress–energy tensor should also satisfy an 1671: 1631: 1600: 1566: 1415: 1395: 1372: 1285: 1221: 1186: 1152: 1094: 1073: 1004: 976: 926: 884: 860: 756: 636: 522: 442: 389: 358: 323: 292: 247: 212: 164: 139: 22380: 22378: 22376: 21663: 21661: 21659: 21657: 21521: 21120:Monthly Notices of the Royal Astronomical Society 20642: 20640: 20638: 20636: 19814: 17457:energy add up to make the universe exactly flat. 17012:10. Modern tests have reduced this to less than 1 16996:10. Modern tests have reduced that to less than 5 14700:The theory seems to contain an asymmetric tensor 14248:is the same as for matter in general relativity. 7984:{\displaystyle {\mathcal {L}}={\sqrt {-g}}\left.} 7611:{\displaystyle {\mathcal {L}}={\sqrt {-g}}\left.} 7430:{\displaystyle {\mathcal {L}}={\sqrt {-g}}\left.} 1672:{\displaystyle \Gamma _{\sigma \nu }^{\alpha }\,} 25030: 24104: 23241: 21952: 21818: 21816: 21814: 21787: 21785: 21783: 21473: 21249: 21247: 21245: 21044: 21006: 20486:"Les équations de la théorie unitaire de Kaluza" 19916: 19914: 19912: 16297:is the exponential of an entire function of the 16151: 14659:{\displaystyle W_{\mu }\approx -2g_{}^{,\nu }\;} 7253:{\displaystyle {\mathcal {L}}={\sqrt {-g}}\left} 7145:). Others include: Starobinsky (R+R^2) gravity, 5963:{\displaystyle N=g^{\mu \nu }K_{\mu }K_{\nu }\;} 5335:{\displaystyle B=B_{\mu \nu }\eta ^{\mu \nu }\,} 1816: 1734:(first metric theory of gravity to be developed) 951: 24263:"Zur Theorie des statischen Gravitationsfeldes" 23013: 21563: 21561: 21559: 21557: 21517: 21515: 21513: 21511: 21430:Ni, Wei-Tou (1973). "A New Theory of Gravity". 21157: 21155: 21153: 21151: 20791: 20747: 20559: 20500: 20410:Proceedings of the National Academy of Sciences 20399: 20397: 20093: 20091: 20089: 20087: 20085: 17065:, Misner et al. and Will for more information. 16584:. These results, however, have been challenged. 15247: 10614:is the completely antisymmetric pseudo-tensor ( 10258:{\displaystyle \omega =\eta =\epsilon =\tau =0} 10157:Hellings and Nordtvedt is a special case where 7671:{\displaystyle {\mathcal {L}}={\sqrt {-g}}f(R)} 24683:Degenerate Higher-Order Scalar-Tensor theories 24299: 24251: 24209: 24098: 23077:Journal of Cosmology and Astroparticle Physics 22621:Journal of Cosmology and Astroparticle Physics 22565:Journal of Cosmology and Astroparticle Physics 22373: 21747: 21745: 21743: 21741: 21739: 21654: 21297: 21295: 21293: 21291: 21205: 21203: 21201: 20977: 20973: 20971: 20969: 20967: 20965: 20922: 20918: 20916: 20914: 20912: 20910: 20714: 20712: 20710: 20708: 20655:(1). Cambridge University Press (CUP): 90–96. 20633: 20198:Theory and Experiment in Gravitational Physics 20059: 20057: 20017: 20015: 19811:, which has been experimentally constrained.) 17460: 11920:. Einstein's field equations are modified to: 11862:{\displaystyle K^{\mu }K^{\nu }g_{\mu \nu }\;} 10870:A distinctively non-metric theory is given by 7713: 3520:gravitational redshift is likely to be wrong. 24374: 24293: 22671: 22614: 22612: 22558: 22556: 22449: 22447: 21866: 21864: 21862: 21860: 21858: 21811: 21780: 21703: 21701: 21699: 21625: 21522:Hellings, Ronald; Nordtvedt, Kenneth (1973). 21242: 20874: 20872: 20836: 20834: 20832: 20830: 20698: 20696: 20694: 20311: 20309: 20282: 20280: 20278: 19909: 17452:, the size of ripples in the spectrum of the 16680:Testing of alternatives to general relativity 16333:, analogous to the self-interaction terms in 9955:{\displaystyle \omega ,\eta ,\epsilon ,\tau } 4563:In Papapetrou there is a second scalar field 1023: 23996:: CS1 maint: multiple names: authors list ( 23937:: CS1 maint: multiple names: authors list ( 23507:: CS1 maint: multiple names: authors list ( 22752: 22435: 22423: 22078:International Journal of Theoretical Physics 21554: 21508: 21377: 21375: 21373: 21337: 21335: 21333: 21253: 21164:International Journal of Theoretical Physics 21148: 21067: 21063: 21061: 21059: 21015: 20479: 20477: 20475: 20461: 20459: 20394: 20360:Proceedings of the Royal Society of London A 20353: 20351: 20082: 16610:formation of the Universe's large structures 16415:in galaxy dynamics that is analogous to the 14831:{\displaystyle S=S_{G}+S_{F}+S_{FM}+S_{M}\;} 13521:{\displaystyle {\tilde {g}}^{\alpha \beta }} 9627:{\displaystyle \omega \rightarrow \infty \;} 4835:Rosen (1975) bimetric theory The action is: 4230:Ni quotes Rosen as having two scalar fields 1081:, then the gravitational part of the action 24388: 23294: 22827: 21736: 21567: 21469: 21467: 21465: 21463: 21461: 21288: 21198: 21109: 21107: 21105: 21103: 21101: 21099: 20962: 20907: 20705: 20192: 20190: 20188: 20186: 20184: 20182: 20180: 20132: 20130: 20128: 20126: 20124: 20122: 20120: 20104: 20054: 20012: 16361:interacting with each other (despite being 16313:The General Relativity Self-interaction or 10100:Will and Nordtvedt is a special case where 9641:The above examples are particular cases of 9301:{\displaystyle \varphi =f(\varphi )^{-r}\;} 8554:is based on the integral of the Lagrangian 2549: 2534: 2474: 2456: 2384: 2340: 2239: 1865: 1823: 112: 26:that attempt to describe the phenomenon of 24381: 24367: 23887:Deur, A.; Sargent, C.; Terzić, B. (2020). 23776: 23774: 23678: 23676: 23622: 23620: 23618: 23547:. Princeton University Press. p. 576. 23457:Deur, A.; Sargent, C.; Terzić, B. (2020). 23350: 23348: 23346: 23007: 22972: 22609: 22553: 22500: 22444: 22384: 21855: 21696: 21667: 21621: 21619: 21617: 21342:Rosen, N (1971). "Theory of gravitation". 21113: 20869: 20827: 20691: 20646: 20601: 20570: 20511: 20357: 20306: 20275: 20136: 17264:is a check for preferred location effects. 16918: 16599:fainter luminosities of distant supernovae 16309:General relativity self-interaction (GRSI) 15229: 15098: 14992: 14827: 14748: 14720: 14686: 14655: 14591: 14563: 14532: 14495: 14467: 14446: 14413: 14237: 14206: 14156: 13426:are constants, square brackets in indices 12540: 12510:model (TeVeS). This has two scalar fields 12490: 11858: 11800: 11767: 11671: 11643: 11613: 11592: 11556: 11427: 11317: 11210: 10978: 10951: 10846: 10648: 10603: 10566: 9623: 9596: 9491: 9318: 9297: 9224: 9203: 9179: 9129: 9096: 9075: 9047: 9017: 8870: 8791: 8665: 8571: 8543: 7107: 7068: 6776: 6710: 6334: 6306: 6079: 6069:) algebraically from the Minkowski metric 6054: 6021: 5993: 5959: 2495: 2435: 2401: 2323: 2257: 2185: 2156: 2139: 1909: 1694: 386: 355: 320: 293:{\displaystyle \partial _{\mu }\varphi \;} 289: 244: 209: 161: 136: 24348:Dark Energy or Worse: Was Einstein Wrong? 24160: 24130: 24089: 24071: 24054:Winters, D.; Deur, A.; Zheng, X. (2022). 24038: 24028: 23965: 23922: 23904: 23847: 23794: 23762: 23741: 23696: 23640: 23582: 23564: 23562: 23560: 23558: 23556: 23554: 23527: 23492: 23474: 23425: 23368: 23255: 23194: 23141: 23088: 23027: 22990: 22931: 22911: 22878: 22794: 22685: 22632: 22576: 22520: 22509:International Journal of Modern Physics D 22467: 22398: 22332: 22262: 22201: 22140: 22075: 22028: 21966: 21937: 21873: 21822: 21791: 21597: 21499: 21425: 21423: 21421: 21370: 21330: 21279: 21139: 21056: 20472: 20456: 20439: 20429: 20348: 20339: 20222: 20220: 20218: 20216: 20214: 20212: 20210: 20208: 20206: 20003: 19997: 19974: 19956: 19938: 19876: 19862: 19860: 19711:{\displaystyle \textstyle {\frac {1}{2}}} 19446:{\displaystyle \textstyle {\frac {1}{2}}} 19364:{\displaystyle \textstyle {\frac {1}{2}}} 18842:Einstein (1912) {Not general relativity} 15944: 15930: 15843: 15829: 15754: 15740: 15684: 15485: 15327:{\displaystyle S=S_{G}+S_{K}+S_{S}+S_{M}} 15045: 14880: 13182: 13057: 12841: 12646:{\displaystyle S=S_{g}+S_{s}+S_{v}+S_{m}} 12364: 12350: 11743: 11732: 11303: 11289: 11196: 11182: 10679: 9648: 8849: 8841: 8756: 8742: 8485: 6655: 6641: 6258: 5776: 5651: 5553:and the stress–energy tensor comes from: 5373: 5352: 5331: 5281: 5246: 4885: 4807: 4788: 4774: 4732: 4718: 4688: 4674: 4531: 4517: 4478: 4464: 4306: 3890: 3876: 3682: 3668: 3219: 3087: 2988: 2648: 2355: 2350:C. G. Bollini, J. J. Giambiagi, J. Tiomno 2308: 2041: 1761: 1668: 1597: 1563: 1369: 1355: 1341: 1282: 1215: 1211: 1183: 1134: 1091: 1070: 1001: 973: 923: 881: 857: 750: 633: 519: 505: 491: 439: 24257: 24215: 23833: 23780: 23682: 22917: 22774: 21458: 21161: 21096: 20403: 20266: 20177: 20117: 20021: 10268: 2708:{\displaystyle \varphi ={\frac {GM}{r}}} 2588: 2061: 1922: 1383:where there is a summation over indices 359:{\displaystyle \nabla _{\mu }\varphi \;} 24987:Gravitational interaction of antimatter 23771: 23673: 23615: 23542: 23343: 21751: 21614: 21301: 20718: 20255: 20110:Einstein, A. and Grossmann, M. (1913), 16337:. Additionally, the model explains the 14167:, the Lagrangian density is split into 12502:relativistic theory , but as this is a 12113:It did not include relativistic effects 11331:which changes the field equation from: 10570:{\displaystyle \omega _{\nu }^{\mu }\;} 8249:infinite derivative theories of gravity 6035: 1240:, a measure of the curvature of space. 25031: 24105:Nordtvedt Jr, K.; Will, C. M. (1972). 23551: 22780: 22618: 22562: 22506: 22453: 21707: 21474:Will, C. M.; Nordtvedt Jr, K. (1972). 21418: 20878: 20840: 20315: 20286: 20203: 19857: 17475:Parameterized post-Newtonian formalism 17405:Strong gravity and gravitational waves 17057:Parameterized post-Newtonian formalism 16603:accelerating expansion of the universe 16374:accelerating expansion of the universe 12256:The relativistic version of this has: 10923:Cosmological constant and quintessence 10864: 10280: 10036:(See Will for the field equations for 9235:, found from a cosmological solution, 5906:{\displaystyle F(N)=-{\frac {N}{2+N}}} 2564: 2418: 1971:Einstein: There is no reference frame. 1887: 977:{\displaystyle g=\det(g_{\mu \nu })\,} 24992:Physics in the medieval Islamic world 24915:(2+1)-dimensional topological gravity 24411:Newton's law of universal gravitation 24362: 22003:Whitehead. The Algebra of Metaphysics 21931: 21916: 21879: 21797:"Relativitätsprinzip und Gravitation" 21381: 21341: 20483: 20112:Zeitschrift für Mathematik und Physik 17454:cosmic microwave background radiation 17423: 15334:with terms for gravity, vector field 12396:with a nonstandard mass action. Here 11911:'s creation tensor in order to allow 11880:In December 2018, the astrophysicist 5973:(see Will for the field equation for 3709:Misner et al. gives this without the 2583:cosmological constant or quintessence 400: 24737:Asymptotic safety in quantum gravity 24300:Einstein, A.; Fokker, A. D. (1914). 24010: 23756: 23626: 23568: 23521: 23407: 23354: 22864: 20165: 19920: 16391:The GRSI model is inspired from the 14121: 12086: 11903:The theory relies on the concept of 11804:{\displaystyle \lambda (\varphi )\;} 11647:{\displaystyle \lambda (\varphi )\;} 11596:{\displaystyle \lambda (\varphi )\;} 10277:is discussed under Modern Theories. 9051:{\displaystyle \lambda (\varphi )\;} 7295:Gauss–Bonnet gravity has the action 4821: 1785: 927:{\displaystyle R=R_{\mu }^{~\mu }\,} 892:is Newton's gravitational constant, 21114:Page, C.; Tupper, B. O. J. (1968). 17051:Parametric post-Newtonian formalism 16694: 16572:List of topics studied in the Model 16399:emitted by static or nearly static 12494:{\displaystyle l_{0}=c^{2}/a_{0}\;} 11875: 9638:match those of general relativity. 9600:{\displaystyle \omega (\varphi )\;} 9021:{\displaystyle \omega (\varphi )\;} 4270:that are related to the metric by: 3986:that are related to the metric by: 13: 24489:Gibbons–Hawking–York boundary term 23545:Quantum Field Theory in a Nutshell 22753:Xaq Rzetelny (February 25, 2017). 21882:General Relativity and Gravitation 21429: 21384:General Relativity and Gravitation 20226: 16973:The Einstein equivalence principle 16933: 16191: 15946: 15932: 15845: 15831: 15756: 15742: 15610: 15587: 15168: 15142: 15079: 14759:vector. The action is split into: 12366: 12352: 12194: 12083:which should come online in 2022. 11573:More generally a scalar potential 11548: 11273: 11085: 11060: 11003: 10969: 10948: 10832: 10479: 10418: 10347: 9620: 8923: 8920: 8917: 8758: 8744: 8442: 8271: 7733: 7638: 7461: 7307: 7187: 7136: 6263: 6157: 5690: 5672: 4790: 4776: 4734: 4720: 4690: 4676: 4533: 4519: 4480: 4466: 4174: 4164: 3892: 3878: 3684: 3670: 3440: 3388: 3340: 3200: 3068: 2983: 2833: 1651: 1620: 1533: 1499: 1445: 1137: 443:{\displaystyle \delta \int ds=0\,} 390:{\displaystyle \varphi _{;\mu }\;} 343: 324:{\displaystyle \varphi _{,\mu }\;} 277: 213:{\displaystyle \eta _{\mu \nu }\;} 20:Alternatives to general relativity 14: 25055: 24604:Modified Newtonian dynamics, MOND 24520:Classical theories of gravitation 24335: 21524:"Vector-Metric Theory of Gravity" 14036:{\displaystyle c=G_{Newtonian}=1} 10896:different in the early universe. 7171:Starobinsky gravity, proposed by 2037:Whitehead's theory of gravitation 2009:Theories from 1917 to the 1980s. 1732:Nordström's theory of gravitation 119:Mathematics of general relativity 24139: 22979:Damour; Deser; McCarthy (1993). 21212:"A linear theory of gravitation" 19921:Will, Clifford M. (2014-12-01). 19746:† The theory is incomplete, and 16956:found a fourth test, called the 16669:overall dynamics of the universe 16582:flat rotation curves of galaxies 14131:non-symmetric gravitation theory 10890: 10882:Modern theories 1980s to present 8259:Lovelock gravity has the action 1988:Isaac Newton's theory of gravity 56:classical unified field theories 24426:History of gravitational theory 24047: 24004: 23945: 23880: 23827: 23750: 23729: 23659:10.1140/epjc/s10052-021-08965-5 23536: 23515: 23450: 23401: 23288: 23235: 23174: 23121: 23068: 22858: 22746: 22718: 22665: 22311: 22242: 22181: 22120: 22069: 22008: 21946: 21925: 16706: 16509:is the mass of the system, and 15569: 15563: 14210:{\displaystyle L=L_{R}+L_{M}\;} 13465:represent anti-symmetrization, 10192: 10179: 10134: 7445:Stelle's 4th derivative gravity 7290: 6554: 6428: 3332: 3181: 3049: 2971: 2821: 2288:Paul Kustaanheimo, V. S. Nuotio 1996:history of gravitational theory 1982:History of gravitational theory 1976:Theories from 1917 to the 1980s 1643:with respect to the metric and 1044:based on the concept of action) 24732:Causal dynamical triangulation 24421:Poisson's equation for gravity 23866:10.1016/j.physletb.2021.136510 23715:10.1140/epjc/s10052-017-4971-x 23601:10.1016/j.physletb.2009.04.060 23444:10.1016/j.physletb.2009.04.060 23387:10.1140/epjc/s10052-019-7393-0 23213:10.1103/PhysRevLett.108.031101 22704:10.1016/j.physletb.2016.12.048 22321:Journal of High Energy Physics 22281:10.1103/PhysRevLett.114.211101 22047:10.1103/PhysRevLett.108.031101 20066: 19991: 19815:Theories that fail other tests 16561:{\displaystyle {\sqrt {GM/L}}} 16458:{\displaystyle {\sqrt {GM/L}}} 16284: 16278: 16244: 16238: 16013: 16007: 15970: 15964: 15869: 15863: 15780: 15774: 15552: 15546: 15443:is moved inside the integral. 15389:{\displaystyle G,\omega ,\mu } 14724:{\displaystyle A_{\mu \nu }\;} 14642: 14633: 14567:{\displaystyle g_{\nu \mu }\;} 14527: 14518: 14443: 14437: 14357: 14348: 14295: 14289: 14160:{\displaystyle g_{\mu \nu }\;} 13941: 13928: 13903: 13891: 13769: 13754: 13639: 13626: 13597: 13591: 13578:is an arbitrary function, and 13503: 13450: 13438: 13385: 13376: 13300: 13147: 13110: 12970: 12958: 12948: 12936: 12823: 12804: 12429: 12311: 12202: 12190: 11797: 11791: 11675:{\displaystyle L_{\varphi }\;} 11640: 11634: 11589: 11583: 11276: 11261: 10828: 10735: 10683:{\displaystyle g^{\nu \xi }\,} 9617: 9593: 9587: 9526: 9520: 9479: 9475: 9469: 9460: 9448: 9439: 9436: 9427: 9421: 9412: 9397: 9394: 9391: 9385: 9348: 9342: 9285: 9278: 9272: 9269: 9263: 9248: 9044: 9038: 9014: 9008: 8788: 8782: 8720: 8714: 8575:{\displaystyle L_{\varphi }\;} 8463: 8460: 8447: 8292: 7697: 7691: 7665: 7659: 7160: 7111:{\displaystyle h_{\mu \nu }\;} 7041: 7020: 6996: 6968: 6942: 6916: 6895: 6864: 6714:{\displaystyle h_{\mu \nu }\;} 6568: 6555: 6542: 6528: 6519: 6505: 6466: 6452: 6443: 6429: 6416: 6402: 6373: 6359: 6317:light cone of the field point 6217: 6203: 6126: 6113: 5997:{\displaystyle T^{\mu \nu }\;} 5876: 5870: 5796: 5790: 5524: 5483: 5462: 5444: 5285:{\displaystyle B_{\mu \nu }\,} 5243: 5197: 5158: 5137: 5036: 5027: 5006: 4971: 4950: 4935: 4636: 4621: 4214: 4208: 4070: 4064: 4032: 4026: 3973: 3967: 3944: 3938: 3422: 3407: 2951: 2929: 2815: 2791: 2779: 2758: 2595:Scalar theories of gravitation 1764:(includes Linear fixed gauge) 1632:{\displaystyle \nabla _{\nu }} 1601:{\displaystyle T^{\mu \nu }\,} 1286:{\displaystyle g_{\mu \nu }\,} 1222:{\displaystyle L\,\propto \,R} 970: 954: 248:{\displaystyle g_{\mu \nu }\;} 76: 1: 23160:10.1088/0264-9381/31/1/015022 23130:Classical and Quantum Gravity 23107:10.1088/1475-7516/2006/03/009 22651:10.1088/1475-7516/2006/03/004 22595:10.1088/1475-7516/2005/05/003 19895:10.1016/j.physrep.2012.01.001 19851: 18305:{\displaystyle c_{0}/c_{1}-1} 16601:and their consequence on the 16384:within a galaxy requires, by 14543:is the antisymmetric part of 9687:The gravitational action is: 6338:{\displaystyle x^{\alpha }\;} 1790:Einstein's general relativity 1774:Whitehead's theory of gravity 185:Einstein summation convention 22783:Astronomy & Astrophysics 22486:10.1016/0370-2693(95)00670-G 21090:10.1016/0003-4916(68)90317-5 21038:10.1016/0031-9163(66)90266-6 21000:10.1016/0083-6656(65)90002-4 20901:10.1016/0003-4916(73)90485-5 20821:10.1016/0003-4916(57)90058-1 20785:10.1016/0003-4916(57)90057-x 20099:The Principles of Relativity 19927:Living Reviews in Relativity 19005:{\displaystyle -4-4\lambda } 18721:{\displaystyle ac_{0}/c_{1}} 18557:{\displaystyle ac_{0}/c_{1}} 17746:Einstein general relativity 16651:radial acceleration relation 16343:radial acceleration relation 15260:Scalar–tensor–vector gravity 15254:Scalar–tensor–vector gravity 15248:Scalar–tensor–vector gravity 14506:are cosmological constants, 12438:{\displaystyle {\tilde {f}}} 12101:Extended theories of gravity 12097:Tensor–vector–scalar gravity 10982:{\displaystyle \Lambda =0\;} 10059:{\displaystyle T^{\mu \nu }} 9133:{\displaystyle \lambda =0\;} 7626:f(R) gravity has the action 3505:{\displaystyle \alpha =-7/2} 2851:In Littlewood and Bergmann, 2579:High-Z Supernova Search Team 2214:Yilmaz theory of gravitation 1750:Yilmaz theory of gravitation 16:Proposed theories of gravity 7: 24594:Infinite derivative gravity 23321:10.1016/j.newar.2023.101673 22950:10.1103/physrevlett.75.2455 22813:10.1051/0004-6361/201832898 21985:10.1016/j.shpsb.2007.04.004 21754:Canadian Journal of Physics 20721:American Journal of Physics 19840:{\displaystyle \alpha _{2}} 19796:{\displaystyle \beta =\xi } 19398:Nordström, Einstein–Fokker 19243:{\displaystyle -2-2\gamma } 19207:{\displaystyle -4-4\gamma } 18811:{\displaystyle \alpha _{2}} 18783:{\displaystyle \alpha _{1}} 18655:{\displaystyle \alpha _{2}} 18627:{\displaystyle \alpha _{1}} 18486:{\displaystyle \alpha _{2}} 18458:{\displaystyle \alpha _{1}} 18365:{\displaystyle \alpha _{2}} 18219:{\displaystyle \alpha _{2}} 18159:{\displaystyle \alpha _{2}} 18131:{\displaystyle \alpha _{1}} 17623:{\displaystyle \alpha _{3}} 17595:{\displaystyle \alpha _{2}} 17567:{\displaystyle \alpha _{1}} 17461:Results of testing theories 17411:Tests of general relativity 17063:Tests of general relativity 16940:Tests of general relativity 16686:Tests of general relativity 16589:Cosmic Microwave Background 16158:Infinite derivative gravity 16152:Infinite derivative gravity 14731:field and a source current 13976:both of which expressed in 12571:{\displaystyle U_{\alpha }} 12093:Modified Newtonian dynamics 8254: 7719:Infinite derivative gravity 7714:Infinite derivative gravity 3979:{\displaystyle k(\varphi )} 3950:{\displaystyle f(\varphi )} 2674:where the scalar field is, 2575:Supernova Cosmology Project 1817:Infinite derivative gravity 1259:: There exists a symmetric 771:for general relativity is: 10: 25060: 24782:Unified-field-theoric and 22897:10.1103/PhysRevD.80.044032 22417:10.1103/physrevd.70.083509 22220:10.1103/PhysRevD.89.064046 22159:10.1103/PhysRevD.79.084003 20469:, Clarendon Press, Oxford. 19766:{\displaystyle \zeta _{4}} 19567:{\displaystyle \zeta _{2}} 19305:{\displaystyle \zeta _{4}} 19274:{\displaystyle \zeta _{2}} 17735:{\displaystyle \zeta _{4}} 17707:{\displaystyle \zeta _{3}} 17679:{\displaystyle \zeta _{2}} 17651:{\displaystyle \zeta _{1}} 17408: 17054: 17045:gauge covariant derivative 16976: 16937: 16683: 16155: 15251: 14752:{\displaystyle J_{\mu }\;} 14674:metric-skew-tensor-gravity 14595:{\displaystyle W_{\mu }\;} 14499:{\displaystyle \mu ^{2}\;} 14471:{\displaystyle \lambda \;} 13567:{\displaystyle G_{Newton}} 12090: 11617:{\displaystyle \varphi \;} 10955:{\displaystyle \Lambda \;} 10941:The cosmological constant 10926: 10577:is the linear connection. 10284: 8489: 8240:{\displaystyle M_{s}^{-1}} 7164: 7155:Lovelock theory of gravity 6025:{\displaystyle K_{\mu }\;} 4825: 2592: 1979: 1811:Lovelock theory of gravity 1024:Classification of theories 647:which can also be written 404: 116: 25005: 24937: 24925:Jackiw–Teitelboim gravity 24895: 24781: 24760: 24704:Canonical quantum gravity 24699:Euclidean quantum gravity 24691: 24538: 24512: 24501: 24434: 24403: 24396: 24111:The Astrophysical Journal 22539:10.1142/S0218271803002366 21801:Physikalische Zeitschrift 21710:The Astrophysical Journal 21480:The Astrophysical Journal 21260:The Astrophysical Journal 21254:Nordtvedt Jr, K. (1970). 20669:10.1017/s0305004100028085 20607:Mathematische Nachrichten 20576:Mathematische Nachrichten 20229:The Astrophysical Journal 16622:The internal dynamics of 15357:{\displaystyle K_{\mu },} 12544:{\displaystyle \sigma \;} 10089:{\displaystyle K_{\mu }.} 9680:{\displaystyle K_{\mu }.} 9507:Barker constant G theory 9183:{\displaystyle \omega \;} 3725:{\displaystyle \varphi R} 2722:may or may not depend on 1994:in 1915 are discussed in 1102:is the integral of that: 1038:principle of least action 333:Covariant differentiation 255:is a tensor, usually the 86:with general relativity. 50:are known as theories of 24801:Superfluid vacuum theory 24625:Nonsymmetric gravitation 24474:Post-Newtonian formalism 24326:10.1002/andp.19143491009 24287:10.1002/andp.19123430709 24245:10.1002/andp.19123430704 24060:Mon. Not. R. Astron. Soc 24017:Mon. Not. R. Astron. Soc 23984:10.1088/1402-4896/ad570f 23924:10.3847/1538-4357/ab94b6 23813:10.1088/1361-6382/ac7029 23494:10.3847/1538-4357/ab94b6 23274:10.1103/PhysRevD.56.3471 23046:10.1103/physrevd.52.3168 21849:10.1002/andp.19133471303 21690:10.1103/PhysRevD.15.1458 21648:10.1103/PhysRevD.10.1685 21216:Lettere al Nuovo Cimento 20863:10.1103/physrev.111.1417 20619:10.1002/mana.19540120302 20588:10.1002/mana.19540120301 20404:Birkhoff, G. D. (1943). 20048:10.1002/andp.19163540702 19871:. 513 num.3 (1): 1–189. 18925:{\displaystyle \lambda } 17715: 17687: 17659: 17631: 17603: 17575: 17547: 17526: 17505: 17484: 16626:, including that of the 16290:{\displaystyle F(\Box )} 13478:{\displaystyle \lambda } 12523:{\displaystyle \varphi } 9155:{\displaystyle \lambda } 7131:anti-de Sitter spacetime 4243:{\displaystyle \varphi } 3101:In Whitrow and Morduch, 3002:In Whitrow and Morduch, 2735:{\displaystyle \varphi } 2318:C. Page, B. O. J. Tupper 1767:Bollini–Giambiagi–Tiomno 1752:(attempted to eliminate 1248:did not have an action. 113:Notation in this article 105:". Investigation of the 24966:Mechanical explanations 24835:Heterotic string theory 24791:Noncommutative geometry 24710:Wheeler–DeWitt equation 24436:General relativity (GR) 24416:Gauss's law for gravity 24390:Theories of gravitation 23183:Physical Review Letters 22920:Physical Review Letters 22805:2018A&A...620A..92F 22351:10.1007/JHEP12(2016)100 22251:Physical Review Letters 22017:Physical Review Letters 21590:10.1103/PhysRevD.8.3293 21548:10.1103/PhysRevD.7.3593 21452:10.1103/PhysRevD.7.2880 21364:10.1103/physrevd.3.2317 21324:10.1103/PhysRevD.1.3209 20613:(3–4). Wiley: 143–154. 20582:(3–4). Wiley: 129–141. 20484:Thiry, M. Yves (1948). 20200:, Cambridge Univ. Press 20159:10.1103/physrev.124.925 20101:, Cambridge Univ. Press 20097:Whitehead, A.N. (1922) 19151:{\displaystyle \gamma } 18406:{\displaystyle \gamma } 18079:{\displaystyle \gamma } 18059:Vector–tensor theories 17781:Scalar–tensor theories 17497:{\displaystyle \gamma } 17213:{\displaystyle \gamma } 16922:{\displaystyle \eta \;} 16897:{\displaystyle \delta } 14241:{\displaystyle L_{M}\;} 10933:Einstein–Hilbert action 9079:{\displaystyle G_{N}\;} 7621: 6310:{\displaystyle \eta \;} 6083:{\displaystyle \eta \;} 1963:Absolute space and time 1196:Einstein–Hilbert action 1005:{\displaystyle S_{m}\,} 769:Einstein–Hilbert action 267:Partial differentiation 24807:Logarithmic BEC vacuum 24752:Rainbow gravity theory 24630:Scalar–tensor theories 24404:Newtonian gravity (NG) 24091:10.1093/mnras/stac3236 23408:Deur, A. (June 2009). 21141:10.1093/mnras/138.1.67 20517:Zeitschrift für Physik 20380:10.1098/rspa.1939.0140 19841: 19797: 19767: 19712: 19682: 19630: 19603: 19568: 19526: 19499: 19447: 19417: 19365: 19335: 19306: 19275: 19244: 19208: 19173: 19172:{\displaystyle \beta } 19152: 19006: 18971: 18926: 18837:Scalar field theories 18812: 18784: 18753: 18752:{\displaystyle bc_{0}} 18722: 18656: 18628: 18600: 18579: 18578:{\displaystyle \beta } 18558: 18487: 18459: 18428: 18427:{\displaystyle \beta } 18407: 18366: 18306: 18220: 18160: 18132: 18101: 18100:{\displaystyle \beta } 18080: 18022: 17947: 17946:{\displaystyle \beta } 17926: 17848: 17847:{\displaystyle \beta } 17827: 17736: 17708: 17680: 17652: 17624: 17596: 17568: 17540: 17519: 17518:{\displaystyle \beta } 17498: 17394: 17313: 17258: 17236: 17235:{\displaystyle \beta } 17214: 17192: 16946:gravitational redshift 16923: 16898: 16874: 16854: 16805: 16749: 16729: 16712:clocks is incomplete. 16562: 16523: 16503: 16487:gravitational constant 16479: 16459: 16335:quantum chromodynamics 16299:D'Alembertian operator 16291: 16259: 16142: 16119: 15985: 15636: 15437: 15417: 15390: 15358: 15328: 15234: 15194: 15103: 14997: 14832: 14753: 14725: 14691: 14660: 14596: 14568: 14537: 14536:{\displaystyle g_{}\;} 14500: 14472: 14451: 14450:{\displaystyle R(W)\;} 14418: 14242: 14211: 14161: 14112: 14037: 13967: 13695: 13694:{\displaystyle \mu =1} 13666: 13568: 13522: 13479: 13459: 13420: 13392: 13279: 13204: 12647: 12572: 12545: 12524: 12495: 12439: 12410: 12387: 12247: 12081:Square Kilometre Array 12069: 11863: 11805: 11772: 11676: 11648: 11618: 11597: 11561: 11432: 11322: 11215: 11123: 11040: 10983: 10956: 10937:Quintessence (physics) 10851: 10684: 10653: 10608: 10571: 10535: 10287:Einstein–Cartan theory 10259: 10212: 10148: 10090: 10060: 10030: 9956: 9915: 9681: 9649:Vector–tensor theories 9628: 9601: 9568: 9498: 9323: 9302: 9229: 9208: 9184: 9156: 9134: 9101: 9080: 9052: 9022: 8989: 8875: 8796: 8670: 8576: 8548: 8486:Scalar–tensor theories 8473: 8241: 8206: 8179: 8149: 7985: 7704: 7672: 7612: 7431: 7281: 7254: 7112: 7073: 6781: 6715: 6677: 6339: 6311: 6287: 6084: 6059: 6044:, the physical metric 6026: 5998: 5964: 5907: 5848: 5717: 5544: 5378: 5357: 5336: 5286: 5252: 5057: 4812: 4577: 4554: 4392: 4264: 4244: 4221: 4134: 3980: 3951: 3913: 3759:is the matter action. 3753: 3726: 3700: 3614: 3506: 3466: 3224: 3092: 2993: 2842: 2736: 2709: 2665: 2057:Einstein–Cartan theory 2032:Alfred North Whitehead 1933:Einstein–Cartan theory 1866:Vector–tensor theories 1824:Scalar–tensor theories 1776:(intended to use only 1709:Einstein–Fokker theory 1673: 1633: 1602: 1568: 1417: 1397: 1374: 1287: 1223: 1188: 1187:{\displaystyle g=-1\,} 1154: 1096: 1075: 1006: 978: 928: 886: 862: 758: 638: 524: 444: 391: 360: 325: 294: 249: 214: 174:gravitational constant 166: 141: 60:theories of everything 24884:Twistor string theory 24863:Type II string theory 24856:Bosonic string theory 24796:Semiclassical gravity 24761:Unified-field-theoric 24546:Poincaré gauge theory 24040:10.1093/mnras/stt2293 23301:New Astronomy Reviews 21997:Cf. Ronny Desmet and 21823:Nordström, G (1913). 20431:10.1073/pnas.29.8.231 19842: 19798: 19777:in these three cases 19768: 19713: 19683: 19631: 19604: 19569: 19527: 19500: 19448: 19418: 19366: 19336: 19307: 19276: 19245: 19209: 19174: 19153: 19007: 18972: 18927: 18813: 18785: 18754: 18723: 18657: 18629: 18601: 18580: 18559: 18488: 18460: 18429: 18408: 18367: 18307: 18221: 18161: 18133: 18102: 18081: 18023: 17948: 17927: 17849: 17828: 17737: 17709: 17681: 17653: 17625: 17597: 17569: 17541: 17520: 17499: 17446:gravitational lensing 17442:Tully–Fisher relation 17438:galaxy rotation curve 17431:luminous red galaxies 17395: 17314: 17259: 17257:{\displaystyle \eta } 17237: 17215: 17193: 16979:Equivalence principle 16950:gravitational lensing 16924: 16899: 16875: 16855: 16806: 16750: 16730: 16728:{\displaystyle \rho } 16644:Tully-Fisher relation 16617:matter power spectrum 16563: 16524: 16504: 16480: 16460: 16413:Tully-Fisher relation 16376:without resorting to 16365:) because they carry 16339:Tully-Fisher relation 16292: 16260: 16143: 16120: 15986: 15637: 15438: 15418: 15416:{\displaystyle S_{G}} 15391: 15359: 15329: 15235: 15195: 15104: 14998: 14833: 14754: 14726: 14692: 14661: 14597: 14569: 14538: 14501: 14473: 14452: 14419: 14243: 14212: 14162: 14113: 14038: 13968: 13696: 13667: 13569: 13523: 13480: 13460: 13421: 13393: 13280: 13205: 12648: 12573: 12546: 12525: 12496: 12440: 12411: 12388: 12248: 12070: 11918:cosmological constant 11864: 11806: 11773: 11677: 11649: 11619: 11598: 11562: 11433: 11323: 11216: 11124: 11041: 10984: 10957: 10929:Cosmological constant 10852: 10685: 10654: 10609: 10572: 10536: 10269:Other metric theories 10260: 10213: 10149: 10091: 10061: 10031: 9957: 9916: 9682: 9629: 9602: 9569: 9499: 9324: 9303: 9230: 9209: 9185: 9164:Cosmological constant 9157: 9135: 9102: 9081: 9053: 9023: 8990: 8876: 8797: 8671: 8577: 8549: 8474: 8242: 8207: 8205:{\displaystyle M_{s}} 8180: 8178:{\displaystyle M_{s}} 8150: 7986: 7705: 7673: 7613: 7432: 7282: 7265:Starobinsky inflation 7255: 7167:Starobinsky inflation 7123:cosmological constant 7113: 7074: 6782: 6716: 6678: 6340: 6312: 6288: 6085: 6060: 6027: 5999: 5965: 5908: 5849: 5718: 5545: 5379: 5358: 5337: 5287: 5253: 5058: 4813: 4578: 4576:{\displaystyle \chi } 4555: 4393: 4265: 4263:{\displaystyle \psi } 4245: 4222: 4135: 3981: 3952: 3914: 3754: 3752:{\displaystyle S_{m}} 3727: 3701: 3615: 3507: 3467: 3225: 3093: 2994: 2843: 2737: 2710: 2666: 2589:Scalar field theories 2090:George David Birkhoff 1910:Other metric theories 1695:Scalar field theories 1674: 1634: 1603: 1569: 1418: 1398: 1375: 1288: 1224: 1189: 1155: 1097: 1076: 1042:variational principle 1007: 979: 929: 887: 863: 759: 639: 525: 445: 392: 361: 326: 295: 250: 215: 167: 142: 24951:Aristotelian physics 24920:Gauss–Bonnet gravity 24870:Little string theory 24849:Type 0 string theory 24842:Type I string theory 24717:Loop quantum gravity 24644:Scalar–tensor–vector 24617:Tensor–vector–scalar 24572:Gauge theory gravity 24530:Theory of everything 23295:Oks, Eugene (2023). 22835:University of Oxford 20603:Papapetrou, Achilles 20572:Papapetrou, Achilles 20467:Kinematic Relativity 20022:Einstein, A (1916). 19824: 19781: 19750: 19693: 19669: 19663:Littlewood, Bergman 19614: 19590: 19551: 19510: 19486: 19428: 19404: 19346: 19322: 19289: 19258: 19222: 19186: 19163: 19142: 18984: 18937: 18916: 18795: 18767: 18733: 18687: 18639: 18611: 18599:{\displaystyle \xi } 18590: 18569: 18523: 18512:Stratified theories 18470: 18442: 18418: 18397: 18349: 18268: 18203: 18143: 18115: 18091: 18070: 17987: 17937: 17891: 17838: 17792: 17719: 17691: 17663: 17635: 17607: 17579: 17551: 17539:{\displaystyle \xi } 17530: 17509: 17488: 17325: 17270: 17248: 17226: 17204: 17076: 16912: 16888: 16864: 16815: 16759: 16739: 16719: 16537: 16531:lattice calculations 16513: 16493: 16469: 16434: 16393:Strong Nuclear Force 16272: 16177: 16132: 16001: 15649: 15450: 15427: 15400: 15368: 15338: 15266: 15207: 15119: 15010: 14848: 14766: 14735: 14704: 14680: 14606: 14578: 14547: 14510: 14482: 14461: 14431: 14255: 14224: 14174: 14140: 14050: 13984: 13710: 13679: 13585: 13536: 13493: 13469: 13458:{\displaystyle U_{}} 13430: 13404: 13290: 13220: 12663: 12585: 12555: 12534: 12514: 12508:tensor–vector–scalar 12449: 12420: 12400: 12263: 12137: 11927: 11886:University of Oxford 11822: 11785: 11689: 11658: 11628: 11607: 11577: 11448: 11338: 11231: 11139: 11056: 10999: 10966: 10945: 10872:gauge theory gravity 10698: 10663: 10622: 10581: 10548: 10311: 10225: 10164: 10107: 10070: 10040: 9969: 9928: 9694: 9661: 9611: 9581: 9514: 9336: 9312: 9308:determines function 9239: 9218: 9197: 9173: 9146: 9117: 9090: 9062: 9032: 9002: 8888: 8809: 8683: 8589: 8558: 8537: 8492:Scalar–tensor theory 8266: 8216: 8189: 8162: 8001: 7728: 7703:{\displaystyle f(R)} 7685: 7633: 7456: 7302: 7271: 7182: 7147:Gauss–Bonnet gravity 7091: 6797: 6728: 6694: 6352: 6321: 6300: 6097: 6073: 6048: 6036:Quasilinear theories 6008: 5977: 5917: 5864: 5733: 5560: 5391: 5367: 5346: 5342:, and two constants 5296: 5265: 5070: 4842: 4590: 4567: 4408: 4277: 4254: 4234: 4147: 3993: 3961: 3932: 3766: 3736: 3713: 3627: 3534: 3479: 3240: 3233:In Page and Tupper, 3108: 3009: 2858: 2752: 2726: 2681: 2609: 2446:Clifford Martin Will 2250:Gerald James Whitrow 2150:Dudley E. Littlewood 2109:Kinematic Relativity 2014:Publication year(s) 1947:Gauge theory gravity 1806:Gauss–Bonnet gravity 1794:Fourth-order gravity 1762:Quasilinear theories 1647: 1641:covariant derivative 1616: 1610:stress–energy tensor 1581: 1435: 1416:{\displaystyle \nu } 1407: 1396:{\displaystyle \mu } 1387: 1304: 1266: 1205: 1168: 1109: 1085: 1064: 988: 942: 896: 875: 778: 654: 537: 457: 418: 370: 339: 304: 273: 228: 193: 155: 130: 30:in competition with 25039:Theories of gravity 24768:Kaluza–Klein theory 24318:1914AnP...349..321E 24279:1912AnP...343..443E 24237:1912AnP...343..355E 24179:10.1038/nature08857 24171:2010Natur.464..256R 24123:1972ApJ...177..775N 24082:2023MNRAS.518.2845W 23976:2024PhyS...99g5043S 23915:2020ApJ...896...94D 23858:2021PhLB..82036510D 23805:2022CQGra..39m5003D 23707:2017EPJC...77..412D 23651:2021EPJC...81..213D 23593:2009PhLB..676...21D 23485:2020ApJ...896...94D 23436:2009PhLB..676...21D 23379:2019EPJC...79..883D 23313:2023NewAR..9601673O 23266:1997PhRvD..56.3471L 23205:2012PhRvL.108c1101B 23152:2014CQGra..31a5022B 23099:2006JCAP...03..009B 23038:1995PhRvD..52.3168H 23001:1993nghu.book.....D 22942:1995PhRvL..75.2455B 22889:2009PhRvD..80d4032S 22837:(5 December 2018). 22734:. February 10, 2017 22696:2017PhLB..765..382L 22643:2006JCAP...03..004M 22587:2005JCAP...05..003M 22531:2003IJMPD..12..281M 22478:1995PhLB..355..447M 22409:2004PhRvD..70h3509B 22343:2016JHEP...12..100A 22273:2015PhRvL.114u1101G 22212:2014PhRvD..89f4046Z 22151:2009PhRvD..79h4003D 22090:1974IJTP...10..363H 22039:2012PhRvL.108c1101B 21977:2008SHPMP..39...41G 21894:1973GReGr...4..435R 21841:1913AnP...347..533N 21766:1979CaJPh..57..944R 21722:1978ApJ...219....5B 21682:1977PhRvD..15.1458B 21640:1974PhRvD..10.1685L 21582:1973PhRvD...8.3293L 21540:1973PhRvD...7.3593H 21492:1972ApJ...177..757W 21444:1973PhRvD...7.2880N 21396:1975GReGr...6..259R 21356:1971PhRvD...3.2317R 21316:1970PhRvD...1.3209W 21272:1970ApJ...161.1059N 21176:1968IJTP....1...25B 21132:1968MNRAS.138...67P 21082:1968AnPhy..50...76D 21030:1966PhL....23...75K 20992:1965VA......6....1W 20980:Vistas in Astronomy 20940:1960Natur.188..790W 20893:1973AnPhy..81..179Y 20855:1958PhRv..111.1417Y 20777:1957AnPhy...1..168B 20733:1956AmJPh..24...38B 20661:1953PCPS...49...90L 20529:1954ZPhy..139..518P 20465:Milne E. A. (1948) 20422:1943PNAS...29..231B 20372:1939RSPSA.173..211F 20241:1972ApJ...176..769N 20151:1961PhRv..124..925B 20040:1916AnP...354..769E 19958:10.12942/lrr-2014-4 19949:2014LRR....17....4W 19887:2012PhR...513....1C 19629:{\displaystyle 1-q} 19525:{\displaystyle 1-q} 18064:Hellings–Nordtvedt 16386:energy conservation 14690:{\displaystyle G\;} 14654: 13419:{\displaystyle k,K} 13160: 12790: 12336: 12291: 12227: 12165: 12043: 12022: 11624:by adding the term 10845: 10827: 10796: 10765: 10565: 10516: 10474: 10456: 10431: 10360: 10281:Non-metric theories 9322:{\displaystyle f\;} 9228:{\displaystyle q\;} 9207:{\displaystyle r\;} 9100:{\displaystyle G\;} 8547:{\displaystyle S\;} 8236: 8129: 8083: 8040: 7947: 7872: 7813: 7770: 7175:has the Lagrangian 7004: 6981: 6955: 6932: 6903: 6880: 6200: 6185: 6065:is constructed (by 6058:{\displaystyle g\;} 5377:{\displaystyle f\,} 5356:{\displaystyle a\,} 3449: 3397: 3349: 3209: 3077: 2196:Frederik Belinfante 2133:Achilles Papapetrou 2104:Edward Arthur Milne 2010: 1938:Kustaanheimo (1967) 1923:Non-metric theories 1778:retarded potentials 1667: 1549: 1515: 1095:{\displaystyle S\,} 1074:{\displaystyle L\,} 922: 885:{\displaystyle G\,} 178:Geometric variables 165:{\displaystyle G\;} 140:{\displaystyle c\;} 71:theoretical physics 25044:General relativity 25013:Gravitational wave 24896:Generalisations / 24784:quantum-mechanical 24692:Quantum-mechanical 24505:general relativity 24479:Linearized gravity 24306:Annalen der Physik 24267:Annalen der Physik 24225:Annalen der Physik 23783:Class. Quant. Grav 22098:10.1007/BF01807638 21902:10.1007/BF01215403 21829:Annalen der Physik 21404:10.1007/BF00751570 21228:10.1007/bf02755901 21184:10.1007/bf00668828 20537:10.1007/bf01374560 20341:10.24033/asens.751 20028:Annalen der Physik 19837: 19805:Whitehead's theory 19793: 19763: 19708: 19707: 19681:{\displaystyle -1} 19678: 19626: 19602:{\displaystyle -1} 19599: 19564: 19522: 19498:{\displaystyle -1} 19495: 19443: 19442: 19416:{\displaystyle -1} 19413: 19361: 19360: 19334:{\displaystyle -1} 19331: 19302: 19271: 19240: 19204: 19169: 19148: 19002: 18967: 18966: 18965: 18922: 18808: 18780: 18749: 18718: 18652: 18624: 18596: 18575: 18554: 18483: 18455: 18424: 18403: 18362: 18302: 18245:Bimetric theories 18216: 18156: 18128: 18097: 18076: 18018: 18017: 17943: 17922: 17921: 17844: 17823: 17822: 17786:Bergmann, Wagoner 17732: 17704: 17676: 17648: 17620: 17592: 17564: 17536: 17515: 17494: 17424:Cosmological tests 17390: 17309: 17254: 17232: 17210: 17188: 16919: 16894: 16870: 16850: 16801: 16745: 16725: 16665:cosmic coincidence 16558: 16519: 16499: 16475: 16455: 16417:Regge trajectories 16331:general relativity 16287: 16255: 16138: 16115: 15981: 15632: 15433: 15413: 15386: 15354: 15324: 15242:Levi-Civita symbol 15230: 15190: 15099: 14993: 14828: 14749: 14721: 14687: 14656: 14628: 14592: 14564: 14533: 14496: 14468: 14447: 14414: 14238: 14207: 14157: 14108: 14033: 13963: 13961: 13691: 13662: 13564: 13518: 13475: 13455: 13416: 13388: 13275: 13200: 13198: 13141: 12773: 12643: 12568: 12541: 12520: 12491: 12435: 12406: 12383: 12322: 12277: 12243: 12213: 12151: 12065: 12026: 12005: 11859: 11801: 11768: 11672: 11644: 11614: 11593: 11557: 11428: 11318: 11211: 11119: 11036: 10979: 10952: 10847: 10831: 10813: 10782: 10751: 10680: 10649: 10616:Levi-Civita symbol 10604: 10567: 10551: 10531: 10529: 10502: 10460: 10442: 10417: 10346: 10255: 10208: 10144: 10086: 10056: 10026: 9962:are constants and 9952: 9911: 9677: 9643:Horndeski's theory 9624: 9597: 9564: 9494: 9493: 9492: 9319: 9298: 9225: 9204: 9180: 9152: 9130: 9097: 9076: 9048: 9018: 8985: 8871: 8792: 8666: 8572: 8544: 8512:Horndeski's theory 8504:Chameleon particle 8496:Brans–Dicke theory 8469: 8237: 8219: 8202: 8175: 8145: 8115: 8069: 8026: 7981: 7933: 7858: 7799: 7756: 7700: 7668: 7608: 7427: 7277: 7250: 7173:Alexei Starobinsky 7108: 7069: 6982: 6959: 6933: 6910: 6881: 6858: 6777: 6711: 6673: 6671: 6335: 6307: 6283: 6186: 6171: 6080: 6055: 6022: 5994: 5960: 5903: 5844: 5713: 5540: 5374: 5353: 5332: 5282: 5248: 5247: 5053: 5052: 4808: 4759: 4659: 4573: 4550: 4505: 4449: 4388: 4260: 4240: 4217: 4130: 3976: 3947: 3909: 3749: 3722: 3696: 3610: 3502: 3462: 3435: 3383: 3335: 3220: 3195: 3088: 3063: 2989: 2838: 2732: 2705: 2661: 2642: 2235:Brans–Dicke theory 2198:, James C. Swihart 2008: 1992:general relativity 1952:A word here about 1929:Belinfante–Swihart 1837:Brans–Dicke theory 1681:Christoffel symbol 1669: 1650: 1629: 1598: 1564: 1532: 1498: 1413: 1393: 1370: 1283: 1219: 1184: 1150: 1092: 1071: 1049:Lagrangian density 1002: 974: 924: 905: 882: 858: 754: 634: 520: 440: 407:General relativity 401:General relativity 387: 356: 321: 290: 245: 210: 162: 137: 36:general relativity 25026: 25025: 24997:Theory of impetus 24933: 24932: 24905:Liouville gravity 24649:Conformal gravity 24577:Composite gravity 24567:Bimetric theories 24497: 24496: 24011:Deur, A. (2014). 23414:Physics Letters B 23244:Physical Review D 23016:Physical Review D 22926:(13): 2455–2459. 22867:Physical Review D 22674:Physics Letters B 22456:Physics Letters B 22387:Physical Review D 22190:Physical Review D 22129:Physical Review D 21670:Physical Review D 21628:Physical Review D 21576:(10): 3293–3302. 21570:Physical Review D 21534:(12): 3593–3602. 21528:Physical Review D 21438:(10): 2880–2883. 21432:Physical Review D 21344:Physical Review D 21310:(12): 3209–3216. 21304:Physical Review D 21070:Annals of Physics 20934:(4753): 790–794. 20881:Annals of Physics 20809:Annals of Physics 20765:Annals of Physics 20741:10.1119/1.1934129 20330:. 3 (in French). 20078:978-0-521-19575-1 19744: 19743: 19705: 19440: 19358: 18963: 18949: 18015: 17919: 17820: 16873:{\displaystyle u} 16748:{\displaystyle T} 16556: 16522:{\displaystyle L} 16502:{\displaystyle M} 16478:{\displaystyle G} 16453: 16405:quark confinement 16227: 16212: 16141:{\displaystyle g} 16073: 16030: 15915: 15900: 15814: 15799: 15725: 15710: 15693: 15567: 15512: 15494: 15436:{\displaystyle G} 14949: 14904: 14889: 14378: 14318: 14279: 14122:Moffat's theories 14103: 14085: 13951: 13877: 13747: 13660: 13611: 13506: 13303: 13180: 13113: 13055: 12991: 12895: 12839: 12768: 12698: 12551:and vector field 12432: 12409:{\displaystyle f} 12314: 12303: 12228: 12177: 12087:Relativistic MOND 11998: 11954: 11907:and reintroduces 11741: 11714: 11514: 11483: 11404: 11373: 11287: 11256: 11180: 11164: 11112: 11083: 11029: 10876:geometric algebra 10865:bimetric theories 10733: 10646: 10344: 10291:Cartan connection 9745: 9719: 9562: 9380: 9366: 8983: 8946: 8944: 8933: 8928: 8906: 8847: 8727: 8640: 8614: 8291: 8287: 8130: 8084: 8041: 7948: 7873: 7814: 7749: 7654: 7477: 7323: 7280:{\displaystyle M} 7243: 7203: 6848: 6822: 6599: 6243: 6227: 5901: 5785: 5758: 5707: 5649: 5442: 5416: 5225: 5195: 4992: 4894: 4867: 4822:Bimetric theories 4758: 4658: 4619: 4504: 4448: 3585: 3559: 3450: 3398: 3360: 3317: 3289: 3265: 3171: 3133: 3034: 2964: 2921: 2883: 2703: 2641: 2570: 2569: 2468:Kenneth Nordtvedt 2466:Ronald Hellings, 2450:Kenneth Nordtvedt 2379:Robert V. Wagoner 2366:Kenneth Nordtvedt 2268:Paul Kustaanheimo 1888:Bimetric theories 1756:from the theory.) 1132: 917: 830: 826: 810: 727: 696: 610: 579: 52:quantized gravity 48:quantum mechanics 24:physical theories 25051: 24981: 24979:Entropic gravity 24974: 24898:extensions of GR 24886: 24872: 24865: 24858: 24851: 24844: 24837: 24830: 24823: 24809: 24726: 24719: 24712: 24673:Geometrodynamics 24662: 24638: 24619: 24612: 24561: 24554: 24510: 24509: 24401: 24400: 24383: 24376: 24369: 24360: 24359: 24349: 24330: 24329: 24297: 24291: 24290: 24255: 24249: 24248: 24213: 24207: 24206: 24164: 24143: 24137: 24136: 24134: 24102: 24096: 24095: 24093: 24075: 24066:(2): 2845–2852. 24051: 24045: 24044: 24042: 24032: 24023:(2): 1535–1551. 24008: 24002: 24001: 23995: 23987: 23969: 23949: 23943: 23942: 23936: 23928: 23926: 23908: 23884: 23878: 23877: 23851: 23831: 23825: 23824: 23798: 23778: 23769: 23768: 23766: 23754: 23748: 23747: 23745: 23733: 23727: 23726: 23700: 23680: 23671: 23670: 23644: 23624: 23613: 23612: 23586: 23566: 23549: 23548: 23543:Zee, A. (2010). 23540: 23534: 23533: 23531: 23529:astro-ph/0309474 23519: 23513: 23512: 23506: 23498: 23496: 23478: 23454: 23448: 23447: 23429: 23405: 23399: 23398: 23372: 23352: 23341: 23340: 23292: 23286: 23285: 23259: 23250:(6): 3471–3477. 23239: 23233: 23232: 23198: 23178: 23172: 23171: 23145: 23125: 23119: 23118: 23092: 23072: 23066: 23065: 23031: 23022:(6): 3168–3175. 23011: 23005: 23004: 22994: 22976: 22970: 22969: 22935: 22915: 22909: 22908: 22882: 22862: 22856: 22855: 22853: 22851: 22831: 22825: 22824: 22798: 22778: 22772: 22771: 22769: 22767: 22750: 22744: 22743: 22741: 22739: 22722: 22716: 22715: 22689: 22669: 22663: 22662: 22636: 22616: 22607: 22606: 22580: 22578:astro-ph/0412195 22560: 22551: 22550: 22524: 22504: 22498: 22497: 22471: 22462:(3–4): 447–452. 22451: 22442: 22439: 22433: 22427: 22421: 22420: 22402: 22400:astro-ph/0403694 22382: 22371: 22370: 22336: 22315: 22309: 22308: 22266: 22246: 22240: 22239: 22205: 22185: 22179: 22178: 22144: 22124: 22118: 22117: 22073: 22067: 22066: 22032: 22012: 22006: 21996: 21970: 21950: 21944: 21943: 21941: 21929: 21923: 21920: 21914: 21913: 21877: 21871: 21868: 21853: 21852: 21820: 21809: 21808: 21789: 21778: 21777: 21749: 21734: 21733: 21705: 21694: 21693: 21676:(6): 1458–1468. 21665: 21652: 21651: 21634:(6): 1685–1700. 21623: 21612: 21611: 21601: 21599:2060/19730019712 21565: 21552: 21551: 21519: 21506: 21505: 21503: 21471: 21456: 21455: 21427: 21416: 21415: 21379: 21368: 21367: 21339: 21328: 21327: 21299: 21286: 21285: 21283: 21251: 21240: 21239: 21207: 21196: 21195: 21159: 21146: 21145: 21143: 21111: 21094: 21093: 21065: 21054: 21051: 21042: 21041: 21013: 21004: 21003: 20975: 20960: 20959: 20948:10.1038/188790a0 20920: 20905: 20904: 20876: 20867: 20866: 20838: 20825: 20824: 20804: 20789: 20788: 20760: 20745: 20744: 20716: 20703: 20700: 20689: 20688: 20644: 20631: 20630: 20599: 20568: 20557: 20556: 20509: 20498: 20497: 20481: 20470: 20463: 20454: 20453: 20443: 20433: 20401: 20392: 20391: 20366:(953): 211–232. 20355: 20346: 20345: 20343: 20325: 20313: 20304: 20303: 20284: 20273: 20270: 20264: 20259: 20253: 20252: 20224: 20201: 20194: 20175: 20169: 20163: 20162: 20134: 20115: 20108: 20102: 20095: 20080: 20070: 20064: 20061: 20052: 20051: 20019: 20010: 20009: 20007: 19995: 19989: 19988: 19978: 19960: 19942: 19918: 19907: 19906: 19880: 19864: 19846: 19844: 19843: 19838: 19836: 19835: 19809:Nordtvedt effect 19802: 19800: 19799: 19794: 19772: 19770: 19769: 19764: 19762: 19761: 19717: 19715: 19714: 19709: 19706: 19698: 19687: 19685: 19684: 19679: 19635: 19633: 19632: 19627: 19608: 19606: 19605: 19600: 19584:Whitrow–Morduch 19573: 19571: 19570: 19565: 19563: 19562: 19531: 19529: 19528: 19523: 19504: 19502: 19501: 19496: 19452: 19450: 19449: 19444: 19441: 19433: 19422: 19420: 19419: 19414: 19370: 19368: 19367: 19362: 19359: 19351: 19340: 19338: 19337: 19332: 19311: 19309: 19308: 19303: 19301: 19300: 19280: 19278: 19277: 19272: 19270: 19269: 19249: 19247: 19246: 19241: 19213: 19211: 19210: 19205: 19178: 19176: 19175: 19170: 19157: 19155: 19154: 19149: 19068:Ni (stratified) 19011: 19009: 19008: 19003: 18976: 18974: 18973: 18968: 18964: 18956: 18950: 18942: 18931: 18929: 18928: 18923: 18876:Whitrow–Morduch 18817: 18815: 18814: 18809: 18807: 18806: 18789: 18787: 18786: 18781: 18779: 18778: 18758: 18756: 18755: 18750: 18748: 18747: 18727: 18725: 18724: 18719: 18717: 18716: 18707: 18702: 18701: 18661: 18659: 18658: 18653: 18651: 18650: 18633: 18631: 18630: 18625: 18623: 18622: 18605: 18603: 18602: 18597: 18584: 18582: 18581: 18576: 18563: 18561: 18560: 18555: 18553: 18552: 18543: 18538: 18537: 18517:Lee–Lightman–Ni 18492: 18490: 18489: 18484: 18482: 18481: 18464: 18462: 18461: 18456: 18454: 18453: 18433: 18431: 18430: 18425: 18412: 18410: 18409: 18404: 18371: 18369: 18368: 18363: 18361: 18360: 18311: 18309: 18308: 18303: 18295: 18294: 18285: 18280: 18279: 18225: 18223: 18222: 18217: 18215: 18214: 18165: 18163: 18162: 18157: 18155: 18154: 18137: 18135: 18134: 18129: 18127: 18126: 18106: 18104: 18103: 18098: 18085: 18083: 18082: 18077: 18027: 18025: 18024: 18019: 18016: 18014: 18003: 17992: 17952: 17950: 17949: 17944: 17931: 17929: 17928: 17923: 17920: 17918: 17907: 17896: 17853: 17851: 17850: 17845: 17832: 17830: 17829: 17824: 17821: 17819: 17808: 17797: 17741: 17739: 17738: 17733: 17731: 17730: 17713: 17711: 17710: 17705: 17703: 17702: 17685: 17683: 17682: 17677: 17675: 17674: 17657: 17655: 17654: 17649: 17647: 17646: 17629: 17627: 17626: 17621: 17619: 17618: 17601: 17599: 17598: 17593: 17591: 17590: 17573: 17571: 17570: 17565: 17563: 17562: 17545: 17543: 17542: 17537: 17524: 17522: 17521: 17516: 17503: 17501: 17500: 17495: 17480: 17479: 17399: 17397: 17396: 17391: 17389: 17388: 17376: 17375: 17363: 17362: 17350: 17349: 17337: 17336: 17318: 17316: 17315: 17310: 17308: 17307: 17295: 17294: 17282: 17281: 17263: 17261: 17260: 17255: 17241: 17239: 17238: 17233: 17219: 17217: 17216: 17211: 17197: 17195: 17194: 17189: 17184: 17183: 17171: 17170: 17158: 17157: 17145: 17144: 17132: 17131: 17119: 17118: 17106: 17105: 17041:minimal coupling 17028: 17015: 17011: 16999: 16995: 16954:Irwin I. Shapiro 16928: 16926: 16925: 16920: 16903: 16901: 16900: 16895: 16879: 16877: 16876: 16871: 16859: 16857: 16856: 16851: 16849: 16848: 16836: 16835: 16810: 16808: 16807: 16802: 16800: 16799: 16790: 16789: 16780: 16779: 16754: 16752: 16751: 16746: 16734: 16732: 16731: 16726: 16695:Self-consistency 16567: 16565: 16564: 16559: 16557: 16552: 16541: 16528: 16526: 16525: 16520: 16508: 16506: 16505: 16500: 16484: 16482: 16481: 16476: 16464: 16462: 16461: 16456: 16454: 16449: 16438: 16380:. The increased 16327:self-interaction 16296: 16294: 16293: 16288: 16264: 16262: 16261: 16256: 16254: 16250: 16228: 16220: 16213: 16205: 16200: 16199: 16194: 16147: 16145: 16144: 16139: 16124: 16122: 16121: 16116: 16114: 16113: 16108: 16104: 16103: 16102: 16093: 16092: 16074: 16066: 16061: 16060: 16051: 16050: 16041: 16040: 16031: 16023: 15990: 15988: 15987: 15982: 15977: 15973: 15954: 15953: 15940: 15939: 15929: 15928: 15916: 15908: 15901: 15899: 15895: 15894: 15881: 15876: 15872: 15853: 15852: 15839: 15838: 15828: 15827: 15815: 15807: 15800: 15792: 15787: 15783: 15764: 15763: 15750: 15749: 15739: 15738: 15726: 15718: 15711: 15709: 15708: 15696: 15694: 15686: 15680: 15679: 15661: 15660: 15641: 15639: 15638: 15633: 15628: 15627: 15618: 15617: 15605: 15604: 15595: 15594: 15582: 15581: 15568: 15565: 15559: 15555: 15539: 15538: 15526: 15525: 15513: 15505: 15495: 15487: 15481: 15480: 15462: 15461: 15442: 15440: 15439: 15434: 15422: 15420: 15419: 15414: 15412: 15411: 15395: 15393: 15392: 15387: 15363: 15361: 15360: 15355: 15350: 15349: 15333: 15331: 15330: 15325: 15323: 15322: 15310: 15309: 15297: 15296: 15284: 15283: 15239: 15237: 15236: 15231: 15228: 15227: 15199: 15197: 15196: 15191: 15189: 15188: 15176: 15175: 15163: 15162: 15150: 15149: 15137: 15136: 15108: 15106: 15105: 15100: 15097: 15096: 15087: 15086: 15077: 15076: 15064: 15063: 15041: 15040: 15025: 15024: 15002: 15000: 14999: 14994: 14991: 14987: 14986: 14985: 14973: 14972: 14960: 14959: 14950: 14942: 14937: 14936: 14921: 14920: 14905: 14897: 14890: 14882: 14876: 14875: 14860: 14859: 14837: 14835: 14834: 14829: 14826: 14825: 14813: 14812: 14797: 14796: 14784: 14783: 14758: 14756: 14755: 14750: 14747: 14746: 14730: 14728: 14727: 14722: 14719: 14718: 14696: 14694: 14693: 14688: 14665: 14663: 14662: 14657: 14653: 14645: 14618: 14617: 14601: 14599: 14598: 14593: 14590: 14589: 14573: 14571: 14570: 14565: 14562: 14561: 14542: 14540: 14539: 14534: 14531: 14530: 14505: 14503: 14502: 14497: 14494: 14493: 14477: 14475: 14474: 14469: 14456: 14454: 14453: 14448: 14423: 14421: 14420: 14415: 14412: 14411: 14402: 14401: 14392: 14391: 14379: 14371: 14366: 14362: 14361: 14360: 14342: 14341: 14329: 14328: 14319: 14311: 14280: 14272: 14267: 14266: 14247: 14245: 14244: 14239: 14236: 14235: 14216: 14214: 14213: 14208: 14205: 14204: 14192: 14191: 14166: 14164: 14163: 14158: 14155: 14154: 14117: 14115: 14114: 14109: 14104: 14102: 14091: 14086: 14084: 14070: 14065: 14064: 14042: 14040: 14039: 14034: 14026: 14025: 13972: 13970: 13969: 13964: 13962: 13952: 13950: 13949: 13948: 13926: 13925: 13924: 13923: 13922: 13883: 13878: 13876: 13865: 13857: 13848: 13847: 13828: 13824: 13817: 13816: 13815: 13814: 13794: 13793: 13792: 13791: 13748: 13743: 13735: 13726: 13725: 13700: 13698: 13697: 13692: 13671: 13669: 13668: 13663: 13661: 13659: 13648: 13647: 13646: 13625: 13624: 13614: 13612: 13604: 13577: 13573: 13571: 13570: 13565: 13563: 13562: 13531: 13527: 13525: 13524: 13519: 13517: 13516: 13508: 13507: 13499: 13488: 13484: 13482: 13481: 13476: 13464: 13462: 13461: 13456: 13454: 13453: 13425: 13423: 13422: 13417: 13397: 13395: 13394: 13389: 13369: 13368: 13359: 13358: 13343: 13342: 13330: 13329: 13314: 13313: 13305: 13304: 13296: 13284: 13282: 13281: 13276: 13274: 13273: 13264: 13263: 13251: 13250: 13235: 13234: 13209: 13207: 13206: 13201: 13199: 13192: 13191: 13181: 13173: 13171: 13167: 13159: 13154: 13150: 13137: 13136: 13124: 13123: 13115: 13114: 13106: 13084: 13083: 13067: 13066: 13056: 13048: 13046: 13042: 13041: 13037: 13030: 13029: 13020: 13019: 13010: 13009: 12992: 12987: 12979: 12974: 12973: 12952: 12951: 12930: 12929: 12917: 12916: 12896: 12894: 12880: 12868: 12867: 12851: 12850: 12840: 12832: 12830: 12826: 12822: 12821: 12800: 12799: 12789: 12781: 12769: 12761: 12756: 12755: 12743: 12742: 12730: 12729: 12717: 12716: 12699: 12691: 12679: 12678: 12652: 12650: 12649: 12644: 12642: 12641: 12629: 12628: 12616: 12615: 12603: 12602: 12577: 12575: 12574: 12569: 12567: 12566: 12550: 12548: 12547: 12542: 12529: 12527: 12526: 12521: 12500: 12498: 12497: 12492: 12489: 12488: 12479: 12474: 12473: 12461: 12460: 12444: 12442: 12441: 12436: 12434: 12433: 12425: 12415: 12413: 12412: 12407: 12392: 12390: 12389: 12384: 12382: 12378: 12374: 12373: 12360: 12359: 12349: 12348: 12335: 12330: 12316: 12315: 12307: 12304: 12302: 12290: 12285: 12276: 12252: 12250: 12249: 12244: 12233: 12229: 12226: 12221: 12212: 12211: 12210: 12205: 12193: 12187: 12178: 12176: 12164: 12159: 12150: 12074: 12072: 12071: 12066: 12064: 12060: 12059: 12058: 12042: 12037: 12021: 12016: 11999: 11997: 11996: 11987: 11976: 11971: 11970: 11955: 11947: 11942: 11941: 11876:Farnes' theories 11868: 11866: 11865: 11860: 11857: 11856: 11844: 11843: 11834: 11833: 11810: 11808: 11807: 11802: 11777: 11775: 11774: 11769: 11766: 11765: 11753: 11752: 11742: 11734: 11728: 11727: 11715: 11713: 11699: 11681: 11679: 11678: 11673: 11670: 11669: 11653: 11651: 11650: 11645: 11623: 11621: 11620: 11615: 11602: 11600: 11599: 11594: 11566: 11564: 11563: 11558: 11555: 11551: 11547: 11546: 11528: 11527: 11515: 11507: 11502: 11501: 11484: 11482: 11468: 11463: 11462: 11437: 11435: 11434: 11429: 11426: 11422: 11418: 11417: 11405: 11397: 11392: 11391: 11374: 11372: 11358: 11353: 11352: 11327: 11325: 11324: 11319: 11316: 11315: 11299: 11298: 11288: 11280: 11257: 11255: 11241: 11220: 11218: 11217: 11212: 11209: 11208: 11192: 11191: 11181: 11173: 11165: 11163: 11149: 11128: 11126: 11125: 11120: 11110: 11097: 11096: 11084: 11076: 11068: 11067: 11045: 11043: 11042: 11037: 11027: 11011: 11010: 10988: 10986: 10985: 10980: 10961: 10959: 10958: 10953: 10856: 10854: 10853: 10848: 10844: 10839: 10826: 10821: 10812: 10811: 10795: 10790: 10781: 10780: 10764: 10759: 10750: 10749: 10734: 10732: 10718: 10713: 10712: 10689: 10687: 10686: 10681: 10678: 10677: 10658: 10656: 10655: 10650: 10647: 10639: 10634: 10633: 10613: 10611: 10610: 10605: 10602: 10601: 10576: 10574: 10573: 10568: 10564: 10559: 10540: 10538: 10537: 10532: 10530: 10526: 10525: 10515: 10510: 10491: 10490: 10473: 10468: 10455: 10450: 10430: 10425: 10412: 10411: 10393: 10392: 10383: 10382: 10373: 10372: 10359: 10354: 10345: 10343: 10329: 10264: 10262: 10261: 10256: 10217: 10215: 10214: 10209: 10153: 10151: 10150: 10145: 10095: 10093: 10092: 10087: 10082: 10081: 10065: 10063: 10062: 10057: 10055: 10054: 10035: 10033: 10032: 10027: 10022: 10021: 10003: 10002: 9984: 9983: 9961: 9959: 9958: 9953: 9920: 9918: 9917: 9912: 9910: 9909: 9897: 9893: 9892: 9891: 9876: 9875: 9854: 9853: 9841: 9840: 9822: 9821: 9809: 9808: 9799: 9798: 9780: 9779: 9770: 9769: 9746: 9738: 9733: 9732: 9720: 9718: 9704: 9686: 9684: 9683: 9678: 9673: 9672: 9633: 9631: 9630: 9625: 9606: 9604: 9603: 9598: 9573: 9571: 9570: 9565: 9563: 9561: 9547: 9533: 9503: 9501: 9500: 9495: 9490: 9489: 9381: 9373: 9367: 9359: 9328: 9326: 9325: 9320: 9307: 9305: 9304: 9299: 9296: 9295: 9234: 9232: 9231: 9226: 9213: 9211: 9210: 9205: 9189: 9187: 9186: 9181: 9161: 9159: 9158: 9153: 9139: 9137: 9136: 9131: 9106: 9104: 9103: 9098: 9085: 9083: 9082: 9077: 9074: 9073: 9057: 9055: 9054: 9049: 9027: 9025: 9024: 9019: 8994: 8992: 8991: 8986: 8984: 8982: 8981: 8980: 8964: 8963: 8962: 8949: 8947: 8945: 8940: 8935: 8931: 8930: 8929: 8927: 8926: 8914: 8909: 8904: 8903: 8902: 8880: 8878: 8877: 8872: 8869: 8868: 8859: 8858: 8848: 8843: 8837: 8836: 8821: 8820: 8801: 8799: 8798: 8793: 8766: 8765: 8752: 8751: 8741: 8740: 8728: 8723: 8709: 8695: 8694: 8675: 8673: 8672: 8667: 8664: 8663: 8651: 8650: 8641: 8633: 8628: 8627: 8615: 8613: 8599: 8581: 8579: 8578: 8573: 8570: 8569: 8553: 8551: 8550: 8545: 8478: 8476: 8475: 8470: 8459: 8458: 8446: 8445: 8439: 8438: 8426: 8422: 8421: 8420: 8408: 8407: 8389: 8388: 8370: 8369: 8348: 8347: 8333: 8332: 8317: 8316: 8304: 8303: 8289: 8288: 8280: 8275: 8274: 8246: 8244: 8243: 8238: 8235: 8227: 8211: 8209: 8208: 8203: 8201: 8200: 8184: 8182: 8181: 8176: 8174: 8173: 8154: 8152: 8151: 8146: 8135: 8131: 8128: 8123: 8111: 8105: 8104: 8089: 8085: 8082: 8077: 8065: 8059: 8058: 8046: 8042: 8039: 8034: 8022: 8016: 8015: 7990: 7988: 7987: 7982: 7977: 7973: 7972: 7971: 7953: 7949: 7946: 7941: 7929: 7923: 7922: 7913: 7912: 7891: 7890: 7878: 7874: 7871: 7866: 7854: 7848: 7847: 7838: 7837: 7819: 7815: 7812: 7807: 7795: 7789: 7788: 7769: 7764: 7750: 7742: 7737: 7736: 7709: 7707: 7706: 7701: 7677: 7675: 7674: 7669: 7655: 7647: 7642: 7641: 7617: 7615: 7614: 7609: 7604: 7600: 7599: 7598: 7580: 7579: 7561: 7560: 7548: 7547: 7535: 7534: 7522: 7521: 7509: 7508: 7499: 7498: 7478: 7470: 7465: 7464: 7436: 7434: 7433: 7428: 7423: 7419: 7418: 7417: 7399: 7398: 7377: 7376: 7364: 7363: 7345: 7344: 7324: 7316: 7311: 7310: 7286: 7284: 7283: 7278: 7259: 7257: 7256: 7251: 7249: 7245: 7244: 7242: 7241: 7240: 7227: 7226: 7217: 7204: 7196: 7191: 7190: 7117: 7115: 7114: 7109: 7106: 7105: 7084:Bianchi identity 7078: 7076: 7075: 7070: 7067: 7066: 7054: 7050: 7049: 7048: 7044: 7028: 7027: 7023: 7003: 6999: 6990: 6980: 6975: 6971: 6954: 6949: 6945: 6931: 6923: 6919: 6902: 6898: 6892: 6879: 6871: 6867: 6849: 6841: 6836: 6835: 6823: 6821: 6807: 6786: 6784: 6783: 6778: 6775: 6774: 6759: 6758: 6743: 6742: 6720: 6718: 6717: 6712: 6709: 6708: 6682: 6680: 6679: 6674: 6672: 6668: 6667: 6654: 6653: 6640: 6639: 6620: 6619: 6600: 6598: 6590: 6589: 6588: 6575: 6567: 6566: 6550: 6549: 6540: 6539: 6527: 6526: 6517: 6516: 6497: 6496: 6474: 6473: 6464: 6463: 6451: 6450: 6441: 6440: 6424: 6423: 6414: 6413: 6398: 6397: 6381: 6380: 6371: 6370: 6344: 6342: 6341: 6336: 6333: 6332: 6316: 6314: 6313: 6308: 6292: 6290: 6289: 6284: 6282: 6281: 6276: 6272: 6271: 6270: 6257: 6256: 6244: 6236: 6228: 6226: 6225: 6224: 6215: 6214: 6201: 6199: 6194: 6184: 6179: 6169: 6167: 6166: 6165: 6164: 6144: 6143: 6125: 6124: 6112: 6111: 6089: 6087: 6086: 6081: 6064: 6062: 6061: 6056: 6031: 6029: 6028: 6023: 6020: 6019: 6003: 6001: 6000: 5995: 5992: 5991: 5969: 5967: 5966: 5961: 5958: 5957: 5948: 5947: 5938: 5937: 5912: 5910: 5909: 5904: 5902: 5900: 5886: 5853: 5851: 5850: 5845: 5843: 5842: 5830: 5829: 5814: 5813: 5786: 5778: 5772: 5771: 5759: 5757: 5743: 5722: 5720: 5719: 5714: 5712: 5708: 5706: 5702: 5701: 5688: 5687: 5686: 5670: 5664: 5663: 5650: 5645: 5637: 5617: 5616: 5607: 5606: 5588: 5587: 5575: 5574: 5549: 5547: 5546: 5541: 5539: 5538: 5523: 5522: 5510: 5509: 5491: 5490: 5486: 5470: 5469: 5465: 5443: 5435: 5430: 5429: 5417: 5415: 5401: 5383: 5381: 5380: 5375: 5362: 5360: 5359: 5354: 5341: 5339: 5338: 5333: 5330: 5329: 5317: 5316: 5291: 5289: 5288: 5283: 5280: 5279: 5257: 5255: 5254: 5249: 5239: 5238: 5226: 5218: 5212: 5211: 5196: 5191: 5183: 5166: 5165: 5161: 5145: 5144: 5140: 5124: 5123: 5111: 5110: 5095: 5094: 5082: 5081: 5062: 5060: 5059: 5054: 5051: 5050: 5035: 5034: 5030: 5014: 5013: 5009: 4993: 4985: 4979: 4978: 4974: 4958: 4957: 4953: 4934: 4933: 4921: 4920: 4908: 4907: 4895: 4887: 4881: 4880: 4868: 4866: 4852: 4817: 4815: 4814: 4809: 4806: 4802: 4798: 4797: 4784: 4783: 4773: 4772: 4760: 4751: 4742: 4741: 4728: 4727: 4717: 4716: 4698: 4697: 4684: 4683: 4673: 4672: 4660: 4651: 4640: 4639: 4620: 4612: 4602: 4601: 4582: 4580: 4579: 4574: 4559: 4557: 4556: 4551: 4549: 4545: 4541: 4540: 4527: 4526: 4516: 4515: 4506: 4497: 4488: 4487: 4474: 4473: 4463: 4462: 4450: 4441: 4433: 4432: 4420: 4419: 4397: 4395: 4394: 4389: 4387: 4383: 4382: 4381: 4366: 4365: 4350: 4349: 4332: 4331: 4319: 4318: 4305: 4304: 4292: 4291: 4269: 4267: 4266: 4261: 4249: 4247: 4246: 4241: 4226: 4224: 4223: 4218: 4204: 4203: 4182: 4181: 4172: 4171: 4162: 4161: 4139: 4137: 4136: 4131: 4129: 4125: 4124: 4123: 4108: 4107: 4092: 4091: 4074: 4073: 4049: 4048: 4036: 4035: 4008: 4007: 3985: 3983: 3982: 3977: 3956: 3954: 3953: 3948: 3924: 3918: 3916: 3915: 3910: 3908: 3904: 3900: 3899: 3886: 3885: 3875: 3871: 3870: 3869: 3851: 3850: 3830: 3829: 3814: 3813: 3796: 3795: 3758: 3756: 3755: 3750: 3748: 3747: 3731: 3729: 3728: 3723: 3705: 3703: 3702: 3697: 3692: 3691: 3678: 3677: 3667: 3666: 3639: 3638: 3619: 3617: 3616: 3611: 3609: 3608: 3596: 3595: 3586: 3578: 3573: 3572: 3560: 3558: 3544: 3511: 3509: 3508: 3503: 3498: 3471: 3469: 3468: 3463: 3461: 3460: 3455: 3451: 3448: 3443: 3431: 3403: 3399: 3396: 3391: 3379: 3361: 3359: 3358: 3348: 3343: 3334: 3328: 3327: 3322: 3318: 3316: 3315: 3303: 3290: 3288: 3287: 3275: 3270: 3266: 3264: 3263: 3251: 3229: 3227: 3226: 3221: 3208: 3203: 3191: 3190: 3177: 3173: 3172: 3170: 3169: 3157: 3138: 3134: 3132: 3131: 3119: 3097: 3095: 3094: 3089: 3076: 3071: 3059: 3058: 3039: 3035: 3033: 3032: 3020: 2998: 2996: 2995: 2990: 2987: 2986: 2970: 2966: 2965: 2960: 2959: 2958: 2949: 2948: 2939: 2927: 2922: 2920: 2919: 2907: 2888: 2884: 2882: 2881: 2869: 2847: 2845: 2844: 2839: 2837: 2836: 2814: 2813: 2804: 2778: 2777: 2768: 2741: 2739: 2738: 2733: 2721: 2714: 2712: 2711: 2706: 2704: 2699: 2691: 2670: 2668: 2667: 2662: 2647: 2643: 2640: 2639: 2627: 2528:Jacob Bekenstein 2276: 2011: 2007: 1954:Mach's principle 1833:Bergmann–Wagoner 1685:energy condition 1678: 1676: 1675: 1670: 1666: 1661: 1638: 1636: 1635: 1630: 1628: 1627: 1607: 1605: 1604: 1599: 1596: 1595: 1573: 1571: 1570: 1565: 1562: 1561: 1548: 1543: 1528: 1527: 1514: 1509: 1494: 1493: 1485: 1484: 1483: 1466: 1465: 1453: 1452: 1422: 1420: 1419: 1414: 1402: 1400: 1399: 1394: 1379: 1377: 1376: 1371: 1368: 1367: 1354: 1353: 1340: 1339: 1321: 1320: 1315: 1292: 1290: 1289: 1284: 1281: 1280: 1238:scalar curvature 1228: 1226: 1225: 1220: 1193: 1191: 1190: 1185: 1159: 1157: 1156: 1151: 1146: 1145: 1140: 1133: 1125: 1101: 1099: 1098: 1093: 1080: 1078: 1077: 1072: 1011: 1009: 1008: 1003: 1000: 999: 983: 981: 980: 975: 969: 968: 933: 931: 930: 925: 921: 915: 913: 891: 889: 888: 883: 867: 865: 864: 859: 856: 855: 840: 839: 828: 827: 819: 811: 809: 798: 797: 788: 763: 761: 760: 755: 749: 745: 741: 740: 728: 720: 715: 714: 697: 695: 684: 683: 674: 669: 668: 643: 641: 640: 635: 632: 628: 624: 623: 611: 603: 598: 597: 580: 578: 577: 568: 557: 552: 551: 529: 527: 526: 521: 518: 517: 504: 503: 490: 489: 474: 473: 468: 449: 447: 446: 441: 396: 394: 393: 388: 385: 384: 365: 363: 362: 357: 351: 350: 330: 328: 327: 322: 319: 318: 299: 297: 296: 291: 285: 284: 254: 252: 251: 246: 243: 242: 222:Minkowski metric 219: 217: 216: 211: 208: 207: 180:" are not used. 171: 169: 168: 163: 146: 144: 143: 138: 25059: 25058: 25054: 25053: 25052: 25050: 25049: 25048: 25029: 25028: 25027: 25022: 25001: 24977: 24970: 24941: 24939: 24929: 24910:Lovelock theory 24897: 24891: 24882: 24868: 24861: 24854: 24847: 24840: 24833: 24826: 24819: 24805: 24783: 24777: 24756: 24722: 24715: 24708: 24687: 24678:Induced gravity 24658: 24654:Scalar theories 24634: 24615: 24608: 24599:Massive gravity 24559:Teleparallelism 24557: 24552:Einstein–Cartan 24550: 24534: 24525:Quantum gravity 24504: 24503:Alternatives to 24493: 24459:Exact solutions 24430: 24392: 24387: 24357: 24347: 24338: 24333: 24312:(10): 321–328. 24298: 24294: 24256: 24252: 24214: 24210: 24144: 24140: 24103: 24099: 24052: 24048: 24009: 24005: 23989: 23988: 23954:Physica Scripta 23950: 23946: 23930: 23929: 23885: 23881: 23832: 23828: 23779: 23772: 23755: 23751: 23734: 23730: 23685:Eur. Phys. J. C 23681: 23674: 23629:Eur. Phys. J. C 23625: 23616: 23567: 23552: 23541: 23537: 23520: 23516: 23500: 23499: 23455: 23451: 23406: 23402: 23357:Eur. Phys. J. C 23353: 23344: 23293: 23289: 23240: 23236: 23179: 23175: 23126: 23122: 23073: 23069: 23012: 23008: 22977: 22973: 22916: 22912: 22863: 22859: 22849: 22847: 22832: 22828: 22779: 22775: 22765: 22763: 22751: 22747: 22737: 22735: 22724: 22723: 22719: 22670: 22666: 22617: 22610: 22561: 22554: 22505: 22501: 22452: 22445: 22440: 22436: 22428: 22424: 22383: 22374: 22316: 22312: 22247: 22243: 22186: 22182: 22125: 22121: 22074: 22070: 22013: 22009: 21951: 21947: 21930: 21926: 21921: 21917: 21878: 21874: 21869: 21856: 21821: 21812: 21790: 21781: 21774:10.1139/p79-133 21750: 21737: 21706: 21697: 21666: 21655: 21624: 21615: 21566: 21555: 21520: 21509: 21472: 21459: 21428: 21419: 21380: 21371: 21340: 21331: 21300: 21289: 21252: 21243: 21208: 21199: 21160: 21149: 21112: 21097: 21066: 21057: 21052: 21045: 21018:Physics Letters 21014: 21007: 20976: 20963: 20921: 20908: 20877: 20870: 20843:Physical Review 20839: 20828: 20805: 20792: 20761: 20748: 20717: 20706: 20701: 20692: 20645: 20634: 20569: 20560: 20510: 20501: 20482: 20473: 20464: 20457: 20402: 20395: 20356: 20349: 20323: 20314: 20307: 20285: 20276: 20271: 20267: 20260: 20256: 20225: 20204: 20195: 20178: 20170: 20166: 20139:Physical Review 20135: 20118: 20109: 20105: 20096: 20083: 20071: 20067: 20062: 20055: 20020: 20013: 19996: 19992: 19919: 19910: 19869:Physics Reports 19865: 19858: 19854: 19831: 19827: 19825: 19822: 19821: 19817: 19782: 19779: 19778: 19757: 19753: 19751: 19748: 19747: 19697: 19694: 19691: 19690: 19670: 19667: 19666: 19615: 19612: 19611: 19591: 19588: 19587: 19558: 19554: 19552: 19549: 19548: 19511: 19508: 19507: 19487: 19484: 19483: 19432: 19429: 19426: 19425: 19405: 19402: 19401: 19350: 19347: 19344: 19343: 19323: 19320: 19319: 19296: 19292: 19290: 19287: 19286: 19265: 19261: 19259: 19256: 19255: 19223: 19220: 19219: 19187: 19184: 19183: 19164: 19161: 19160: 19143: 19140: 19139: 18985: 18982: 18981: 18955: 18941: 18938: 18935: 18934: 18917: 18914: 18913: 18802: 18798: 18796: 18793: 18792: 18774: 18770: 18768: 18765: 18764: 18743: 18739: 18734: 18731: 18730: 18712: 18708: 18703: 18697: 18693: 18688: 18685: 18684: 18646: 18642: 18640: 18637: 18636: 18618: 18614: 18612: 18609: 18608: 18591: 18588: 18587: 18570: 18567: 18566: 18548: 18544: 18539: 18533: 18529: 18524: 18521: 18520: 18477: 18473: 18471: 18468: 18467: 18449: 18445: 18443: 18440: 18439: 18419: 18416: 18415: 18398: 18395: 18394: 18356: 18352: 18350: 18347: 18346: 18290: 18286: 18281: 18275: 18271: 18269: 18266: 18265: 18210: 18206: 18204: 18201: 18200: 18185:Will–Nordtvedt 18150: 18146: 18144: 18141: 18140: 18122: 18118: 18116: 18113: 18112: 18092: 18089: 18088: 18071: 18068: 18067: 18004: 17993: 17991: 17988: 17985: 17984: 17938: 17935: 17934: 17908: 17897: 17895: 17892: 17889: 17888: 17839: 17836: 17835: 17809: 17798: 17796: 17793: 17790: 17789: 17726: 17722: 17720: 17717: 17716: 17698: 17694: 17692: 17689: 17688: 17670: 17666: 17664: 17661: 17660: 17642: 17638: 17636: 17633: 17632: 17614: 17610: 17608: 17605: 17604: 17586: 17582: 17580: 17577: 17576: 17558: 17554: 17552: 17549: 17548: 17531: 17528: 17527: 17510: 17507: 17506: 17489: 17486: 17485: 17468: 17463: 17426: 17413: 17407: 17384: 17380: 17371: 17367: 17358: 17354: 17345: 17341: 17332: 17328: 17326: 17323: 17322: 17303: 17299: 17290: 17286: 17277: 17273: 17271: 17268: 17267: 17249: 17246: 17245: 17227: 17224: 17223: 17205: 17202: 17201: 17179: 17175: 17166: 17162: 17153: 17149: 17140: 17136: 17127: 17123: 17114: 17110: 17101: 17097: 17077: 17074: 17073: 17072:These ten are: 17059: 17053: 17026: 17013: 17009: 16997: 16993: 16981: 16975: 16966: 16942: 16936: 16934:Classical tests 16913: 16910: 16909: 16906:Kronecker delta 16889: 16886: 16885: 16865: 16862: 16861: 16841: 16837: 16828: 16824: 16816: 16813: 16812: 16795: 16791: 16785: 16781: 16772: 16768: 16760: 16757: 16756: 16740: 16737: 16736: 16720: 16717: 16716: 16709: 16697: 16688: 16682: 16624:galaxy clusters 16574: 16548: 16540: 16538: 16535: 16534: 16514: 16511: 16510: 16494: 16491: 16490: 16470: 16467: 16466: 16445: 16437: 16435: 16432: 16431: 16367:energy-momentum 16311: 16273: 16270: 16269: 16219: 16218: 16214: 16204: 16195: 16190: 16189: 16178: 16175: 16174: 16160: 16154: 16133: 16130: 16129: 16109: 16098: 16094: 16088: 16084: 16083: 16079: 16078: 16065: 16056: 16052: 16046: 16042: 16036: 16032: 16022: 16002: 15999: 15998: 15949: 15945: 15935: 15931: 15921: 15917: 15907: 15906: 15902: 15890: 15886: 15885: 15880: 15848: 15844: 15834: 15830: 15820: 15816: 15806: 15805: 15801: 15791: 15759: 15755: 15745: 15741: 15731: 15727: 15717: 15716: 15712: 15704: 15700: 15695: 15685: 15675: 15671: 15656: 15652: 15650: 15647: 15646: 15623: 15619: 15613: 15609: 15600: 15596: 15590: 15586: 15574: 15570: 15564: 15531: 15527: 15518: 15514: 15504: 15503: 15499: 15486: 15476: 15472: 15457: 15453: 15451: 15448: 15447: 15428: 15425: 15424: 15407: 15403: 15401: 15398: 15397: 15369: 15366: 15365: 15345: 15341: 15339: 15336: 15335: 15318: 15314: 15305: 15301: 15292: 15288: 15279: 15275: 15267: 15264: 15263: 15256: 15250: 15214: 15210: 15208: 15205: 15204: 15181: 15177: 15171: 15167: 15155: 15151: 15145: 15141: 15126: 15122: 15120: 15117: 15116: 15092: 15088: 15082: 15078: 15069: 15065: 15050: 15046: 15036: 15032: 15017: 15013: 15011: 15008: 15007: 14978: 14974: 14965: 14961: 14955: 14951: 14941: 14926: 14922: 14910: 14906: 14896: 14895: 14891: 14881: 14871: 14867: 14855: 14851: 14849: 14846: 14845: 14821: 14817: 14805: 14801: 14792: 14788: 14779: 14775: 14767: 14764: 14763: 14742: 14738: 14736: 14733: 14732: 14711: 14707: 14705: 14702: 14701: 14681: 14678: 14677: 14646: 14632: 14613: 14609: 14607: 14604: 14603: 14585: 14581: 14579: 14576: 14575: 14554: 14550: 14548: 14545: 14544: 14517: 14513: 14511: 14508: 14507: 14489: 14485: 14483: 14480: 14479: 14462: 14459: 14458: 14432: 14429: 14428: 14407: 14403: 14397: 14393: 14384: 14380: 14370: 14347: 14343: 14334: 14330: 14324: 14320: 14310: 14285: 14281: 14271: 14262: 14258: 14256: 14253: 14252: 14231: 14227: 14225: 14222: 14221: 14200: 14196: 14187: 14183: 14175: 14172: 14171: 14147: 14143: 14141: 14138: 14137: 14124: 14095: 14090: 14074: 14069: 14057: 14053: 14051: 14048: 14047: 13997: 13993: 13985: 13982: 13981: 13978:geometric units 13960: 13959: 13944: 13940: 13927: 13918: 13914: 13910: 13906: 13884: 13882: 13866: 13858: 13856: 13849: 13843: 13839: 13836: 13835: 13810: 13806: 13802: 13798: 13787: 13783: 13776: 13772: 13753: 13749: 13736: 13734: 13727: 13721: 13717: 13713: 13711: 13708: 13707: 13680: 13677: 13676: 13649: 13642: 13638: 13620: 13616: 13615: 13613: 13603: 13586: 13583: 13582: 13575: 13543: 13539: 13537: 13534: 13533: 13529: 13509: 13498: 13497: 13496: 13494: 13491: 13490: 13486: 13470: 13467: 13466: 13437: 13433: 13431: 13428: 13427: 13405: 13402: 13401: 13364: 13360: 13354: 13350: 13335: 13331: 13322: 13318: 13306: 13295: 13294: 13293: 13291: 13288: 13287: 13269: 13265: 13259: 13255: 13243: 13239: 13227: 13223: 13221: 13218: 13217: 13197: 13196: 13187: 13183: 13172: 13155: 13146: 13145: 13132: 13128: 13116: 13105: 13104: 13103: 13102: 13098: 13085: 13079: 13075: 13072: 13071: 13062: 13058: 13047: 13025: 13021: 13015: 13011: 13002: 12998: 12997: 12993: 12980: 12978: 12957: 12953: 12935: 12931: 12922: 12918: 12909: 12905: 12904: 12900: 12884: 12879: 12869: 12863: 12859: 12856: 12855: 12846: 12842: 12831: 12817: 12813: 12795: 12791: 12782: 12777: 12760: 12748: 12744: 12735: 12731: 12722: 12718: 12712: 12708: 12707: 12703: 12690: 12680: 12674: 12670: 12666: 12664: 12661: 12660: 12637: 12633: 12624: 12620: 12611: 12607: 12598: 12594: 12586: 12583: 12582: 12562: 12558: 12556: 12553: 12552: 12535: 12532: 12531: 12515: 12512: 12511: 12504:preferred frame 12484: 12480: 12475: 12469: 12465: 12456: 12452: 12450: 12447: 12446: 12424: 12423: 12421: 12418: 12417: 12401: 12398: 12397: 12369: 12365: 12355: 12351: 12341: 12337: 12331: 12326: 12321: 12317: 12306: 12305: 12292: 12286: 12281: 12275: 12264: 12261: 12260: 12222: 12217: 12206: 12201: 12200: 12189: 12188: 12186: 12182: 12166: 12160: 12155: 12149: 12138: 12135: 12134: 12103: 12091:Main articles: 12089: 12051: 12047: 12038: 12030: 12017: 12009: 12004: 12000: 11992: 11988: 11977: 11975: 11963: 11959: 11946: 11934: 11930: 11928: 11925: 11924: 11913:matter creation 11894:Albert Einstein 11878: 11849: 11845: 11839: 11835: 11829: 11825: 11823: 11820: 11819: 11786: 11783: 11782: 11761: 11757: 11748: 11744: 11733: 11723: 11719: 11703: 11698: 11690: 11687: 11686: 11665: 11661: 11659: 11656: 11655: 11629: 11626: 11625: 11608: 11605: 11604: 11578: 11575: 11574: 11539: 11535: 11520: 11516: 11506: 11494: 11490: 11489: 11485: 11472: 11467: 11455: 11451: 11449: 11446: 11445: 11410: 11406: 11396: 11384: 11380: 11379: 11375: 11362: 11357: 11345: 11341: 11339: 11336: 11335: 11311: 11307: 11294: 11290: 11279: 11245: 11240: 11232: 11229: 11228: 11204: 11200: 11187: 11183: 11172: 11153: 11148: 11140: 11137: 11136: 11092: 11088: 11075: 11063: 11059: 11057: 11054: 11053: 11006: 11002: 11000: 10997: 10996: 10967: 10964: 10963: 10946: 10943: 10942: 10939: 10925: 10917:Pioneer anomaly 10901:horizon problem 10893: 10884: 10840: 10835: 10822: 10817: 10804: 10800: 10791: 10786: 10773: 10769: 10760: 10755: 10742: 10738: 10722: 10717: 10705: 10701: 10699: 10696: 10695: 10670: 10666: 10664: 10661: 10660: 10638: 10629: 10625: 10623: 10620: 10619: 10588: 10584: 10582: 10579: 10578: 10560: 10555: 10549: 10546: 10545: 10528: 10527: 10521: 10517: 10511: 10506: 10492: 10486: 10482: 10476: 10475: 10469: 10464: 10451: 10446: 10432: 10426: 10421: 10414: 10413: 10398: 10394: 10388: 10384: 10378: 10374: 10365: 10361: 10355: 10350: 10333: 10328: 10321: 10314: 10312: 10309: 10308: 10293: 10283: 10271: 10226: 10223: 10222: 10165: 10162: 10161: 10108: 10105: 10104: 10077: 10073: 10071: 10068: 10067: 10047: 10043: 10041: 10038: 10037: 10011: 10007: 9992: 9988: 9976: 9972: 9970: 9967: 9966: 9929: 9926: 9925: 9905: 9901: 9881: 9877: 9865: 9861: 9846: 9842: 9833: 9829: 9814: 9810: 9804: 9800: 9794: 9790: 9775: 9771: 9765: 9761: 9751: 9747: 9737: 9728: 9724: 9708: 9703: 9695: 9692: 9691: 9668: 9664: 9662: 9659: 9658: 9651: 9612: 9609: 9608: 9582: 9579: 9578: 9548: 9534: 9532: 9515: 9512: 9511: 9482: 9478: 9372: 9358: 9337: 9334: 9333: 9313: 9310: 9309: 9288: 9284: 9240: 9237: 9236: 9219: 9216: 9215: 9198: 9195: 9194: 9174: 9171: 9170: 9147: 9144: 9143: 9118: 9115: 9114: 9091: 9088: 9087: 9069: 9065: 9063: 9060: 9059: 9033: 9030: 9029: 9003: 9000: 8999: 8973: 8969: 8965: 8958: 8954: 8950: 8948: 8939: 8934: 8916: 8915: 8910: 8908: 8907: 8895: 8891: 8889: 8886: 8885: 8864: 8860: 8854: 8850: 8842: 8832: 8828: 8816: 8812: 8810: 8807: 8806: 8761: 8757: 8747: 8743: 8733: 8729: 8710: 8708: 8690: 8686: 8684: 8681: 8680: 8659: 8655: 8646: 8642: 8632: 8623: 8619: 8603: 8598: 8590: 8587: 8586: 8565: 8561: 8559: 8556: 8555: 8538: 8535: 8534: 8514: 8488: 8454: 8450: 8441: 8440: 8434: 8430: 8413: 8409: 8400: 8396: 8375: 8371: 8356: 8352: 8343: 8339: 8338: 8334: 8328: 8324: 8312: 8308: 8299: 8295: 8279: 8270: 8269: 8267: 8264: 8263: 8257: 8228: 8223: 8217: 8214: 8213: 8196: 8192: 8190: 8187: 8186: 8169: 8165: 8163: 8160: 8159: 8124: 8119: 8110: 8106: 8100: 8096: 8078: 8073: 8064: 8060: 8054: 8050: 8035: 8030: 8021: 8017: 8011: 8007: 8002: 7999: 7998: 7958: 7954: 7942: 7937: 7928: 7924: 7918: 7914: 7899: 7895: 7883: 7879: 7867: 7862: 7853: 7849: 7843: 7839: 7830: 7826: 7808: 7803: 7794: 7790: 7784: 7780: 7765: 7760: 7755: 7751: 7741: 7732: 7731: 7729: 7726: 7725: 7716: 7686: 7683: 7682: 7646: 7637: 7636: 7634: 7631: 7630: 7624: 7585: 7581: 7566: 7562: 7556: 7552: 7540: 7536: 7527: 7523: 7517: 7513: 7504: 7500: 7494: 7490: 7483: 7479: 7469: 7460: 7459: 7457: 7454: 7453: 7447: 7404: 7400: 7385: 7381: 7369: 7365: 7356: 7352: 7340: 7336: 7329: 7325: 7315: 7306: 7305: 7303: 7300: 7299: 7293: 7287:is a constant. 7272: 7269: 7268: 7236: 7232: 7228: 7222: 7218: 7216: 7209: 7205: 7195: 7186: 7185: 7183: 7180: 7179: 7169: 7163: 7139: 7137:Tensor theories 7098: 7094: 7092: 7089: 7088: 7062: 7058: 7040: 7033: 7029: 7019: 7012: 7008: 6995: 6991: 6986: 6976: 6967: 6963: 6950: 6941: 6937: 6924: 6915: 6914: 6894: 6893: 6885: 6872: 6863: 6862: 6854: 6850: 6840: 6831: 6827: 6811: 6806: 6798: 6795: 6794: 6790:The action is: 6767: 6763: 6751: 6747: 6735: 6731: 6729: 6726: 6725: 6701: 6697: 6695: 6692: 6691: 6670: 6669: 6663: 6659: 6649: 6645: 6632: 6628: 6621: 6615: 6611: 6605: 6604: 6591: 6584: 6580: 6576: 6574: 6562: 6558: 6545: 6541: 6535: 6531: 6522: 6518: 6512: 6508: 6498: 6492: 6488: 6485: 6484: 6469: 6465: 6459: 6455: 6446: 6442: 6436: 6432: 6419: 6415: 6409: 6405: 6393: 6389: 6382: 6376: 6372: 6366: 6362: 6355: 6353: 6350: 6349: 6328: 6324: 6322: 6319: 6318: 6301: 6298: 6297: 6277: 6266: 6262: 6252: 6248: 6235: 6234: 6230: 6229: 6220: 6216: 6210: 6206: 6202: 6195: 6190: 6180: 6175: 6170: 6168: 6160: 6156: 6155: 6151: 6136: 6132: 6120: 6116: 6104: 6100: 6098: 6095: 6094: 6074: 6071: 6070: 6049: 6046: 6045: 6038: 6015: 6011: 6009: 6006: 6005: 5984: 5980: 5978: 5975: 5974: 5953: 5949: 5943: 5939: 5930: 5926: 5918: 5915: 5914: 5890: 5885: 5865: 5862: 5861: 5838: 5834: 5819: 5815: 5803: 5799: 5777: 5767: 5763: 5747: 5742: 5734: 5731: 5730: 5697: 5693: 5689: 5679: 5675: 5671: 5669: 5665: 5656: 5652: 5641: 5636: 5612: 5608: 5599: 5595: 5580: 5576: 5570: 5566: 5561: 5558: 5557: 5534: 5530: 5515: 5511: 5502: 5498: 5482: 5475: 5471: 5461: 5454: 5450: 5434: 5425: 5421: 5405: 5400: 5392: 5389: 5388: 5384:the action is: 5368: 5365: 5364: 5347: 5344: 5343: 5322: 5318: 5309: 5305: 5297: 5294: 5293: 5272: 5268: 5266: 5263: 5262: 5231: 5227: 5217: 5204: 5200: 5187: 5182: 5157: 5150: 5146: 5136: 5129: 5125: 5116: 5112: 5103: 5099: 5087: 5083: 5077: 5073: 5071: 5068: 5067: 5046: 5042: 5026: 5019: 5015: 5005: 4998: 4994: 4984: 4970: 4963: 4959: 4949: 4942: 4938: 4926: 4922: 4913: 4909: 4900: 4896: 4886: 4876: 4872: 4856: 4851: 4843: 4840: 4839: 4830: 4828:Bimetric theory 4824: 4793: 4789: 4779: 4775: 4765: 4761: 4749: 4737: 4733: 4723: 4719: 4709: 4705: 4693: 4689: 4679: 4675: 4665: 4661: 4649: 4645: 4641: 4611: 4610: 4606: 4597: 4593: 4591: 4588: 4587: 4568: 4565: 4564: 4536: 4532: 4522: 4518: 4511: 4507: 4495: 4483: 4479: 4469: 4465: 4455: 4451: 4439: 4438: 4434: 4428: 4424: 4415: 4411: 4409: 4406: 4405: 4377: 4373: 4361: 4357: 4345: 4341: 4337: 4333: 4327: 4323: 4314: 4310: 4300: 4296: 4287: 4283: 4278: 4275: 4274: 4255: 4252: 4251: 4235: 4232: 4231: 4199: 4195: 4177: 4173: 4167: 4163: 4154: 4150: 4148: 4145: 4144: 4119: 4115: 4103: 4099: 4087: 4083: 4079: 4075: 4057: 4053: 4044: 4040: 4016: 4012: 4003: 3999: 3994: 3991: 3990: 3962: 3959: 3958: 3933: 3930: 3929: 3922: 3895: 3891: 3881: 3877: 3859: 3855: 3843: 3839: 3838: 3834: 3819: 3815: 3806: 3802: 3801: 3797: 3788: 3784: 3767: 3764: 3763: 3743: 3739: 3737: 3734: 3733: 3714: 3711: 3710: 3687: 3683: 3673: 3669: 3659: 3655: 3634: 3630: 3628: 3625: 3624: 3604: 3600: 3591: 3587: 3577: 3568: 3564: 3548: 3543: 3535: 3532: 3531: 3527:The action is: 3494: 3480: 3477: 3476: 3456: 3444: 3439: 3430: 3426: 3425: 3392: 3387: 3378: 3374: 3354: 3350: 3344: 3339: 3333: 3323: 3311: 3307: 3302: 3298: 3297: 3283: 3279: 3274: 3259: 3255: 3250: 3246: 3241: 3238: 3237: 3204: 3199: 3186: 3182: 3165: 3161: 3156: 3152: 3148: 3127: 3123: 3118: 3114: 3109: 3106: 3105: 3072: 3067: 3054: 3050: 3028: 3024: 3019: 3015: 3010: 3007: 3006: 2982: 2978: 2954: 2950: 2944: 2940: 2935: 2928: 2926: 2915: 2911: 2906: 2902: 2898: 2877: 2873: 2868: 2864: 2859: 2856: 2855: 2832: 2828: 2809: 2805: 2800: 2773: 2769: 2764: 2753: 2750: 2749: 2727: 2724: 2723: 2719: 2692: 2690: 2682: 2679: 2678: 2635: 2631: 2625: 2621: 2610: 2607: 2606: 2597: 2591: 2581:. How to add a 2303:, B. E. Laurent 2270: 2252:, G. E. Morduch 2230:Robert H. Dicke 1984: 1978: 1942:Teleparallelism 1917:Modern theories 1786:Tensor theories 1746:Whitrow–Morduch 1706:Einstein (1912) 1662: 1654: 1648: 1645: 1644: 1623: 1619: 1617: 1614: 1613: 1588: 1584: 1582: 1579: 1578: 1554: 1550: 1544: 1536: 1520: 1516: 1510: 1502: 1486: 1476: 1472: 1471: 1470: 1458: 1454: 1448: 1444: 1436: 1433: 1432: 1424: 1408: 1405: 1404: 1388: 1385: 1384: 1363: 1359: 1349: 1345: 1332: 1328: 1316: 1308: 1307: 1305: 1302: 1301: 1273: 1269: 1267: 1264: 1263: 1255: 1206: 1203: 1202: 1169: 1166: 1165: 1141: 1136: 1135: 1124: 1110: 1107: 1106: 1086: 1083: 1082: 1065: 1062: 1061: 1026: 995: 991: 989: 986: 985: 961: 957: 943: 940: 939: 936:Ricci curvature 914: 909: 897: 894: 893: 876: 873: 872: 851: 847: 835: 831: 818: 799: 793: 789: 787: 779: 776: 775: 733: 729: 719: 707: 703: 702: 698: 685: 679: 675: 673: 661: 657: 655: 652: 651: 616: 612: 602: 590: 586: 585: 581: 573: 569: 558: 556: 544: 540: 538: 535: 534: 513: 509: 499: 495: 482: 478: 469: 461: 460: 458: 455: 454: 419: 416: 415: 409: 403: 377: 373: 371: 368: 367: 346: 342: 340: 337: 336: 311: 307: 305: 302: 301: 280: 276: 274: 271: 270: 235: 231: 229: 226: 225: 200: 196: 194: 191: 190: 156: 153: 152: 131: 128: 127: 125: 117:Main articles: 115: 107:Pioneer anomaly 79: 17: 12: 11: 5: 25057: 25047: 25046: 25041: 25024: 25023: 25021: 25020: 25015: 25009: 25007: 25006:Related topics 25003: 25002: 25000: 24999: 24994: 24989: 24984: 24983: 24982: 24975: 24963: 24958: 24953: 24947: 24945: 24935: 24934: 24931: 24930: 24928: 24927: 24922: 24917: 24912: 24907: 24901: 24899: 24893: 24892: 24890: 24889: 24888: 24887: 24878:Twistor theory 24875: 24874: 24873: 24866: 24859: 24852: 24845: 24838: 24831: 24824: 24812: 24811: 24810: 24798: 24793: 24787: 24785: 24779: 24778: 24776: 24775: 24770: 24764: 24762: 24758: 24757: 24755: 24754: 24749: 24744: 24739: 24734: 24729: 24728: 24727: 24720: 24713: 24701: 24695: 24693: 24689: 24688: 24686: 24685: 24680: 24675: 24670: 24665: 24664: 24663: 24651: 24646: 24641: 24640: 24639: 24627: 24622: 24621: 24620: 24613: 24601: 24596: 24591: 24579: 24574: 24569: 24564: 24563: 24562: 24555: 24542: 24540: 24536: 24535: 24533: 24532: 24527: 24522: 24516: 24514: 24507: 24499: 24498: 24495: 24494: 24492: 24491: 24486: 24481: 24476: 24471: 24466: 24461: 24456: 24451: 24446: 24440: 24438: 24432: 24431: 24429: 24428: 24423: 24418: 24413: 24407: 24405: 24398: 24394: 24393: 24386: 24385: 24378: 24371: 24363: 24356: 24355: 24339: 24337: 24336:External links 24334: 24332: 24331: 24292: 24250: 24231:(7): 355–369. 24208: 24138: 24132:10.1086/151755 24097: 24046: 24003: 23944: 23879: 23826: 23789:(13): 135003. 23770: 23749: 23728: 23672: 23614: 23577:(1–3): 21–24. 23550: 23535: 23514: 23449: 23420:(1–3): 21–24. 23400: 23342: 23287: 23234: 23173: 23120: 23090:hep-th/0508194 23067: 23006: 22971: 22910: 22857: 22826: 22773: 22745: 22717: 22664: 22608: 22552: 22515:(2): 281–298. 22499: 22443: 22434: 22422: 22372: 22310: 22257:(21): 211101. 22241: 22180: 22119: 22084:(6): 363–384. 22068: 22007: 21945: 21924: 21915: 21888:(6): 435–447. 21872: 21854: 21810: 21779: 21760:(7): 944–973. 21735: 21730:10.1086/155749 21695: 21653: 21613: 21553: 21507: 21501:10.1086/151754 21457: 21417: 21390:(3): 259–268. 21369: 21329: 21287: 21281:10.1086/150607 21241: 21197: 21147: 21095: 21055: 21043: 21005: 20961: 20924:Whitrow, G. J. 20906: 20868: 20826: 20790: 20746: 20704: 20690: 20632: 20558: 20513:Papapetrou, A. 20499: 20471: 20455: 20416:(8): 231–239. 20393: 20347: 20305: 20274: 20265: 20254: 20249:10.1086/151677 20202: 20176: 20173:Mach principle 20164: 20145:(3): 925–935. 20116: 20103: 20081: 20065: 20053: 20011: 19990: 19908: 19855: 19853: 19850: 19834: 19830: 19816: 19813: 19792: 19789: 19786: 19760: 19756: 19742: 19741: 19738: 19735: 19732: 19729: 19726: 19723: 19720: 19718: 19704: 19701: 19688: 19677: 19674: 19664: 19660: 19659: 19656: 19653: 19650: 19647: 19644: 19641: 19638: 19636: 19625: 19622: 19619: 19609: 19598: 19595: 19585: 19581: 19580: 19577: 19574: 19561: 19557: 19546: 19543: 19540: 19537: 19534: 19532: 19521: 19518: 19515: 19505: 19494: 19491: 19481: 19477: 19476: 19473: 19470: 19467: 19464: 19461: 19458: 19455: 19453: 19439: 19436: 19423: 19412: 19409: 19399: 19395: 19394: 19391: 19388: 19385: 19382: 19379: 19376: 19373: 19371: 19357: 19354: 19341: 19330: 19327: 19317: 19313: 19312: 19299: 19295: 19284: 19281: 19268: 19264: 19253: 19250: 19239: 19236: 19233: 19230: 19227: 19217: 19214: 19203: 19200: 19197: 19194: 19191: 19181: 19179: 19168: 19158: 19147: 19137: 19133: 19132: 19129: 19126: 19123: 19120: 19117: 19114: 19111: 19109: 19106: 19103: 19102:Yilmaz (1962) 19099: 19098: 19095: 19092: 19089: 19086: 19083: 19080: 19077: 19075: 19072: 19069: 19065: 19064: 19061: 19058: 19055: 19052: 19049: 19046: 19043: 19041: 19038: 19035: 19031: 19030: 19027: 19024: 19021: 19018: 19015: 19012: 19001: 18998: 18995: 18992: 18989: 18979: 18977: 18962: 18959: 18953: 18948: 18945: 18932: 18921: 18911: 18907: 18906: 18903: 18900: 18897: 18894: 18891: 18888: 18885: 18883: 18880: 18877: 18873: 18872: 18869: 18866: 18863: 18860: 18857: 18854: 18851: 18849: 18846: 18843: 18839: 18838: 18834: 18833: 18830: 18827: 18824: 18821: 18818: 18805: 18801: 18790: 18777: 18773: 18762: 18759: 18746: 18742: 18738: 18728: 18715: 18711: 18706: 18700: 18696: 18692: 18682: 18678: 18677: 18674: 18671: 18668: 18665: 18662: 18649: 18645: 18634: 18621: 18617: 18606: 18595: 18585: 18574: 18564: 18551: 18547: 18542: 18536: 18532: 18528: 18518: 18514: 18513: 18509: 18508: 18505: 18502: 18499: 18496: 18493: 18480: 18476: 18465: 18452: 18448: 18437: 18434: 18423: 18413: 18402: 18392: 18388: 18387: 18384: 18381: 18378: 18375: 18372: 18359: 18355: 18344: 18341: 18338: 18335: 18332: 18328: 18327: 18324: 18321: 18318: 18315: 18312: 18301: 18298: 18293: 18289: 18284: 18278: 18274: 18263: 18260: 18257: 18254: 18251: 18247: 18246: 18242: 18241: 18238: 18235: 18232: 18229: 18226: 18213: 18209: 18198: 18195: 18192: 18189: 18186: 18182: 18181: 18178: 18175: 18172: 18169: 18166: 18153: 18149: 18138: 18125: 18121: 18110: 18107: 18096: 18086: 18075: 18065: 18061: 18060: 18056: 18055: 18052: 18049: 18046: 18043: 18040: 18037: 18034: 18031: 18028: 18013: 18010: 18007: 18002: 17999: 17996: 17982: 17978: 17977: 17974: 17971: 17968: 17965: 17962: 17959: 17956: 17953: 17942: 17932: 17917: 17914: 17911: 17906: 17903: 17900: 17886: 17879: 17878: 17875: 17872: 17869: 17866: 17863: 17860: 17857: 17854: 17843: 17833: 17818: 17815: 17812: 17807: 17804: 17801: 17787: 17783: 17782: 17778: 17777: 17774: 17771: 17768: 17765: 17762: 17759: 17756: 17753: 17750: 17747: 17743: 17742: 17729: 17725: 17714: 17701: 17697: 17686: 17673: 17669: 17658: 17645: 17641: 17630: 17617: 17613: 17602: 17589: 17585: 17574: 17561: 17557: 17546: 17535: 17525: 17514: 17504: 17493: 17483: 17467: 17464: 17462: 17459: 17425: 17422: 17409:Main article: 17406: 17403: 17402: 17401: 17387: 17383: 17379: 17374: 17370: 17366: 17361: 17357: 17353: 17348: 17344: 17340: 17335: 17331: 17320: 17306: 17302: 17298: 17293: 17289: 17285: 17280: 17276: 17265: 17253: 17243: 17231: 17221: 17209: 17187: 17182: 17178: 17174: 17169: 17165: 17161: 17156: 17152: 17148: 17143: 17139: 17135: 17130: 17126: 17122: 17117: 17113: 17109: 17104: 17100: 17096: 17093: 17090: 17087: 17084: 17081: 17055:Main article: 17052: 17049: 17008:to less than 5 16992:to less than 5 16977:Main article: 16974: 16971: 16965: 16962: 16938:Main article: 16935: 16932: 16917: 16893: 16869: 16847: 16844: 16840: 16834: 16831: 16827: 16823: 16820: 16798: 16794: 16788: 16784: 16778: 16775: 16771: 16767: 16764: 16744: 16724: 16708: 16705: 16696: 16693: 16684:Main article: 16681: 16678: 16673: 16672: 16661: 16658:Hubble tension 16654: 16647: 16632: 16631: 16628:Bullet Cluster 16620: 16613: 16606: 16595: 16585: 16573: 16570: 16555: 16551: 16547: 16544: 16518: 16498: 16474: 16452: 16448: 16444: 16441: 16382:binding energy 16310: 16307: 16286: 16283: 16280: 16277: 16266: 16265: 16253: 16249: 16246: 16243: 16240: 16237: 16234: 16231: 16226: 16223: 16217: 16211: 16208: 16203: 16198: 16193: 16188: 16185: 16182: 16156:Main article: 16153: 16150: 16137: 16126: 16125: 16112: 16107: 16101: 16097: 16091: 16087: 16082: 16077: 16072: 16069: 16064: 16059: 16055: 16049: 16045: 16039: 16035: 16029: 16026: 16021: 16018: 16015: 16012: 16009: 16006: 15992: 15991: 15980: 15976: 15972: 15969: 15966: 15963: 15960: 15957: 15952: 15948: 15943: 15938: 15934: 15927: 15924: 15920: 15914: 15911: 15905: 15898: 15893: 15889: 15884: 15879: 15875: 15871: 15868: 15865: 15862: 15859: 15856: 15851: 15847: 15842: 15837: 15833: 15826: 15823: 15819: 15813: 15810: 15804: 15798: 15795: 15790: 15786: 15782: 15779: 15776: 15773: 15770: 15767: 15762: 15758: 15753: 15748: 15744: 15737: 15734: 15730: 15724: 15721: 15715: 15707: 15703: 15699: 15692: 15689: 15683: 15678: 15674: 15670: 15667: 15664: 15659: 15655: 15643: 15642: 15631: 15626: 15622: 15616: 15612: 15608: 15603: 15599: 15593: 15589: 15585: 15580: 15577: 15573: 15562: 15558: 15554: 15551: 15548: 15545: 15542: 15537: 15534: 15530: 15524: 15521: 15517: 15511: 15508: 15502: 15498: 15493: 15490: 15484: 15479: 15475: 15471: 15468: 15465: 15460: 15456: 15432: 15410: 15406: 15385: 15382: 15379: 15376: 15373: 15364:scalar fields 15353: 15348: 15344: 15321: 15317: 15313: 15308: 15304: 15300: 15295: 15291: 15287: 15282: 15278: 15274: 15271: 15252:Main article: 15249: 15246: 15226: 15223: 15220: 15217: 15213: 15201: 15200: 15187: 15184: 15180: 15174: 15170: 15166: 15161: 15158: 15154: 15148: 15144: 15140: 15135: 15132: 15129: 15125: 15110: 15109: 15095: 15091: 15085: 15081: 15075: 15072: 15068: 15062: 15059: 15056: 15053: 15049: 15044: 15039: 15035: 15031: 15028: 15023: 15020: 15016: 15004: 15003: 14990: 14984: 14981: 14977: 14971: 14968: 14964: 14958: 14954: 14948: 14945: 14940: 14935: 14932: 14929: 14925: 14919: 14916: 14913: 14909: 14903: 14900: 14894: 14888: 14885: 14879: 14874: 14870: 14866: 14863: 14858: 14854: 14839: 14838: 14824: 14820: 14816: 14811: 14808: 14804: 14800: 14795: 14791: 14787: 14782: 14778: 14774: 14771: 14745: 14741: 14717: 14714: 14710: 14685: 14652: 14649: 14644: 14641: 14638: 14635: 14631: 14627: 14624: 14621: 14616: 14612: 14588: 14584: 14560: 14557: 14553: 14529: 14526: 14523: 14520: 14516: 14492: 14488: 14466: 14445: 14442: 14439: 14436: 14425: 14424: 14410: 14406: 14400: 14396: 14390: 14387: 14383: 14377: 14374: 14369: 14365: 14359: 14356: 14353: 14350: 14346: 14340: 14337: 14333: 14327: 14323: 14317: 14314: 14309: 14306: 14303: 14300: 14297: 14294: 14291: 14288: 14284: 14278: 14275: 14270: 14265: 14261: 14234: 14230: 14218: 14217: 14203: 14199: 14195: 14190: 14186: 14182: 14179: 14153: 14150: 14146: 14123: 14120: 14119: 14118: 14107: 14101: 14098: 14094: 14089: 14083: 14080: 14077: 14073: 14068: 14063: 14060: 14056: 14032: 14029: 14024: 14021: 14018: 14015: 14012: 14009: 14006: 14003: 14000: 13996: 13992: 13989: 13974: 13973: 13958: 13955: 13947: 13943: 13939: 13936: 13933: 13930: 13921: 13917: 13913: 13909: 13905: 13902: 13899: 13896: 13893: 13890: 13887: 13881: 13875: 13872: 13869: 13864: 13861: 13855: 13852: 13850: 13846: 13842: 13838: 13837: 13834: 13831: 13827: 13823: 13820: 13813: 13809: 13805: 13801: 13797: 13790: 13786: 13782: 13779: 13775: 13771: 13768: 13765: 13762: 13759: 13756: 13752: 13746: 13742: 13739: 13733: 13730: 13728: 13724: 13720: 13716: 13715: 13690: 13687: 13684: 13673: 13672: 13658: 13655: 13652: 13645: 13641: 13637: 13634: 13631: 13628: 13623: 13619: 13610: 13607: 13602: 13599: 13596: 13593: 13590: 13561: 13558: 13555: 13552: 13549: 13546: 13542: 13515: 13512: 13505: 13502: 13474: 13452: 13449: 13446: 13443: 13440: 13436: 13415: 13412: 13409: 13399: 13398: 13387: 13384: 13381: 13378: 13375: 13372: 13367: 13363: 13357: 13353: 13349: 13346: 13341: 13338: 13334: 13328: 13325: 13321: 13317: 13312: 13309: 13302: 13299: 13285: 13272: 13268: 13262: 13258: 13254: 13249: 13246: 13242: 13238: 13233: 13230: 13226: 13211: 13210: 13195: 13190: 13186: 13179: 13176: 13170: 13166: 13163: 13158: 13153: 13149: 13144: 13140: 13135: 13131: 13127: 13122: 13119: 13112: 13109: 13101: 13097: 13094: 13091: 13088: 13086: 13082: 13078: 13074: 13073: 13070: 13065: 13061: 13054: 13051: 13045: 13040: 13036: 13033: 13028: 13024: 13018: 13014: 13008: 13005: 13001: 12996: 12990: 12986: 12983: 12977: 12972: 12969: 12966: 12963: 12960: 12956: 12950: 12947: 12944: 12941: 12938: 12934: 12928: 12925: 12921: 12915: 12912: 12908: 12903: 12899: 12893: 12890: 12887: 12883: 12878: 12875: 12872: 12870: 12866: 12862: 12858: 12857: 12854: 12849: 12845: 12838: 12835: 12829: 12825: 12820: 12816: 12812: 12809: 12806: 12803: 12798: 12794: 12788: 12785: 12780: 12776: 12772: 12767: 12764: 12759: 12754: 12751: 12747: 12741: 12738: 12734: 12728: 12725: 12721: 12715: 12711: 12706: 12702: 12697: 12694: 12689: 12686: 12683: 12681: 12677: 12673: 12669: 12668: 12654: 12653: 12640: 12636: 12632: 12627: 12623: 12619: 12614: 12610: 12606: 12601: 12597: 12593: 12590: 12565: 12561: 12539: 12519: 12487: 12483: 12478: 12472: 12468: 12464: 12459: 12455: 12431: 12428: 12405: 12394: 12393: 12381: 12377: 12372: 12368: 12363: 12358: 12354: 12347: 12344: 12340: 12334: 12329: 12325: 12320: 12313: 12310: 12301: 12298: 12295: 12289: 12284: 12280: 12274: 12271: 12268: 12254: 12253: 12242: 12239: 12236: 12232: 12225: 12220: 12216: 12209: 12204: 12199: 12196: 12192: 12185: 12181: 12175: 12172: 12169: 12163: 12158: 12154: 12148: 12145: 12142: 12124: 12123: 12120: 12117: 12114: 12088: 12085: 12076: 12075: 12063: 12057: 12054: 12050: 12046: 12041: 12036: 12033: 12029: 12025: 12020: 12015: 12012: 12008: 12003: 11995: 11991: 11986: 11983: 11980: 11974: 11969: 11966: 11962: 11958: 11953: 11950: 11945: 11940: 11937: 11933: 11877: 11874: 11870: 11869: 11855: 11852: 11848: 11842: 11838: 11832: 11828: 11799: 11796: 11793: 11790: 11779: 11778: 11764: 11760: 11756: 11751: 11747: 11740: 11737: 11731: 11726: 11722: 11718: 11712: 11709: 11706: 11702: 11697: 11694: 11668: 11664: 11642: 11639: 11636: 11633: 11612: 11591: 11588: 11585: 11582: 11568: 11567: 11554: 11550: 11545: 11542: 11538: 11534: 11531: 11526: 11523: 11519: 11513: 11510: 11505: 11500: 11497: 11493: 11488: 11481: 11478: 11475: 11471: 11466: 11461: 11458: 11454: 11439: 11438: 11425: 11421: 11416: 11413: 11409: 11403: 11400: 11395: 11390: 11387: 11383: 11378: 11371: 11368: 11365: 11361: 11356: 11351: 11348: 11344: 11329: 11328: 11314: 11310: 11306: 11302: 11297: 11293: 11286: 11283: 11278: 11275: 11272: 11269: 11266: 11263: 11260: 11254: 11251: 11248: 11244: 11239: 11236: 11222: 11221: 11207: 11203: 11199: 11195: 11190: 11186: 11179: 11176: 11171: 11168: 11162: 11159: 11156: 11152: 11147: 11144: 11130: 11129: 11118: 11115: 11109: 11106: 11103: 11100: 11095: 11091: 11087: 11082: 11079: 11074: 11071: 11066: 11062: 11047: 11046: 11035: 11032: 11026: 11023: 11020: 11017: 11014: 11009: 11005: 10977: 10974: 10971: 10950: 10924: 10921: 10892: 10889: 10883: 10880: 10858: 10857: 10843: 10838: 10834: 10830: 10825: 10820: 10816: 10810: 10807: 10803: 10799: 10794: 10789: 10785: 10779: 10776: 10772: 10768: 10763: 10758: 10754: 10748: 10745: 10741: 10737: 10731: 10728: 10725: 10721: 10716: 10711: 10708: 10704: 10676: 10673: 10669: 10645: 10642: 10637: 10632: 10628: 10600: 10597: 10594: 10591: 10587: 10563: 10558: 10554: 10542: 10541: 10524: 10520: 10514: 10509: 10505: 10501: 10498: 10495: 10493: 10489: 10485: 10481: 10478: 10477: 10472: 10467: 10463: 10459: 10454: 10449: 10445: 10441: 10438: 10435: 10433: 10429: 10424: 10420: 10416: 10415: 10410: 10407: 10404: 10401: 10397: 10391: 10387: 10381: 10377: 10371: 10368: 10364: 10358: 10353: 10349: 10342: 10339: 10336: 10332: 10327: 10324: 10322: 10320: 10317: 10316: 10282: 10279: 10270: 10267: 10254: 10251: 10248: 10245: 10242: 10239: 10236: 10233: 10230: 10219: 10218: 10207: 10204: 10201: 10198: 10195: 10191: 10188: 10185: 10182: 10178: 10175: 10172: 10169: 10155: 10154: 10143: 10140: 10137: 10133: 10130: 10127: 10124: 10121: 10118: 10115: 10112: 10098: 10097: 10085: 10080: 10076: 10053: 10050: 10046: 10025: 10020: 10017: 10014: 10010: 10006: 10001: 9998: 9995: 9991: 9987: 9982: 9979: 9975: 9951: 9948: 9945: 9942: 9939: 9936: 9933: 9922: 9921: 9908: 9904: 9900: 9896: 9890: 9887: 9884: 9880: 9874: 9871: 9868: 9864: 9860: 9857: 9852: 9849: 9845: 9839: 9836: 9832: 9828: 9825: 9820: 9817: 9813: 9807: 9803: 9797: 9793: 9789: 9786: 9783: 9778: 9774: 9768: 9764: 9760: 9757: 9754: 9750: 9744: 9741: 9736: 9731: 9727: 9723: 9717: 9714: 9711: 9707: 9702: 9699: 9676: 9671: 9667: 9650: 9647: 9622: 9619: 9616: 9595: 9592: 9589: 9586: 9577:Adjustment of 9575: 9574: 9560: 9557: 9554: 9551: 9546: 9543: 9540: 9537: 9531: 9528: 9525: 9522: 9519: 9505: 9504: 9488: 9485: 9481: 9477: 9474: 9471: 9468: 9465: 9462: 9459: 9456: 9453: 9450: 9447: 9444: 9441: 9438: 9435: 9432: 9429: 9426: 9423: 9420: 9417: 9414: 9411: 9408: 9405: 9402: 9399: 9396: 9393: 9390: 9387: 9384: 9379: 9376: 9370: 9365: 9362: 9356: 9353: 9350: 9347: 9344: 9341: 9317: 9294: 9291: 9287: 9283: 9280: 9277: 9274: 9271: 9268: 9265: 9262: 9259: 9256: 9253: 9250: 9247: 9244: 9223: 9202: 9178: 9151: 9128: 9125: 9122: 9095: 9072: 9068: 9046: 9043: 9040: 9037: 9016: 9013: 9010: 9007: 8996: 8995: 8979: 8976: 8972: 8968: 8961: 8957: 8953: 8943: 8938: 8925: 8922: 8919: 8913: 8901: 8898: 8894: 8882: 8881: 8867: 8863: 8857: 8853: 8846: 8840: 8835: 8831: 8827: 8824: 8819: 8815: 8803: 8802: 8790: 8787: 8784: 8781: 8778: 8775: 8772: 8769: 8764: 8760: 8755: 8750: 8746: 8739: 8736: 8732: 8726: 8722: 8719: 8716: 8713: 8707: 8704: 8701: 8698: 8693: 8689: 8677: 8676: 8662: 8658: 8654: 8649: 8645: 8639: 8636: 8631: 8626: 8622: 8618: 8612: 8609: 8606: 8602: 8597: 8594: 8568: 8564: 8542: 8487: 8484: 8480: 8479: 8468: 8465: 8462: 8457: 8453: 8449: 8444: 8437: 8433: 8429: 8425: 8419: 8416: 8412: 8406: 8403: 8399: 8395: 8392: 8387: 8384: 8381: 8378: 8374: 8368: 8365: 8362: 8359: 8355: 8351: 8346: 8342: 8337: 8331: 8327: 8323: 8320: 8315: 8311: 8307: 8302: 8298: 8294: 8286: 8283: 8278: 8273: 8256: 8253: 8234: 8231: 8226: 8222: 8199: 8195: 8172: 8168: 8156: 8155: 8144: 8141: 8138: 8134: 8127: 8122: 8118: 8114: 8109: 8103: 8099: 8095: 8092: 8088: 8081: 8076: 8072: 8068: 8063: 8057: 8053: 8049: 8045: 8038: 8033: 8029: 8025: 8020: 8014: 8010: 8006: 7992: 7991: 7980: 7976: 7970: 7967: 7964: 7961: 7957: 7952: 7945: 7940: 7936: 7932: 7927: 7921: 7917: 7911: 7908: 7905: 7902: 7898: 7894: 7889: 7886: 7882: 7877: 7870: 7865: 7861: 7857: 7852: 7846: 7842: 7836: 7833: 7829: 7825: 7822: 7818: 7811: 7806: 7802: 7798: 7793: 7787: 7783: 7779: 7776: 7773: 7768: 7763: 7759: 7754: 7748: 7745: 7740: 7735: 7715: 7712: 7699: 7696: 7693: 7690: 7679: 7678: 7667: 7664: 7661: 7658: 7653: 7650: 7645: 7640: 7623: 7620: 7619: 7618: 7607: 7603: 7597: 7594: 7591: 7588: 7584: 7578: 7575: 7572: 7569: 7565: 7559: 7555: 7551: 7546: 7543: 7539: 7533: 7530: 7526: 7520: 7516: 7512: 7507: 7503: 7497: 7493: 7489: 7486: 7482: 7476: 7473: 7468: 7463: 7446: 7443: 7438: 7437: 7426: 7422: 7416: 7413: 7410: 7407: 7403: 7397: 7394: 7391: 7388: 7384: 7380: 7375: 7372: 7368: 7362: 7359: 7355: 7351: 7348: 7343: 7339: 7335: 7332: 7328: 7322: 7319: 7314: 7309: 7292: 7289: 7276: 7261: 7260: 7248: 7239: 7235: 7231: 7225: 7221: 7215: 7212: 7208: 7202: 7199: 7194: 7189: 7162: 7159: 7138: 7135: 7104: 7101: 7097: 7080: 7079: 7065: 7061: 7057: 7053: 7047: 7043: 7039: 7036: 7032: 7026: 7022: 7018: 7015: 7011: 7007: 7002: 6998: 6994: 6989: 6985: 6979: 6974: 6970: 6966: 6962: 6958: 6953: 6948: 6944: 6940: 6936: 6930: 6927: 6922: 6918: 6913: 6909: 6906: 6901: 6897: 6891: 6888: 6884: 6878: 6875: 6870: 6866: 6861: 6857: 6853: 6847: 6844: 6839: 6834: 6830: 6826: 6820: 6817: 6814: 6810: 6805: 6802: 6788: 6787: 6773: 6770: 6766: 6762: 6757: 6754: 6750: 6746: 6741: 6738: 6734: 6707: 6704: 6700: 6684: 6683: 6666: 6662: 6658: 6652: 6648: 6644: 6638: 6635: 6631: 6627: 6624: 6622: 6618: 6614: 6610: 6607: 6606: 6603: 6597: 6594: 6587: 6583: 6579: 6573: 6570: 6565: 6561: 6557: 6553: 6548: 6544: 6538: 6534: 6530: 6525: 6521: 6515: 6511: 6507: 6504: 6501: 6499: 6495: 6491: 6487: 6486: 6483: 6480: 6477: 6472: 6468: 6462: 6458: 6454: 6449: 6445: 6439: 6435: 6431: 6427: 6422: 6418: 6412: 6408: 6404: 6401: 6396: 6392: 6388: 6385: 6383: 6379: 6375: 6369: 6365: 6361: 6358: 6357: 6331: 6327: 6305: 6294: 6293: 6280: 6275: 6269: 6265: 6261: 6255: 6251: 6247: 6242: 6239: 6233: 6223: 6219: 6213: 6209: 6205: 6198: 6193: 6189: 6183: 6178: 6174: 6163: 6159: 6154: 6150: 6147: 6142: 6139: 6135: 6131: 6128: 6123: 6119: 6115: 6110: 6107: 6103: 6078: 6053: 6037: 6034: 6018: 6014: 5990: 5987: 5983: 5971: 5970: 5956: 5952: 5946: 5942: 5936: 5933: 5929: 5925: 5922: 5899: 5896: 5893: 5889: 5884: 5881: 5878: 5875: 5872: 5869: 5855: 5854: 5841: 5837: 5833: 5828: 5825: 5822: 5818: 5812: 5809: 5806: 5802: 5798: 5795: 5792: 5789: 5784: 5781: 5775: 5770: 5766: 5762: 5756: 5753: 5750: 5746: 5741: 5738: 5724: 5723: 5711: 5705: 5700: 5696: 5692: 5685: 5682: 5678: 5674: 5668: 5662: 5659: 5655: 5648: 5644: 5640: 5635: 5632: 5629: 5626: 5623: 5620: 5615: 5611: 5605: 5602: 5598: 5594: 5591: 5586: 5583: 5579: 5573: 5569: 5565: 5551: 5550: 5537: 5533: 5529: 5526: 5521: 5518: 5514: 5508: 5505: 5501: 5497: 5494: 5489: 5485: 5481: 5478: 5474: 5468: 5464: 5460: 5457: 5453: 5449: 5446: 5441: 5438: 5433: 5428: 5424: 5420: 5414: 5411: 5408: 5404: 5399: 5396: 5372: 5351: 5328: 5325: 5321: 5315: 5312: 5308: 5304: 5301: 5278: 5275: 5271: 5259: 5258: 5245: 5242: 5237: 5234: 5230: 5224: 5221: 5215: 5210: 5207: 5203: 5199: 5194: 5190: 5186: 5181: 5178: 5175: 5172: 5169: 5164: 5160: 5156: 5153: 5149: 5143: 5139: 5135: 5132: 5128: 5122: 5119: 5115: 5109: 5106: 5102: 5098: 5093: 5090: 5086: 5080: 5076: 5064: 5063: 5049: 5045: 5041: 5038: 5033: 5029: 5025: 5022: 5018: 5012: 5008: 5004: 5001: 4997: 4991: 4988: 4982: 4977: 4973: 4969: 4966: 4962: 4956: 4952: 4948: 4945: 4941: 4937: 4932: 4929: 4925: 4919: 4916: 4912: 4906: 4903: 4899: 4893: 4890: 4884: 4879: 4875: 4871: 4865: 4862: 4859: 4855: 4850: 4847: 4823: 4820: 4819: 4818: 4805: 4801: 4796: 4792: 4787: 4782: 4778: 4771: 4768: 4764: 4757: 4754: 4748: 4745: 4740: 4736: 4731: 4726: 4722: 4715: 4712: 4708: 4704: 4701: 4696: 4692: 4687: 4682: 4678: 4671: 4668: 4664: 4657: 4654: 4648: 4644: 4638: 4635: 4632: 4629: 4626: 4623: 4618: 4615: 4609: 4605: 4600: 4596: 4572: 4561: 4560: 4548: 4544: 4539: 4535: 4530: 4525: 4521: 4514: 4510: 4503: 4500: 4494: 4491: 4486: 4482: 4477: 4472: 4468: 4461: 4458: 4454: 4447: 4444: 4437: 4431: 4427: 4423: 4418: 4414: 4399: 4398: 4386: 4380: 4376: 4372: 4369: 4364: 4360: 4356: 4353: 4348: 4344: 4340: 4336: 4330: 4326: 4322: 4317: 4313: 4309: 4303: 4299: 4295: 4290: 4286: 4282: 4259: 4239: 4228: 4227: 4216: 4213: 4210: 4207: 4202: 4198: 4194: 4191: 4188: 4185: 4180: 4176: 4170: 4166: 4160: 4157: 4153: 4141: 4140: 4128: 4122: 4118: 4114: 4111: 4106: 4102: 4098: 4095: 4090: 4086: 4082: 4078: 4072: 4069: 4066: 4063: 4060: 4056: 4052: 4047: 4043: 4039: 4034: 4031: 4028: 4025: 4022: 4019: 4015: 4011: 4006: 4002: 3998: 3975: 3972: 3969: 3966: 3946: 3943: 3940: 3937: 3920: 3919: 3907: 3903: 3898: 3894: 3889: 3884: 3880: 3874: 3868: 3865: 3862: 3858: 3854: 3849: 3846: 3842: 3837: 3833: 3828: 3825: 3822: 3818: 3812: 3809: 3805: 3800: 3794: 3791: 3787: 3783: 3780: 3777: 3774: 3771: 3746: 3742: 3721: 3718: 3707: 3706: 3695: 3690: 3686: 3681: 3676: 3672: 3665: 3662: 3658: 3654: 3651: 3648: 3645: 3642: 3637: 3633: 3621: 3620: 3607: 3603: 3599: 3594: 3590: 3584: 3581: 3576: 3571: 3567: 3563: 3557: 3554: 3551: 3547: 3542: 3539: 3501: 3497: 3493: 3490: 3487: 3484: 3473: 3472: 3459: 3454: 3447: 3442: 3438: 3434: 3429: 3424: 3421: 3418: 3415: 3412: 3409: 3406: 3402: 3395: 3390: 3386: 3382: 3377: 3373: 3370: 3367: 3364: 3357: 3353: 3347: 3342: 3338: 3331: 3326: 3321: 3314: 3310: 3306: 3301: 3296: 3293: 3286: 3282: 3278: 3273: 3269: 3262: 3258: 3254: 3249: 3245: 3231: 3230: 3218: 3215: 3212: 3207: 3202: 3198: 3194: 3189: 3185: 3180: 3176: 3168: 3164: 3160: 3155: 3151: 3147: 3144: 3141: 3137: 3130: 3126: 3122: 3117: 3113: 3099: 3098: 3086: 3083: 3080: 3075: 3070: 3066: 3062: 3057: 3053: 3048: 3045: 3042: 3038: 3031: 3027: 3023: 3018: 3014: 3000: 2999: 2985: 2981: 2977: 2974: 2969: 2963: 2957: 2953: 2947: 2943: 2938: 2934: 2931: 2925: 2918: 2914: 2910: 2905: 2901: 2897: 2894: 2891: 2887: 2880: 2876: 2872: 2867: 2863: 2849: 2848: 2835: 2831: 2827: 2824: 2820: 2817: 2812: 2808: 2803: 2799: 2796: 2793: 2790: 2787: 2784: 2781: 2776: 2772: 2767: 2763: 2760: 2757: 2745:In Nordström, 2731: 2716: 2715: 2702: 2698: 2695: 2689: 2686: 2672: 2671: 2660: 2657: 2654: 2651: 2646: 2638: 2634: 2630: 2624: 2620: 2617: 2614: 2590: 2587: 2568: 2567: 2562: 2560: 2557: 2553: 2552: 2547: 2545: 2542: 2538: 2537: 2532: 2530: 2525: 2521: 2520: 2518: 2516: 2503: 2499: 2498: 2493: 2491: 2482: 2478: 2477: 2472: 2470: 2464: 2460: 2459: 2454: 2452: 2443: 2439: 2438: 2433: 2431: 2426: 2422: 2421: 2416: 2414: 2409: 2405: 2404: 2399: 2397: 2392: 2388: 2387: 2382: 2380: 2377: 2373: 2372: 2370: 2368: 2363: 2359: 2358: 2353: 2351: 2348: 2344: 2343: 2338: 2336: 2334:Peter Bergmann 2331: 2327: 2326: 2321: 2319: 2316: 2312: 2311: 2306: 2304: 2298: 2294: 2293: 2291: 2289: 2286: 2282: 2281: 2279: 2277: 2265: 2261: 2260: 2255: 2253: 2247: 2243: 2242: 2237: 2232: 2223: 2219: 2218: 2216: 2211: 2210:Huseyin Yilmaz 2208: 2204: 2203: 2201: 2199: 2193: 2189: 2188: 2183: 2181: 2178: 2174: 2173: 2171: 2169: 2167:Pascual Jordan 2164: 2160: 2159: 2154: 2152: 2147: 2143: 2142: 2137: 2135: 2130: 2126: 2125: 2123: 2121: 2118: 2114: 2113: 2111: 2106: 2101: 2097: 2096: 2094: 2092: 2087: 2083: 2082: 2080: 2078: 2076:Wolfgang Pauli 2069: 2065: 2064: 2059: 2054: 2049: 2045: 2044: 2039: 2034: 2029: 2025: 2024: 2021: 2018: 2015: 1980:Main article: 1977: 1974: 1973: 1972: 1969: 1966: 1950: 1949: 1944: 1939: 1936: 1930: 1913: 1912: 1907: 1906: 1905: 1902: 1899: 1885: 1884: 1883: 1874: 1863: 1862: 1861: 1856: 1851: 1848: 1843: 1840: 1834: 1831: 1821: 1820: 1819: 1814: 1808: 1803: 1797: 1791: 1783: 1782: 1781: 1771: 1768: 1759: 1758: 1757: 1754:event horizons 1747: 1744: 1741: 1738: 1735: 1729: 1726: 1723: 1710: 1707: 1704: 1701: 1665: 1660: 1657: 1653: 1626: 1622: 1594: 1591: 1587: 1575: 1574: 1560: 1557: 1553: 1547: 1542: 1539: 1535: 1531: 1526: 1523: 1519: 1513: 1508: 1505: 1501: 1497: 1492: 1489: 1482: 1479: 1475: 1469: 1464: 1461: 1457: 1451: 1447: 1443: 1440: 1412: 1392: 1381: 1380: 1366: 1362: 1358: 1352: 1348: 1344: 1338: 1335: 1331: 1327: 1324: 1319: 1314: 1311: 1279: 1276: 1272: 1230: 1229: 1218: 1214: 1210: 1182: 1179: 1176: 1173: 1162: 1161: 1149: 1144: 1139: 1131: 1128: 1123: 1120: 1117: 1114: 1090: 1069: 1058: 1057: 1051: 1045: 1025: 1022: 998: 994: 972: 967: 964: 960: 956: 953: 950: 947: 920: 912: 908: 904: 901: 880: 869: 868: 854: 850: 846: 843: 838: 834: 825: 822: 817: 814: 808: 805: 802: 796: 792: 786: 783: 765: 764: 753: 748: 744: 739: 736: 732: 726: 723: 718: 713: 710: 706: 701: 694: 691: 688: 682: 678: 672: 667: 664: 660: 645: 644: 631: 627: 622: 619: 615: 609: 606: 601: 596: 593: 589: 584: 576: 572: 567: 564: 561: 555: 550: 547: 543: 531: 530: 516: 512: 508: 502: 498: 494: 488: 485: 481: 477: 472: 467: 464: 451: 450: 438: 435: 432: 429: 426: 423: 405:Main article: 402: 399: 383: 380: 376: 354: 349: 345: 317: 314: 310: 288: 283: 279: 241: 238: 234: 206: 203: 199: 160: 149:speed of light 135: 123:Ricci calculus 114: 111: 78: 75: 15: 9: 6: 4: 3: 2: 25056: 25045: 25042: 25040: 25037: 25036: 25034: 25019: 25016: 25014: 25011: 25010: 25008: 25004: 24998: 24995: 24993: 24990: 24988: 24985: 24980: 24976: 24973: 24972:Fatio–Le Sage 24969: 24968: 24967: 24964: 24962: 24959: 24957: 24954: 24952: 24949: 24948: 24946: 24944: 24938:Pre-Newtonian 24936: 24926: 24923: 24921: 24918: 24916: 24913: 24911: 24908: 24906: 24903: 24902: 24900: 24894: 24885: 24881: 24880: 24879: 24876: 24871: 24867: 24864: 24860: 24857: 24853: 24850: 24846: 24843: 24839: 24836: 24832: 24829: 24825: 24822: 24818: 24817: 24816: 24815:String theory 24813: 24808: 24804: 24803: 24802: 24799: 24797: 24794: 24792: 24789: 24788: 24786: 24780: 24774: 24771: 24769: 24766: 24765: 24763: 24759: 24753: 24750: 24748: 24745: 24743: 24740: 24738: 24735: 24733: 24730: 24725: 24721: 24718: 24714: 24711: 24707: 24706: 24705: 24702: 24700: 24697: 24696: 24694: 24690: 24684: 24681: 24679: 24676: 24674: 24671: 24669: 24666: 24661: 24657: 24656: 24655: 24652: 24650: 24647: 24645: 24642: 24637: 24633: 24632: 24631: 24628: 24626: 24623: 24618: 24614: 24611: 24607: 24606: 24605: 24602: 24600: 24597: 24595: 24592: 24590: 24588: 24584: 24580: 24578: 24575: 24573: 24570: 24568: 24565: 24560: 24556: 24553: 24549: 24548: 24547: 24544: 24543: 24541: 24537: 24531: 24528: 24526: 24523: 24521: 24518: 24517: 24515: 24511: 24508: 24506: 24500: 24490: 24487: 24485: 24484:ADM formalism 24482: 24480: 24477: 24475: 24472: 24470: 24467: 24465: 24462: 24460: 24457: 24455: 24452: 24450: 24447: 24445: 24442: 24441: 24439: 24437: 24433: 24427: 24424: 24422: 24419: 24417: 24414: 24412: 24409: 24408: 24406: 24402: 24399: 24395: 24391: 24384: 24379: 24377: 24372: 24370: 24365: 24364: 24361: 24354: 24350: 24344: 24343:Carroll, Sean 24341: 24340: 24327: 24323: 24319: 24315: 24311: 24307: 24303: 24296: 24288: 24284: 24280: 24276: 24272: 24269:(in German). 24268: 24264: 24260: 24254: 24246: 24242: 24238: 24234: 24230: 24227:(in German). 24226: 24222: 24218: 24212: 24204: 24200: 24196: 24192: 24188: 24184: 24180: 24176: 24172: 24168: 24163: 24158: 24154: 24150: 24142: 24133: 24128: 24124: 24120: 24116: 24112: 24108: 24101: 24092: 24087: 24083: 24079: 24074: 24069: 24065: 24061: 24057: 24050: 24041: 24036: 24031: 24026: 24022: 24018: 24014: 24007: 23999: 23993: 23985: 23981: 23977: 23973: 23968: 23963: 23959: 23955: 23948: 23940: 23934: 23925: 23920: 23916: 23912: 23907: 23902: 23898: 23894: 23890: 23883: 23875: 23871: 23867: 23863: 23859: 23855: 23850: 23845: 23841: 23837: 23836:Phys. Lett. B 23830: 23822: 23818: 23814: 23810: 23806: 23802: 23797: 23792: 23788: 23784: 23777: 23775: 23765: 23760: 23753: 23744: 23739: 23732: 23724: 23720: 23716: 23712: 23708: 23704: 23699: 23694: 23690: 23686: 23679: 23677: 23668: 23664: 23660: 23656: 23652: 23648: 23643: 23638: 23634: 23630: 23623: 23621: 23619: 23610: 23606: 23602: 23598: 23594: 23590: 23585: 23580: 23576: 23572: 23571:Phys. Lett. B 23565: 23563: 23561: 23559: 23557: 23555: 23546: 23539: 23530: 23525: 23518: 23510: 23504: 23495: 23490: 23486: 23482: 23477: 23472: 23468: 23464: 23460: 23453: 23445: 23441: 23437: 23433: 23428: 23423: 23419: 23415: 23411: 23404: 23396: 23392: 23388: 23384: 23380: 23376: 23371: 23366: 23362: 23358: 23351: 23349: 23347: 23338: 23334: 23330: 23326: 23322: 23318: 23314: 23310: 23306: 23302: 23298: 23291: 23283: 23279: 23275: 23271: 23267: 23263: 23258: 23257:gr-qc/9611009 23253: 23249: 23245: 23238: 23230: 23226: 23222: 23218: 23214: 23210: 23206: 23202: 23197: 23192: 23189:(3): 031101. 23188: 23184: 23177: 23169: 23165: 23161: 23157: 23153: 23149: 23144: 23139: 23136:(1): 015022. 23135: 23131: 23124: 23116: 23112: 23108: 23104: 23100: 23096: 23091: 23086: 23082: 23078: 23071: 23063: 23059: 23055: 23051: 23047: 23043: 23039: 23035: 23030: 23029:gr-qc/9504032 23025: 23021: 23017: 23010: 23002: 22998: 22993: 22992:gr-qc/9312030 22988: 22984: 22983: 22975: 22967: 22963: 22959: 22955: 22951: 22947: 22943: 22939: 22934: 22933:gr-qc/9506033 22929: 22925: 22921: 22914: 22906: 22902: 22898: 22894: 22890: 22886: 22881: 22876: 22873:(4): 044032. 22872: 22868: 22861: 22846: 22845: 22840: 22836: 22830: 22822: 22818: 22814: 22810: 22806: 22802: 22797: 22792: 22788: 22784: 22777: 22762: 22761: 22756: 22749: 22733: 22732: 22727: 22721: 22713: 22709: 22705: 22701: 22697: 22693: 22688: 22683: 22679: 22675: 22668: 22660: 22656: 22652: 22648: 22644: 22640: 22635: 22634:gr-qc/0506021 22630: 22626: 22622: 22615: 22613: 22604: 22600: 22596: 22592: 22588: 22584: 22579: 22574: 22570: 22566: 22559: 22557: 22548: 22544: 22540: 22536: 22532: 22528: 22523: 22522:gr-qc/0202012 22518: 22514: 22510: 22503: 22495: 22491: 22487: 22483: 22479: 22475: 22470: 22469:gr-qc/9411006 22465: 22461: 22457: 22450: 22448: 22438: 22432: 22426: 22418: 22414: 22410: 22406: 22401: 22396: 22393:(8): 083509. 22392: 22388: 22381: 22379: 22377: 22368: 22364: 22360: 22356: 22352: 22348: 22344: 22340: 22335: 22330: 22326: 22322: 22314: 22306: 22302: 22298: 22294: 22290: 22286: 22282: 22278: 22274: 22270: 22265: 22260: 22256: 22252: 22245: 22237: 22233: 22229: 22225: 22221: 22217: 22213: 22209: 22204: 22199: 22196:(6): 064046. 22195: 22191: 22184: 22176: 22172: 22168: 22164: 22160: 22156: 22152: 22148: 22143: 22138: 22135:(8): 084003. 22134: 22130: 22123: 22115: 22111: 22107: 22103: 22099: 22095: 22091: 22087: 22083: 22079: 22072: 22064: 22060: 22056: 22052: 22048: 22044: 22040: 22036: 22031: 22026: 22023:(3): 031101. 22022: 22018: 22011: 22004: 22001:(edited by), 22000: 21994: 21990: 21986: 21982: 21978: 21974: 21969: 21968:gr-qc/0611006 21964: 21960: 21956: 21949: 21940: 21935: 21928: 21919: 21911: 21907: 21903: 21899: 21895: 21891: 21887: 21883: 21876: 21867: 21865: 21863: 21861: 21859: 21850: 21846: 21842: 21838: 21834: 21830: 21826: 21819: 21817: 21815: 21806: 21803:(in German). 21802: 21798: 21794: 21788: 21786: 21784: 21775: 21771: 21767: 21763: 21759: 21755: 21748: 21746: 21744: 21742: 21740: 21731: 21727: 21723: 21719: 21715: 21711: 21704: 21702: 21700: 21691: 21687: 21683: 21679: 21675: 21671: 21664: 21662: 21660: 21658: 21649: 21645: 21641: 21637: 21633: 21629: 21622: 21620: 21618: 21609: 21605: 21600: 21595: 21591: 21587: 21583: 21579: 21575: 21571: 21564: 21562: 21560: 21558: 21549: 21545: 21541: 21537: 21533: 21529: 21525: 21518: 21516: 21514: 21512: 21502: 21497: 21493: 21489: 21485: 21481: 21477: 21470: 21468: 21466: 21464: 21462: 21453: 21449: 21445: 21441: 21437: 21433: 21426: 21424: 21422: 21413: 21409: 21405: 21401: 21397: 21393: 21389: 21385: 21378: 21376: 21374: 21365: 21361: 21357: 21353: 21349: 21345: 21338: 21336: 21334: 21325: 21321: 21317: 21313: 21309: 21305: 21298: 21296: 21294: 21292: 21282: 21277: 21273: 21269: 21265: 21261: 21257: 21250: 21248: 21246: 21237: 21233: 21229: 21225: 21221: 21217: 21213: 21206: 21204: 21202: 21193: 21189: 21185: 21181: 21177: 21173: 21169: 21165: 21158: 21156: 21154: 21152: 21142: 21137: 21133: 21129: 21125: 21121: 21117: 21110: 21108: 21106: 21104: 21102: 21100: 21091: 21087: 21083: 21079: 21076:(1): 76–101. 21075: 21071: 21064: 21062: 21060: 21050: 21048: 21039: 21035: 21031: 21027: 21023: 21019: 21012: 21010: 21001: 20997: 20993: 20989: 20985: 20981: 20974: 20972: 20970: 20968: 20966: 20957: 20953: 20949: 20945: 20941: 20937: 20933: 20929: 20925: 20919: 20917: 20915: 20913: 20911: 20902: 20898: 20894: 20890: 20886: 20882: 20875: 20873: 20864: 20860: 20856: 20852: 20848: 20844: 20837: 20835: 20833: 20831: 20822: 20818: 20814: 20810: 20803: 20801: 20799: 20797: 20795: 20786: 20782: 20778: 20774: 20770: 20766: 20759: 20757: 20755: 20753: 20751: 20742: 20738: 20734: 20730: 20726: 20722: 20715: 20713: 20711: 20709: 20699: 20697: 20695: 20686: 20682: 20678: 20674: 20670: 20666: 20662: 20658: 20654: 20650: 20643: 20641: 20639: 20637: 20628: 20624: 20620: 20616: 20612: 20609:(in German). 20608: 20604: 20597: 20593: 20589: 20585: 20581: 20578:(in German). 20577: 20573: 20567: 20565: 20563: 20554: 20550: 20546: 20542: 20538: 20534: 20530: 20526: 20522: 20519:(in German). 20518: 20514: 20508: 20506: 20504: 20495: 20491: 20487: 20480: 20478: 20476: 20468: 20462: 20460: 20451: 20447: 20442: 20437: 20432: 20427: 20423: 20419: 20415: 20411: 20407: 20400: 20398: 20389: 20385: 20381: 20377: 20373: 20369: 20365: 20361: 20354: 20352: 20342: 20337: 20333: 20329: 20322: 20318: 20312: 20310: 20301: 20298:(in French). 20297: 20293: 20289: 20283: 20281: 20279: 20269: 20263: 20258: 20250: 20246: 20242: 20238: 20234: 20230: 20223: 20221: 20219: 20217: 20215: 20213: 20211: 20209: 20207: 20199: 20193: 20191: 20189: 20187: 20185: 20183: 20181: 20174: 20168: 20160: 20156: 20152: 20148: 20144: 20140: 20133: 20131: 20129: 20127: 20125: 20123: 20121: 20113: 20107: 20100: 20094: 20092: 20090: 20088: 20086: 20079: 20075: 20069: 20060: 20058: 20049: 20045: 20041: 20037: 20033: 20029: 20025: 20018: 20016: 20006: 20001: 19994: 19986: 19982: 19977: 19972: 19968: 19964: 19959: 19954: 19950: 19946: 19941: 19936: 19932: 19928: 19924: 19917: 19915: 19913: 19904: 19900: 19896: 19892: 19888: 19884: 19879: 19874: 19870: 19863: 19861: 19856: 19849: 19832: 19828: 19812: 19810: 19806: 19790: 19787: 19784: 19774: 19758: 19754: 19739: 19736: 19733: 19730: 19727: 19724: 19721: 19719: 19702: 19699: 19689: 19675: 19672: 19665: 19662: 19661: 19657: 19654: 19651: 19648: 19645: 19642: 19639: 19637: 19623: 19620: 19617: 19610: 19596: 19593: 19586: 19583: 19582: 19578: 19575: 19559: 19555: 19547: 19544: 19541: 19538: 19535: 19533: 19519: 19516: 19513: 19506: 19492: 19489: 19482: 19479: 19478: 19474: 19471: 19468: 19465: 19462: 19459: 19456: 19454: 19437: 19434: 19424: 19410: 19407: 19400: 19397: 19396: 19392: 19389: 19386: 19383: 19380: 19377: 19374: 19372: 19355: 19352: 19342: 19328: 19325: 19318: 19315: 19314: 19297: 19293: 19285: 19282: 19266: 19262: 19254: 19251: 19237: 19234: 19231: 19228: 19225: 19218: 19215: 19201: 19198: 19195: 19192: 19189: 19182: 19180: 19166: 19159: 19145: 19138: 19135: 19134: 19130: 19127: 19124: 19121: 19118: 19115: 19112: 19110: 19107: 19104: 19101: 19100: 19096: 19093: 19090: 19087: 19084: 19081: 19078: 19076: 19073: 19070: 19067: 19066: 19062: 19059: 19056: 19053: 19050: 19047: 19044: 19042: 19039: 19036: 19033: 19032: 19028: 19025: 19022: 19019: 19016: 19013: 18999: 18996: 18993: 18990: 18987: 18980: 18978: 18960: 18957: 18951: 18946: 18943: 18933: 18919: 18912: 18909: 18908: 18904: 18901: 18898: 18895: 18892: 18889: 18886: 18884: 18881: 18878: 18875: 18874: 18870: 18867: 18864: 18861: 18858: 18855: 18852: 18850: 18847: 18844: 18841: 18840: 18836: 18835: 18831: 18828: 18825: 18822: 18819: 18803: 18799: 18791: 18775: 18771: 18763: 18760: 18744: 18740: 18736: 18729: 18713: 18709: 18704: 18698: 18694: 18690: 18683: 18680: 18679: 18675: 18672: 18669: 18666: 18663: 18647: 18643: 18635: 18619: 18615: 18607: 18593: 18586: 18572: 18565: 18549: 18545: 18540: 18534: 18530: 18526: 18519: 18516: 18515: 18511: 18510: 18506: 18503: 18500: 18497: 18494: 18478: 18474: 18466: 18450: 18446: 18438: 18435: 18421: 18414: 18400: 18393: 18391:Lightman–Lee 18390: 18389: 18385: 18382: 18379: 18376: 18373: 18357: 18353: 18345: 18342: 18339: 18336: 18333: 18330: 18329: 18325: 18322: 18319: 18316: 18313: 18299: 18296: 18291: 18287: 18282: 18276: 18272: 18264: 18261: 18258: 18255: 18252: 18249: 18248: 18244: 18243: 18239: 18236: 18233: 18230: 18227: 18211: 18207: 18199: 18196: 18193: 18190: 18187: 18184: 18183: 18179: 18176: 18173: 18170: 18167: 18151: 18147: 18139: 18123: 18119: 18111: 18108: 18094: 18087: 18073: 18066: 18063: 18062: 18058: 18057: 18053: 18050: 18047: 18044: 18041: 18038: 18035: 18032: 18029: 18011: 18008: 18005: 18000: 17997: 17994: 17983: 17980: 17979: 17975: 17972: 17969: 17966: 17963: 17960: 17957: 17954: 17940: 17933: 17915: 17912: 17909: 17904: 17901: 17898: 17887: 17885: 17881: 17880: 17876: 17873: 17870: 17867: 17864: 17861: 17858: 17855: 17841: 17834: 17816: 17813: 17810: 17805: 17802: 17799: 17788: 17785: 17784: 17780: 17779: 17775: 17772: 17769: 17766: 17763: 17760: 17757: 17754: 17751: 17748: 17745: 17744: 17727: 17723: 17699: 17695: 17671: 17667: 17643: 17639: 17615: 17611: 17587: 17583: 17559: 17555: 17533: 17512: 17491: 17482: 17481: 17478: 17476: 17471: 17458: 17455: 17451: 17447: 17443: 17439: 17434: 17432: 17421: 17419: 17412: 17385: 17381: 17377: 17372: 17368: 17364: 17359: 17355: 17351: 17346: 17342: 17338: 17333: 17329: 17321: 17304: 17300: 17296: 17291: 17287: 17283: 17278: 17274: 17266: 17251: 17244: 17229: 17222: 17207: 17200: 17199: 17198: 17185: 17180: 17176: 17172: 17167: 17163: 17159: 17154: 17150: 17146: 17141: 17137: 17133: 17128: 17124: 17120: 17115: 17111: 17107: 17102: 17098: 17094: 17091: 17088: 17085: 17082: 17079: 17070: 17066: 17064: 17058: 17048: 17046: 17042: 17038: 17034: 17030: 17024: 17020: 17007: 17003: 16991: 16987: 16980: 16970: 16961: 16959: 16958:Shapiro delay 16955: 16951: 16947: 16941: 16931: 16915: 16907: 16891: 16883: 16882:four-velocity 16867: 16845: 16842: 16838: 16832: 16829: 16825: 16821: 16818: 16796: 16792: 16786: 16782: 16776: 16773: 16769: 16765: 16762: 16742: 16722: 16713: 16704: 16702: 16692: 16687: 16677: 16670: 16666: 16662: 16659: 16655: 16652: 16648: 16645: 16641: 16640: 16639: 16637: 16629: 16625: 16621: 16618: 16614: 16611: 16607: 16604: 16600: 16596: 16593: 16590: 16586: 16583: 16579: 16578: 16577: 16569: 16553: 16549: 16545: 16542: 16532: 16516: 16496: 16488: 16472: 16450: 16446: 16442: 16439: 16429: 16425: 16420: 16418: 16414: 16410: 16406: 16402: 16398: 16394: 16389: 16387: 16383: 16379: 16375: 16370: 16368: 16364: 16360: 16356: 16350: 16348: 16344: 16340: 16336: 16332: 16328: 16324: 16320: 16316: 16306: 16304: 16300: 16281: 16275: 16251: 16247: 16241: 16235: 16232: 16229: 16224: 16221: 16215: 16209: 16206: 16201: 16196: 16186: 16183: 16180: 16173: 16172: 16171: 16169: 16165: 16159: 16149: 16135: 16110: 16105: 16099: 16095: 16089: 16085: 16080: 16075: 16070: 16067: 16062: 16057: 16053: 16047: 16043: 16037: 16033: 16027: 16024: 16019: 16016: 16010: 16004: 15997: 15996: 15995: 15978: 15974: 15967: 15961: 15958: 15955: 15950: 15941: 15936: 15925: 15922: 15918: 15912: 15909: 15903: 15896: 15891: 15887: 15882: 15877: 15873: 15866: 15860: 15857: 15854: 15849: 15840: 15835: 15824: 15821: 15817: 15811: 15808: 15802: 15796: 15793: 15788: 15784: 15777: 15771: 15768: 15765: 15760: 15751: 15746: 15735: 15732: 15728: 15722: 15719: 15713: 15705: 15701: 15697: 15690: 15687: 15681: 15676: 15672: 15668: 15665: 15662: 15657: 15653: 15645: 15644: 15629: 15624: 15620: 15614: 15606: 15601: 15597: 15591: 15583: 15578: 15575: 15571: 15560: 15556: 15549: 15543: 15540: 15535: 15532: 15528: 15522: 15519: 15515: 15509: 15506: 15500: 15496: 15491: 15488: 15482: 15477: 15473: 15469: 15466: 15463: 15458: 15454: 15446: 15445: 15444: 15430: 15408: 15404: 15383: 15380: 15377: 15374: 15371: 15351: 15346: 15342: 15319: 15315: 15311: 15306: 15302: 15298: 15293: 15289: 15285: 15280: 15276: 15272: 15269: 15261: 15255: 15245: 15243: 15224: 15221: 15218: 15215: 15211: 15185: 15182: 15178: 15172: 15164: 15159: 15156: 15152: 15146: 15138: 15133: 15130: 15127: 15123: 15115: 15114: 15113: 15093: 15089: 15083: 15073: 15070: 15066: 15060: 15057: 15054: 15051: 15047: 15042: 15037: 15033: 15029: 15026: 15021: 15018: 15014: 15006: 15005: 14988: 14982: 14979: 14975: 14969: 14966: 14962: 14956: 14952: 14946: 14943: 14938: 14933: 14930: 14927: 14923: 14917: 14914: 14911: 14907: 14901: 14898: 14892: 14886: 14883: 14877: 14872: 14868: 14864: 14861: 14856: 14852: 14844: 14843: 14842: 14822: 14818: 14814: 14809: 14806: 14802: 14798: 14793: 14789: 14785: 14780: 14776: 14772: 14769: 14762: 14761: 14760: 14743: 14739: 14715: 14712: 14708: 14698: 14683: 14675: 14670: 14666: 14650: 14647: 14639: 14636: 14629: 14625: 14622: 14619: 14614: 14610: 14586: 14582: 14558: 14555: 14551: 14524: 14521: 14514: 14490: 14486: 14464: 14440: 14434: 14408: 14404: 14398: 14394: 14388: 14385: 14381: 14375: 14372: 14367: 14363: 14354: 14351: 14344: 14338: 14335: 14331: 14325: 14321: 14315: 14312: 14307: 14304: 14301: 14298: 14292: 14286: 14282: 14276: 14273: 14268: 14263: 14259: 14251: 14250: 14249: 14232: 14228: 14201: 14197: 14193: 14188: 14184: 14180: 14177: 14170: 14169: 14168: 14151: 14148: 14144: 14134: 14132: 14128: 14105: 14099: 14096: 14092: 14087: 14081: 14078: 14075: 14071: 14066: 14061: 14058: 14054: 14046: 14045: 14044: 14030: 14027: 14022: 14019: 14016: 14013: 14010: 14007: 14004: 14001: 13998: 13994: 13990: 13987: 13979: 13956: 13953: 13945: 13937: 13934: 13931: 13919: 13915: 13911: 13907: 13900: 13897: 13894: 13888: 13885: 13879: 13873: 13870: 13867: 13862: 13859: 13853: 13851: 13844: 13840: 13832: 13829: 13825: 13821: 13818: 13811: 13807: 13803: 13799: 13795: 13788: 13784: 13780: 13777: 13773: 13766: 13763: 13760: 13757: 13750: 13744: 13740: 13737: 13731: 13729: 13722: 13718: 13706: 13705: 13704: 13701: 13688: 13685: 13682: 13656: 13653: 13650: 13643: 13635: 13632: 13629: 13621: 13617: 13608: 13605: 13600: 13594: 13588: 13581: 13580: 13579: 13559: 13556: 13553: 13550: 13547: 13544: 13540: 13513: 13510: 13500: 13472: 13447: 13444: 13441: 13434: 13413: 13410: 13407: 13382: 13379: 13373: 13370: 13365: 13361: 13355: 13351: 13347: 13344: 13339: 13336: 13332: 13326: 13323: 13319: 13315: 13310: 13307: 13297: 13286: 13270: 13266: 13260: 13256: 13252: 13247: 13244: 13240: 13236: 13231: 13228: 13224: 13216: 13215: 13214: 13193: 13188: 13184: 13177: 13174: 13168: 13164: 13161: 13156: 13151: 13142: 13138: 13133: 13129: 13125: 13120: 13117: 13107: 13099: 13095: 13092: 13089: 13087: 13080: 13076: 13068: 13063: 13059: 13052: 13049: 13043: 13038: 13034: 13031: 13026: 13022: 13016: 13012: 13006: 13003: 12999: 12994: 12988: 12984: 12981: 12975: 12967: 12964: 12961: 12954: 12945: 12942: 12939: 12932: 12926: 12923: 12919: 12913: 12910: 12906: 12901: 12897: 12891: 12888: 12885: 12881: 12876: 12873: 12871: 12864: 12860: 12852: 12847: 12843: 12836: 12833: 12827: 12818: 12814: 12810: 12807: 12801: 12796: 12792: 12786: 12783: 12778: 12774: 12770: 12765: 12762: 12757: 12752: 12749: 12745: 12739: 12736: 12732: 12726: 12723: 12719: 12713: 12709: 12704: 12700: 12695: 12692: 12687: 12684: 12682: 12675: 12671: 12659: 12658: 12657: 12638: 12634: 12630: 12625: 12621: 12617: 12612: 12608: 12604: 12599: 12595: 12591: 12588: 12581: 12580: 12579: 12563: 12559: 12537: 12517: 12509: 12505: 12485: 12481: 12476: 12470: 12466: 12462: 12457: 12453: 12426: 12403: 12379: 12375: 12370: 12361: 12356: 12345: 12342: 12338: 12332: 12327: 12323: 12318: 12308: 12299: 12296: 12293: 12287: 12282: 12278: 12272: 12269: 12266: 12259: 12258: 12257: 12240: 12237: 12234: 12230: 12223: 12218: 12214: 12207: 12197: 12183: 12179: 12173: 12170: 12167: 12161: 12156: 12152: 12146: 12143: 12140: 12133: 12132: 12131: 12129: 12121: 12118: 12115: 12112: 12111: 12110: 12107: 12102: 12098: 12094: 12084: 12082: 12061: 12055: 12052: 12048: 12044: 12039: 12034: 12031: 12027: 12023: 12018: 12013: 12010: 12006: 12001: 11993: 11989: 11984: 11981: 11978: 11972: 11967: 11964: 11960: 11956: 11951: 11948: 11943: 11938: 11935: 11931: 11923: 11922: 11921: 11919: 11914: 11910: 11906: 11905:negative mass 11901: 11899: 11895: 11891: 11887: 11883: 11873: 11853: 11850: 11846: 11840: 11836: 11830: 11826: 11818: 11817: 11816: 11813: 11794: 11788: 11762: 11758: 11754: 11749: 11745: 11738: 11735: 11729: 11724: 11720: 11716: 11710: 11707: 11704: 11700: 11695: 11692: 11685: 11684: 11683: 11666: 11662: 11637: 11631: 11610: 11586: 11580: 11571: 11552: 11543: 11540: 11536: 11532: 11529: 11524: 11521: 11517: 11511: 11508: 11503: 11498: 11495: 11491: 11486: 11479: 11476: 11473: 11469: 11464: 11459: 11456: 11452: 11444: 11443: 11442: 11423: 11419: 11414: 11411: 11407: 11401: 11398: 11393: 11388: 11385: 11381: 11376: 11369: 11366: 11363: 11359: 11354: 11349: 11346: 11342: 11334: 11333: 11332: 11312: 11308: 11304: 11300: 11295: 11291: 11284: 11281: 11270: 11267: 11264: 11258: 11252: 11249: 11246: 11242: 11237: 11234: 11227: 11226: 11225: 11205: 11201: 11197: 11193: 11188: 11184: 11177: 11174: 11169: 11166: 11160: 11157: 11154: 11150: 11145: 11142: 11135: 11134: 11133: 11116: 11113: 11107: 11104: 11101: 11098: 11093: 11089: 11080: 11077: 11072: 11069: 11064: 11052: 11051: 11050: 11033: 11030: 11024: 11021: 11018: 11015: 11012: 11007: 10995: 10994: 10993: 10990: 10975: 10972: 10938: 10934: 10930: 10920: 10918: 10914: 10910: 10905: 10902: 10897: 10888: 10879: 10877: 10873: 10868: 10866: 10861: 10841: 10836: 10823: 10818: 10814: 10808: 10805: 10801: 10797: 10792: 10787: 10783: 10777: 10774: 10770: 10766: 10761: 10756: 10752: 10746: 10743: 10739: 10729: 10726: 10723: 10719: 10714: 10709: 10706: 10702: 10694: 10693: 10692: 10674: 10671: 10667: 10643: 10640: 10635: 10630: 10626: 10617: 10598: 10595: 10592: 10589: 10585: 10561: 10556: 10552: 10522: 10518: 10512: 10507: 10503: 10499: 10496: 10494: 10487: 10483: 10470: 10465: 10461: 10457: 10452: 10447: 10443: 10439: 10436: 10434: 10427: 10422: 10408: 10405: 10402: 10399: 10395: 10389: 10385: 10379: 10375: 10369: 10366: 10362: 10356: 10351: 10340: 10337: 10334: 10330: 10325: 10323: 10318: 10307: 10306: 10305: 10301: 10297: 10292: 10288: 10278: 10276: 10266: 10252: 10249: 10246: 10243: 10240: 10237: 10234: 10231: 10228: 10205: 10202: 10199: 10196: 10193: 10189: 10186: 10183: 10180: 10176: 10173: 10170: 10167: 10160: 10159: 10158: 10141: 10138: 10135: 10131: 10128: 10125: 10122: 10119: 10116: 10113: 10110: 10103: 10102: 10101: 10083: 10078: 10074: 10051: 10048: 10044: 10023: 10018: 10015: 10012: 10008: 10004: 9999: 9996: 9993: 9989: 9985: 9980: 9977: 9973: 9965: 9964: 9963: 9949: 9946: 9943: 9940: 9937: 9934: 9931: 9906: 9902: 9898: 9894: 9888: 9885: 9882: 9878: 9872: 9869: 9866: 9862: 9858: 9855: 9850: 9847: 9843: 9837: 9834: 9830: 9826: 9823: 9818: 9815: 9811: 9805: 9801: 9795: 9791: 9787: 9784: 9781: 9776: 9772: 9766: 9762: 9758: 9755: 9752: 9748: 9742: 9739: 9734: 9729: 9725: 9721: 9715: 9712: 9709: 9705: 9700: 9697: 9690: 9689: 9688: 9674: 9669: 9665: 9655: 9646: 9644: 9639: 9635: 9614: 9590: 9584: 9558: 9555: 9552: 9549: 9544: 9541: 9538: 9535: 9529: 9523: 9517: 9510: 9509: 9508: 9486: 9483: 9472: 9466: 9463: 9457: 9454: 9451: 9445: 9442: 9433: 9430: 9424: 9418: 9415: 9409: 9406: 9403: 9400: 9388: 9382: 9377: 9374: 9368: 9363: 9360: 9354: 9351: 9345: 9339: 9332: 9331: 9330: 9315: 9292: 9289: 9281: 9275: 9266: 9260: 9257: 9254: 9251: 9245: 9242: 9221: 9200: 9191: 9176: 9169:Brans–Dicke, 9167: 9165: 9149: 9140: 9126: 9123: 9120: 9111: 9108: 9093: 9070: 9066: 9041: 9035: 9011: 9005: 8977: 8974: 8970: 8966: 8959: 8955: 8951: 8941: 8936: 8911: 8899: 8896: 8892: 8884: 8883: 8865: 8861: 8855: 8851: 8844: 8838: 8833: 8829: 8825: 8822: 8817: 8813: 8805: 8804: 8785: 8779: 8776: 8773: 8770: 8767: 8762: 8753: 8748: 8737: 8734: 8730: 8724: 8717: 8711: 8705: 8702: 8699: 8696: 8691: 8687: 8679: 8678: 8660: 8656: 8652: 8647: 8643: 8637: 8634: 8629: 8624: 8620: 8616: 8610: 8607: 8604: 8600: 8595: 8592: 8585: 8584: 8583: 8566: 8562: 8540: 8531: 8528: 8526: 8522: 8517: 8513: 8509: 8505: 8501: 8497: 8493: 8483: 8466: 8455: 8451: 8435: 8431: 8427: 8423: 8417: 8414: 8410: 8404: 8401: 8397: 8393: 8390: 8385: 8382: 8379: 8376: 8372: 8366: 8363: 8360: 8357: 8353: 8349: 8344: 8340: 8335: 8329: 8325: 8321: 8318: 8313: 8309: 8305: 8300: 8296: 8284: 8281: 8276: 8262: 8261: 8260: 8252: 8250: 8232: 8229: 8224: 8220: 8197: 8193: 8170: 8166: 8142: 8139: 8136: 8132: 8125: 8120: 8116: 8112: 8107: 8101: 8097: 8093: 8090: 8086: 8079: 8074: 8070: 8066: 8061: 8055: 8051: 8047: 8043: 8036: 8031: 8027: 8023: 8018: 8012: 8008: 8004: 7997: 7996: 7995: 7978: 7974: 7968: 7965: 7962: 7959: 7955: 7950: 7943: 7938: 7934: 7930: 7925: 7919: 7915: 7909: 7906: 7903: 7900: 7896: 7892: 7887: 7884: 7880: 7875: 7868: 7863: 7859: 7855: 7850: 7844: 7840: 7834: 7831: 7827: 7823: 7820: 7816: 7809: 7804: 7800: 7796: 7791: 7785: 7781: 7777: 7774: 7771: 7766: 7761: 7757: 7752: 7746: 7743: 7738: 7724: 7723: 7722: 7720: 7711: 7694: 7688: 7662: 7656: 7651: 7648: 7643: 7629: 7628: 7627: 7605: 7601: 7595: 7592: 7589: 7586: 7582: 7576: 7573: 7570: 7567: 7563: 7557: 7553: 7549: 7544: 7541: 7537: 7531: 7528: 7524: 7518: 7514: 7510: 7505: 7501: 7495: 7491: 7487: 7484: 7480: 7474: 7471: 7466: 7452: 7451: 7450: 7442: 7424: 7420: 7414: 7411: 7408: 7405: 7401: 7395: 7392: 7389: 7386: 7382: 7378: 7373: 7370: 7366: 7360: 7357: 7353: 7349: 7346: 7341: 7337: 7333: 7330: 7326: 7320: 7317: 7312: 7298: 7297: 7296: 7288: 7274: 7266: 7246: 7237: 7233: 7229: 7223: 7219: 7213: 7210: 7206: 7200: 7197: 7192: 7178: 7177: 7176: 7174: 7168: 7158: 7156: 7152: 7148: 7144: 7143:metric tensor 7134: 7132: 7128: 7124: 7119: 7102: 7099: 7095: 7085: 7063: 7059: 7055: 7051: 7045: 7037: 7034: 7030: 7024: 7016: 7013: 7009: 7005: 7000: 6992: 6987: 6983: 6977: 6972: 6964: 6960: 6956: 6951: 6946: 6938: 6934: 6928: 6925: 6920: 6911: 6907: 6904: 6899: 6889: 6886: 6882: 6876: 6873: 6868: 6859: 6855: 6851: 6845: 6842: 6837: 6832: 6828: 6824: 6818: 6815: 6812: 6808: 6803: 6800: 6793: 6792: 6791: 6771: 6768: 6764: 6760: 6755: 6752: 6748: 6744: 6739: 6736: 6732: 6724: 6723: 6722: 6705: 6702: 6698: 6687: 6664: 6660: 6656: 6650: 6646: 6642: 6636: 6633: 6629: 6625: 6623: 6616: 6612: 6608: 6601: 6595: 6592: 6585: 6581: 6577: 6571: 6563: 6559: 6551: 6546: 6536: 6532: 6523: 6513: 6509: 6502: 6500: 6493: 6489: 6481: 6478: 6475: 6470: 6460: 6456: 6447: 6437: 6433: 6425: 6420: 6410: 6406: 6399: 6394: 6390: 6386: 6384: 6377: 6367: 6363: 6348: 6347: 6346: 6329: 6325: 6303: 6278: 6273: 6267: 6259: 6253: 6249: 6245: 6240: 6237: 6231: 6221: 6211: 6207: 6196: 6191: 6187: 6181: 6176: 6172: 6161: 6152: 6148: 6145: 6140: 6137: 6133: 6129: 6121: 6117: 6108: 6105: 6101: 6093: 6092: 6091: 6076: 6068: 6051: 6043: 6033: 6016: 6012: 5988: 5985: 5981: 5954: 5950: 5944: 5940: 5934: 5931: 5927: 5923: 5920: 5897: 5894: 5891: 5887: 5882: 5879: 5873: 5867: 5860: 5859: 5858: 5839: 5835: 5831: 5826: 5823: 5820: 5816: 5810: 5807: 5804: 5800: 5793: 5787: 5782: 5779: 5773: 5768: 5764: 5760: 5754: 5751: 5748: 5744: 5739: 5736: 5729: 5728: 5727: 5709: 5703: 5698: 5694: 5683: 5680: 5676: 5666: 5660: 5657: 5653: 5646: 5642: 5638: 5633: 5630: 5627: 5624: 5621: 5618: 5613: 5609: 5603: 5600: 5596: 5592: 5589: 5584: 5581: 5577: 5571: 5567: 5563: 5556: 5555: 5554: 5535: 5531: 5527: 5519: 5516: 5512: 5506: 5503: 5499: 5495: 5492: 5487: 5479: 5476: 5472: 5466: 5458: 5455: 5451: 5447: 5439: 5436: 5431: 5426: 5422: 5418: 5412: 5409: 5406: 5402: 5397: 5394: 5387: 5386: 5385: 5370: 5349: 5326: 5323: 5319: 5313: 5310: 5306: 5302: 5299: 5276: 5273: 5269: 5240: 5235: 5232: 5228: 5222: 5219: 5213: 5208: 5205: 5201: 5192: 5188: 5184: 5179: 5176: 5173: 5170: 5167: 5162: 5154: 5151: 5147: 5141: 5133: 5130: 5126: 5120: 5117: 5113: 5107: 5104: 5100: 5096: 5091: 5088: 5084: 5078: 5074: 5066: 5065: 5047: 5043: 5039: 5031: 5023: 5020: 5016: 5010: 5002: 4999: 4995: 4989: 4986: 4980: 4975: 4967: 4964: 4960: 4954: 4946: 4943: 4939: 4930: 4927: 4923: 4917: 4914: 4910: 4904: 4901: 4897: 4891: 4888: 4882: 4877: 4873: 4869: 4863: 4860: 4857: 4853: 4848: 4845: 4838: 4837: 4836: 4833: 4829: 4803: 4799: 4794: 4785: 4780: 4769: 4766: 4762: 4755: 4752: 4746: 4743: 4738: 4729: 4724: 4713: 4710: 4706: 4702: 4699: 4694: 4685: 4680: 4669: 4666: 4662: 4655: 4652: 4646: 4642: 4633: 4630: 4627: 4624: 4616: 4613: 4607: 4603: 4598: 4594: 4586: 4585: 4584: 4570: 4546: 4542: 4537: 4528: 4523: 4512: 4508: 4501: 4498: 4492: 4489: 4484: 4475: 4470: 4459: 4456: 4452: 4445: 4442: 4435: 4429: 4425: 4421: 4416: 4412: 4404: 4403: 4402: 4384: 4378: 4374: 4370: 4367: 4362: 4358: 4354: 4351: 4346: 4342: 4338: 4334: 4328: 4324: 4320: 4315: 4311: 4307: 4301: 4297: 4293: 4288: 4284: 4280: 4273: 4272: 4271: 4257: 4237: 4211: 4205: 4200: 4196: 4192: 4189: 4186: 4183: 4178: 4168: 4158: 4155: 4151: 4143: 4142: 4126: 4120: 4116: 4112: 4109: 4104: 4100: 4096: 4093: 4088: 4084: 4080: 4076: 4067: 4061: 4058: 4054: 4050: 4045: 4041: 4037: 4029: 4023: 4020: 4017: 4013: 4009: 4004: 4000: 3996: 3989: 3988: 3987: 3970: 3964: 3941: 3935: 3926: 3905: 3901: 3896: 3887: 3882: 3872: 3866: 3863: 3860: 3856: 3852: 3847: 3844: 3840: 3835: 3831: 3826: 3823: 3820: 3816: 3810: 3807: 3803: 3798: 3792: 3789: 3785: 3781: 3778: 3775: 3772: 3769: 3762: 3761: 3760: 3744: 3740: 3719: 3716: 3693: 3688: 3679: 3674: 3663: 3660: 3656: 3652: 3649: 3646: 3643: 3640: 3635: 3631: 3623: 3622: 3605: 3601: 3597: 3592: 3588: 3582: 3579: 3574: 3569: 3565: 3561: 3555: 3552: 3549: 3545: 3540: 3537: 3530: 3529: 3528: 3525: 3521: 3518: 3513: 3499: 3495: 3491: 3488: 3485: 3482: 3457: 3452: 3445: 3436: 3432: 3427: 3419: 3416: 3413: 3410: 3404: 3400: 3393: 3384: 3380: 3375: 3371: 3368: 3365: 3362: 3355: 3351: 3345: 3336: 3329: 3324: 3319: 3312: 3308: 3304: 3299: 3294: 3291: 3284: 3280: 3276: 3271: 3267: 3260: 3256: 3252: 3247: 3243: 3236: 3235: 3234: 3216: 3213: 3210: 3205: 3196: 3192: 3187: 3183: 3178: 3174: 3166: 3162: 3158: 3153: 3149: 3145: 3142: 3139: 3135: 3128: 3124: 3120: 3115: 3111: 3104: 3103: 3102: 3084: 3081: 3078: 3073: 3064: 3060: 3055: 3051: 3046: 3043: 3040: 3036: 3029: 3025: 3021: 3016: 3012: 3005: 3004: 3003: 2979: 2975: 2972: 2967: 2961: 2955: 2945: 2941: 2936: 2932: 2923: 2916: 2912: 2908: 2903: 2899: 2895: 2892: 2889: 2885: 2878: 2874: 2870: 2865: 2861: 2854: 2853: 2852: 2829: 2825: 2822: 2818: 2810: 2806: 2801: 2797: 2794: 2788: 2785: 2782: 2774: 2770: 2765: 2761: 2755: 2748: 2747: 2746: 2743: 2729: 2700: 2696: 2693: 2687: 2684: 2677: 2676: 2675: 2658: 2655: 2652: 2649: 2644: 2636: 2632: 2628: 2622: 2618: 2615: 2612: 2605: 2604: 2603: 2600: 2596: 2586: 2584: 2580: 2576: 2566: 2563: 2561: 2558: 2555: 2554: 2551: 2550:Scalar–tensor 2548: 2546: 2543: 2540: 2539: 2536: 2535:Scalar–tensor 2533: 2531: 2529: 2526: 2523: 2522: 2519: 2517: 2515: 2511: 2510:Alan Lightman 2507: 2504: 2501: 2500: 2497: 2494: 2492: 2490: 2486: 2485:Alan Lightman 2483: 2480: 2479: 2476: 2475:Vector–tensor 2473: 2471: 2469: 2465: 2462: 2461: 2458: 2457:Vector–tensor 2455: 2453: 2451: 2447: 2444: 2441: 2440: 2437: 2434: 2432: 2430: 2427: 2424: 2423: 2420: 2417: 2415: 2413: 2410: 2407: 2406: 2403: 2400: 2398: 2396: 2393: 2390: 2389: 2386: 2385:Scalar–tensor 2383: 2381: 2378: 2375: 2374: 2371: 2369: 2367: 2364: 2361: 2360: 2357: 2354: 2352: 2349: 2346: 2345: 2342: 2341:Scalar–tensor 2339: 2337: 2335: 2332: 2329: 2328: 2325: 2322: 2320: 2317: 2314: 2313: 2310: 2307: 2305: 2302: 2301:Stanley Deser 2299: 2296: 2295: 2292: 2290: 2287: 2284: 2283: 2280: 2278: 2274: 2269: 2266: 2263: 2262: 2259: 2256: 2254: 2251: 2248: 2245: 2244: 2241: 2240:Scalar–tensor 2238: 2236: 2233: 2231: 2227: 2226:Carl H. Brans 2224: 2221: 2220: 2217: 2215: 2212: 2209: 2206: 2205: 2202: 2200: 2197: 2194: 2191: 2190: 2187: 2184: 2182: 2180:Otto Bergmann 2179: 2176: 2175: 2172: 2170: 2168: 2165: 2162: 2161: 2158: 2155: 2153: 2151: 2148: 2145: 2144: 2141: 2138: 2136: 2134: 2131: 2128: 2127: 2124: 2122: 2119: 2116: 2115: 2112: 2110: 2107: 2105: 2102: 2099: 2098: 2095: 2093: 2091: 2088: 2085: 2084: 2081: 2079: 2077: 2073: 2070: 2067: 2066: 2063: 2060: 2058: 2055: 2053: 2050: 2047: 2046: 2043: 2040: 2038: 2035: 2033: 2030: 2027: 2026: 2022: 2019: 2016: 2013: 2012: 2006: 2004: 1999: 1997: 1993: 1989: 1983: 1970: 1967: 1964: 1960: 1959: 1958: 1955: 1948: 1945: 1943: 1940: 1937: 1934: 1931: 1928: 1927: 1926: 1924: 1920: 1918: 1915:(see section 1911: 1908: 1903: 1900: 1898: 1894: 1891: 1890: 1889: 1886: 1882: 1878: 1875: 1873: 1869: 1868: 1867: 1864: 1860: 1857: 1855: 1852: 1849: 1847: 1844: 1841: 1838: 1835: 1832: 1830: 1827: 1826: 1825: 1822: 1818: 1815: 1812: 1809: 1807: 1804: 1801: 1798: 1795: 1792: 1789: 1788: 1787: 1784: 1779: 1775: 1772: 1770:Deser–Laurent 1769: 1766: 1765: 1763: 1760: 1755: 1751: 1748: 1745: 1742: 1739: 1736: 1733: 1730: 1727: 1724: 1722: 1718: 1714: 1711: 1708: 1705: 1702: 1699: 1698: 1696: 1693: 1692: 1691: 1688: 1686: 1682: 1663: 1658: 1655: 1642: 1624: 1611: 1592: 1589: 1585: 1558: 1555: 1551: 1545: 1540: 1537: 1529: 1524: 1521: 1517: 1511: 1506: 1503: 1495: 1490: 1487: 1480: 1477: 1473: 1467: 1462: 1459: 1455: 1449: 1441: 1438: 1431: 1430: 1429: 1427: 1410: 1390: 1364: 1360: 1356: 1350: 1346: 1342: 1336: 1333: 1329: 1325: 1322: 1317: 1312: 1309: 1300: 1299: 1298: 1296: 1277: 1274: 1270: 1262: 1261:metric tensor 1258: 1252: 1249: 1247: 1241: 1239: 1235: 1216: 1212: 1208: 1201: 1200: 1199: 1197: 1180: 1177: 1174: 1171: 1147: 1142: 1129: 1126: 1121: 1118: 1115: 1112: 1105: 1104: 1103: 1088: 1067: 1056: 1052: 1050: 1046: 1043: 1039: 1035: 1031: 1030: 1029: 1021: 1017: 1016:due to mass. 1015: 996: 992: 965: 962: 958: 948: 945: 937: 918: 910: 906: 902: 899: 878: 852: 848: 844: 841: 836: 832: 823: 820: 815: 812: 806: 803: 800: 794: 790: 784: 781: 774: 773: 772: 770: 751: 746: 742: 737: 734: 730: 724: 721: 716: 711: 708: 704: 699: 692: 689: 686: 680: 676: 670: 665: 662: 658: 650: 649: 648: 629: 625: 620: 617: 613: 607: 604: 599: 594: 591: 587: 582: 574: 570: 565: 562: 559: 553: 548: 545: 541: 533: 532: 514: 510: 506: 500: 496: 492: 486: 483: 479: 475: 470: 465: 462: 453: 452: 436: 433: 430: 427: 424: 421: 414: 413: 412: 408: 398: 381: 378: 374: 352: 347: 334: 315: 312: 308: 286: 281: 268: 264: 262: 259:. These have 258: 257:metric tensor 239: 236: 232: 223: 204: 201: 197: 188: 186: 181: 179: 175: 158: 150: 133: 124: 120: 110: 108: 104: 100: 96: 91: 87: 83: 74: 72: 68: 63: 61: 57: 53: 49: 43: 41: 37: 33: 29: 25: 21: 24940:theories and 24773:Supergravity 24586: 24582: 24519: 24502: 24444:Introduction 24309: 24305: 24295: 24270: 24266: 24253: 24228: 24224: 24211: 24152: 24148: 24141: 24114: 24110: 24100: 24063: 24059: 24049: 24020: 24016: 24006: 23992:cite journal 23957: 23953: 23947: 23933:cite journal 23896: 23893:Astrophys. J 23892: 23882: 23839: 23835: 23829: 23786: 23782: 23752: 23731: 23688: 23684: 23632: 23628: 23574: 23570: 23544: 23538: 23517: 23503:cite journal 23466: 23463:Astrophys. J 23462: 23452: 23417: 23413: 23403: 23360: 23356: 23304: 23300: 23290: 23247: 23243: 23237: 23186: 23182: 23176: 23133: 23129: 23123: 23080: 23076: 23070: 23019: 23015: 23009: 22981: 22974: 22923: 22919: 22913: 22870: 22866: 22860: 22848:. Retrieved 22842: 22829: 22786: 22782: 22776: 22764:. Retrieved 22760:Ars Technica 22758: 22748: 22736:. Retrieved 22729: 22720: 22677: 22673: 22667: 22624: 22620: 22568: 22564: 22512: 22508: 22502: 22459: 22455: 22437: 22425: 22390: 22386: 22324: 22320: 22313: 22254: 22250: 22244: 22193: 22189: 22183: 22132: 22128: 22122: 22081: 22077: 22071: 22020: 22016: 22010: 21999:Michel Weber 21961:(1): 41–61. 21958: 21954: 21948: 21927: 21918: 21885: 21881: 21875: 21832: 21828: 21804: 21800: 21793:Nordström, G 21757: 21753: 21713: 21709: 21673: 21669: 21631: 21627: 21573: 21569: 21531: 21527: 21483: 21479: 21435: 21431: 21387: 21383: 21350:(10): 2317. 21347: 21343: 21307: 21303: 21263: 21259: 21222:(3): 65–70. 21219: 21215: 21170:(1): 25–36. 21167: 21163: 21123: 21119: 21073: 21069: 21024:(1): 75–77. 21021: 21017: 20983: 20979: 20931: 20927: 20884: 20880: 20846: 20842: 20812: 20808: 20768: 20764: 20724: 20720: 20652: 20648: 20610: 20606: 20579: 20575: 20520: 20516: 20493: 20489: 20466: 20413: 20409: 20363: 20359: 20331: 20327: 20299: 20295: 20268: 20257: 20232: 20228: 20197: 20167: 20142: 20138: 20111: 20106: 20098: 20068: 20031: 20027: 20005:1705.04397v1 19993: 19930: 19926: 19868: 19818: 19775: 19745: 19136:Page–Tupper 17981:Brans–Dicke 17472: 17469: 17435: 17427: 17414: 17071: 17067: 17060: 17036: 17031: 17022: 17018: 17017:for this is 17005: 17001: 16989: 16985: 16982: 16967: 16943: 16714: 16710: 16707:Completeness 16698: 16689: 16674: 16633: 16592:anisotropies 16575: 16421: 16390: 16371: 16351: 16314: 16312: 16267: 16161: 16127: 15993: 15257: 15202: 15111: 14840: 14699: 14671: 14667: 14426: 14219: 14135: 14129:developed a 14127:J. W. Moffat 14125: 13975: 13702: 13674: 13528:. Note that 13400: 13212: 12655: 12395: 12255: 12125: 12108: 12104: 12077: 11902: 11882:Jamie Farnes 11879: 11871: 11814: 11780: 11572: 11569: 11440: 11330: 11223: 11131: 11048: 10991: 10940: 10906: 10898: 10894: 10885: 10869: 10862: 10859: 10543: 10302: 10298: 10294: 10272: 10220: 10156: 10099: 9923: 9656: 9652: 9640: 9636: 9576: 9506: 9192: 9190:is constant 9168: 9141: 9112: 9109: 8997: 8532: 8529: 8525:Kaluza–Klein 8521:Kaluza–Klein 8518: 8515: 8481: 8258: 8157: 7993: 7717: 7680: 7625: 7448: 7439: 7294: 7291:Gauss–Bonnet 7262: 7170: 7151:f(R) gravity 7140: 7120: 7081: 6789: 6688: 6685: 6295: 6039: 5972: 5856: 5725: 5552: 5260: 4834: 4831: 4562: 4400: 4229: 3927: 3921: 3708: 3526: 3522: 3516: 3514: 3474: 3232: 3100: 3001: 2850: 2744: 2717: 2673: 2601: 2598: 2571: 2544:B. M. Barker 2506:David L. Lee 2496:Scalar field 2489:David L. Lee 2436:Scalar field 2412:Nathan Rosen 2402:Scalar field 2395:Nathan Rosen 2324:Scalar field 2258:Scalar field 2186:Scalar field 2157:Scalar field 2140:Scalar field 2072:Markus Fierz 2023:Theory type 2020:Theory name 2000: 1985: 1951: 1921: 1914: 1904:Rosen (1975) 1800:f(R) gravity 1743:Rosen (1971) 1689: 1576: 1425: 1382: 1256: 1253: 1250: 1242: 1233: 1231: 1163: 1059: 1027: 1018: 870: 766: 646: 410: 265: 189: 182: 126: 92: 88: 84: 80: 64: 44: 19: 18: 24742:Causal sets 24636:Brans–Dicke 24454:Mathematics 24259:Einstein, A 24217:Einstein, A 23363:(10): 883. 22844:EurekAlert! 22766:October 27, 22738:October 29, 22680:: 382–385. 22327:(12): 100. 21835:(13): 533. 20986:(1): 1–67. 20887:: 179–200. 20849:(5): 1417. 20334:: 325–412. 19034:Papapetrou 17882:Nordtvedt, 16424:Lagrangians 16378:dark energy 16323:dark energy 16319:dark matter 15566:where 11888:proposed a 10909:dark energy 10891:Motivations 9113:Nordtvedt, 8533:The action 7161:Starobinsky 2356:Quasilinear 2309:Quasilinear 2271: [ 2052:Élie Cartan 2042:Quasilinear 2003:dark matter 1737:Page–Tupper 1426:Condition 2 1257:Condition 1 1036:' (see the 335:is written 269:is written 263:(−,+,+,+). 103:dark energy 99:dark matter 77:Motivations 28:gravitation 25033:Categories 24956:CGHS model 24943:toy models 24273:(7): 443. 24073:2207.02945 23967:2301.10861 23906:1909.00095 23849:2108.04649 23842:: 136510. 23796:2203.02350 23764:2306.00992 23743:2303.11094 23698:1611.05515 23691:(6): 412. 23642:2004.05905 23635:(3): 213. 23476:1909.00095 23370:1709.02481 23307:: 101673. 23083:(3): 009. 22850:6 December 22796:1712.07962 22687:1602.07670 22627:(3): 004. 22571:(5): 003. 22334:1608.08135 20771:(2): 168. 20317:Cartan, É. 20302:: 593–595. 20034:(7): 769. 19852:References 19480:Ni (flat) 19316:Nordström 17884:Bekenstein 16636:Lambda-CDM 16355:non-linear 16347:Lambda-CDM 16325:by adding 16315:GRSI model 15396:and mass. 11909:Fred Hoyle 11890:dark fluid 10927:See also: 10285:See also: 10275:Bekenstein 8490:See also: 7165:See also: 6721:to define 4826:See also: 2593:See also: 2559:P. Rastall 2514:Ni Wei-tou 2429:Ni Wei-tou 2425:1972, 1973 2246:1960, 1965 2207:1958, 1973 2120:Yves Thiry 2062:Non-metric 2048:1922, 1923 2017:Author(s) 1829:Bekenstein 1740:Papapetrou 1725:Littlewood 938:of space, 34:theory of 32:Einstein's 24961:RST model 24747:DGP model 24724:Spin foam 24668:Whitehead 24660:Nordström 24589:) gravity 24539:Classical 24513:Paradigms 24464:Resources 24203:205219902 24187:0028-0836 24162:1003.2185 24030:1304.6932 23899:(2): 94. 23874:236965796 23821:247244759 23723:254106132 23667:215745418 23609:118596512 23584:0901.4005 23469:(2): 94. 23427:0901.4005 23395:119218121 23337:256262366 23329:1387-6473 23196:1110.5249 23168:119103482 23143:1308.2319 22905:118854650 22880:0905.4001 22712:118486016 22359:1029-8479 22305:119117834 22289:0031-9007 22264:1404.6495 22236:119201221 22228:1550-7998 22203:1308.4685 22175:118855364 22167:1550-7998 22142:0901.1314 22114:122346086 22106:0020-7748 22030:1110.5249 21939:0704.1574 21910:189831561 21608:122756259 21412:120122429 21236:123522840 21192:119985328 21126:: 67–72. 20727:(1): 39. 20685:122974469 20677:0305-0041 20627:0025-584X 20596:0025-584X 20553:121257875 20545:1434-6001 20388:123189221 20288:Cartan, É 19967:2367-3613 19940:1403.7377 19903:119258154 19878:1106.2476 19829:α 19791:ξ 19785:β 19755:ζ 19673:− 19621:− 19594:− 19556:ζ 19517:− 19490:− 19408:− 19326:− 19294:ζ 19263:ζ 19238:γ 19232:− 19226:− 19202:γ 19196:− 19190:− 19167:β 19146:γ 19000:λ 18994:− 18988:− 18958:λ 18920:λ 18800:α 18772:α 18644:α 18616:α 18594:ξ 18573:β 18475:α 18447:α 18422:β 18401:γ 18354:α 18297:− 18208:α 18148:α 18120:α 18095:β 18074:γ 18012:ω 18001:ω 17941:β 17916:ω 17905:ω 17842:β 17817:ω 17806:ω 17724:ζ 17696:ζ 17668:ζ 17640:ζ 17612:α 17584:α 17556:α 17534:ξ 17513:β 17492:γ 17450:inflation 17382:α 17369:ζ 17356:ζ 17343:ζ 17330:ζ 17301:α 17288:α 17275:α 17252:η 17230:β 17208:γ 17177:ζ 17164:ζ 17151:ζ 17138:ζ 17125:α 17112:α 17099:α 17092:η 17086:β 17080:γ 17061:See also 16916:η 16892:δ 16846:ν 16843:μ 16839:δ 16833:ν 16830:μ 16819:ρ 16797:ν 16787:μ 16777:ν 16774:μ 16763:ρ 16723:ρ 16359:gravitons 16282:◻ 16242:◻ 16207:− 16187:∫ 16100:μ 16096:φ 16090:μ 16086:φ 16063:− 16058:μ 16054:φ 16048:μ 16044:φ 16034:μ 16020:− 15968:μ 15959:− 15956:μ 15951:ν 15947:∇ 15942:μ 15937:μ 15933:∇ 15926:ν 15923:μ 15888:μ 15867:ω 15858:− 15855:ω 15850:ν 15846:∇ 15841:ω 15836:μ 15832:∇ 15825:ν 15822:μ 15769:− 15761:ν 15757:∇ 15747:μ 15743:∇ 15736:ν 15733:μ 15688:− 15669:∫ 15666:− 15625:μ 15615:ν 15611:∂ 15607:− 15602:ν 15592:μ 15588:∂ 15579:ν 15576:μ 15536:ν 15533:μ 15523:ν 15520:μ 15497:ω 15489:− 15470:∫ 15467:− 15384:μ 15378:ω 15347:μ 15258:Moffat's 15225:ν 15222:μ 15219:β 15216:α 15212:ϵ 15186:ν 15183:μ 15173:ρ 15169:∂ 15160:ρ 15157:ν 15147:μ 15143:∂ 15134:ρ 15131:ν 15128:μ 15094:ν 15084:μ 15080:∂ 15074:β 15071:α 15061:ν 15058:μ 15055:β 15052:α 15048:ϵ 15030:∫ 14983:ν 14980:μ 14970:ν 14967:μ 14953:μ 14939:− 14934:ρ 14931:ν 14928:μ 14918:ρ 14915:ν 14912:μ 14884:− 14865:∫ 14744:μ 14716:ν 14713:μ 14672:Moffat's 14651:ν 14640:ν 14637:μ 14623:− 14620:≈ 14615:μ 14587:μ 14559:μ 14556:ν 14525:μ 14522:ν 14487:μ 14465:λ 14409:ν 14399:μ 14389:ν 14386:μ 14368:− 14355:ν 14352:μ 14339:ν 14336:μ 14322:μ 14308:− 14305:λ 14299:− 14274:− 14152:ν 14149:μ 14100:π 14079:− 14059:− 13954:− 13935:− 13916:φ 13880:− 13871:− 13841:α 13830:− 13808:φ 13796:− 13785:φ 13778:− 13764:− 13719:α 13683:μ 13657:μ 13654:− 13633:− 13630:μ 13618:μ 13595:μ 13514:β 13511:α 13504:~ 13473:λ 13448:μ 13442:α 13383:φ 13374:⁡ 13366:β 13356:α 13340:β 13337:α 13327:φ 13311:β 13308:α 13301:~ 13271:β 13261:α 13253:− 13248:β 13245:α 13232:β 13229:α 13175:− 13165:… 13157:α 13152:μ 13134:α 13121:ν 13118:μ 13111:~ 13093:∫ 13050:− 13027:ν 13017:μ 13007:ν 13004:μ 12985:λ 12976:− 12968:ν 12962:β 12946:μ 12940:α 12927:ν 12924:μ 12914:β 12911:α 12898:∫ 12889:π 12877:− 12834:− 12815:σ 12793:σ 12784:− 12775:ℓ 12753:β 12746:φ 12740:α 12733:φ 12727:β 12724:α 12710:σ 12701:∫ 12688:− 12564:α 12538:σ 12518:φ 12430:~ 12376:φ 12371:ν 12367:∂ 12362:φ 12357:μ 12353:∂ 12346:ν 12343:μ 12324:ℓ 12312:~ 12297:π 12273:− 12241:φ 12238:ρ 12235:− 12198:φ 12195:∇ 12171:π 12147:− 12056:ν 12053:μ 12040:− 12035:ν 12032:μ 12014:ν 12011:μ 11982:π 11968:ν 11965:μ 11944:− 11939:ν 11936:μ 11884:from the 11854:ν 11851:μ 11841:ν 11831:μ 11795:φ 11789:λ 11750:φ 11736:− 11717:∫ 11708:π 11667:φ 11638:φ 11632:λ 11611:φ 11587:φ 11581:λ 11549:Λ 11544:ν 11541:μ 11525:ν 11522:μ 11504:− 11499:ν 11496:μ 11477:π 11460:ν 11457:μ 11415:ν 11412:μ 11394:− 11389:ν 11386:μ 11367:π 11350:ν 11347:μ 11282:− 11274:Λ 11268:− 11259:∫ 11250:π 11175:− 11167:∫ 11158:π 11108:ρ 11105:π 11086:Λ 11070:φ 11061:∇ 11025:ρ 11022:π 11013:φ 11004:∇ 10970:Λ 10949:Λ 10842:η 10837:ξ 10833:Ω 10824:μ 10819:η 10815:η 10809:ν 10806:ξ 10798:− 10793:ν 10788:η 10784:η 10778:μ 10775:ξ 10767:− 10762:ξ 10757:η 10753:η 10747:ν 10744:μ 10727:π 10710:ν 10707:μ 10675:ξ 10672:ν 10641:− 10627:ε 10599:ζ 10596:η 10593:μ 10590:ξ 10586:ε 10562:μ 10557:ν 10553:ω 10523:ν 10513:μ 10508:ν 10504:ω 10500:− 10488:μ 10480:∇ 10471:η 10466:ξ 10462:ω 10453:μ 10448:ν 10444:ω 10428:μ 10423:ν 10419:Ω 10409:ζ 10406:η 10403:μ 10400:ξ 10396:ε 10390:ζ 10380:η 10370:ξ 10367:ν 10357:μ 10352:ν 10348:Ω 10338:π 10247:τ 10241:ϵ 10235:η 10229:ω 10206:ω 10200:− 10194:η 10181:ϵ 10168:τ 10136:τ 10123:ϵ 10117:η 10111:ω 10079:μ 10052:ν 10049:μ 10019:ν 10013:μ 10005:− 10000:μ 9994:ν 9981:ν 9978:μ 9950:τ 9944:ϵ 9938:η 9932:ω 9889:ν 9883:μ 9873:ν 9867:μ 9859:τ 9851:ν 9848:μ 9838:ν 9835:μ 9827:ϵ 9824:− 9819:ν 9816:μ 9806:ν 9796:μ 9788:η 9777:μ 9767:μ 9759:ω 9740:− 9722:∫ 9713:π 9670:μ 9621:∞ 9618:→ 9615:ω 9591:φ 9585:ω 9556:− 9553:φ 9545:φ 9539:− 9524:φ 9518:ω 9484:− 9473:φ 9455:− 9431:− 9425:φ 9404:− 9389:φ 9369:− 9355:− 9346:φ 9340:ω 9290:− 9282:φ 9267:φ 9255:− 9243:φ 9177:ω 9150:λ 9121:λ 9042:φ 9036:λ 9012:φ 9006:ω 8978:ν 8975:μ 8967:δ 8952:δ 8900:ν 8897:μ 8826:∫ 8786:φ 8780:λ 8777:φ 8768:φ 8763:ν 8759:∂ 8754:φ 8749:μ 8745:∂ 8738:ν 8735:μ 8725:φ 8718:φ 8712:ω 8706:− 8700:φ 8692:φ 8648:φ 8635:− 8617:∫ 8608:π 8567:φ 8508:Pressuron 8432:α 8418:ν 8415:μ 8405:ν 8402:μ 8391:− 8386:ν 8383:μ 8380:β 8377:α 8367:ν 8364:μ 8361:β 8358:α 8326:α 8310:α 8297:α 8282:− 8230:− 8113:◻ 8067:◻ 8024:◻ 7969:σ 7966:ρ 7963:ν 7960:μ 7931:◻ 7910:σ 7907:ρ 7904:ν 7901:μ 7888:ν 7885:μ 7856:◻ 7835:ν 7832:μ 7797:◻ 7744:− 7649:− 7596:σ 7593:ρ 7590:ν 7587:μ 7577:σ 7574:ρ 7571:ν 7568:μ 7545:ν 7542:μ 7532:ν 7529:μ 7472:− 7415:σ 7412:ρ 7409:ν 7406:μ 7396:σ 7393:ρ 7390:ν 7387:μ 7374:ν 7371:μ 7361:ν 7358:μ 7347:− 7318:− 7198:− 7127:de Sitter 7103:ν 7100:μ 7046:λ 7038:ν 7035:μ 7025:λ 7017:ν 7014:μ 7006:− 7001:μ 6993:λ 6988:λ 6978:ν 6973:μ 6965:ν 6952:λ 6947:μ 6939:λ 6929:ν 6926:μ 6921:ν 6905:− 6900:λ 6890:λ 6887:μ 6877:ν 6874:μ 6869:ν 6846:η 6843:− 6825:∫ 6816:π 6772:ν 6769:μ 6756:ν 6753:μ 6749:η 6740:ν 6737:μ 6706:ν 6703:μ 6665:ν 6651:μ 6637:ν 6634:μ 6630:η 6613:σ 6596:σ 6586:μ 6564:μ 6547:− 6537:μ 6524:− 6514:μ 6494:− 6471:− 6461:μ 6448:− 6438:μ 6421:− 6411:μ 6400:− 6395:μ 6378:− 6368:μ 6330:α 6304:η 6279:− 6268:α 6264:Σ 6254:α 6246:ρ 6238:− 6212:− 6197:− 6192:ν 6182:− 6177:μ 6162:− 6158:Σ 6153:∫ 6146:− 6141:ν 6138:μ 6134:η 6122:α 6109:ν 6106:μ 6077:η 6042:Whitehead 6017:μ 5989:ν 5986:μ 5955:ν 5945:μ 5935:ν 5932:μ 5883:− 5827:ν 5821:μ 5811:ν 5805:μ 5780:− 5761:∫ 5752:π 5704:ν 5699:μ 5691:∂ 5684:β 5681:α 5673:∂ 5661:β 5658:α 5647:η 5631:π 5625:− 5614:η 5610:◻ 5604:ν 5601:μ 5597:η 5585:ν 5582:μ 5572:η 5568:◻ 5520:α 5507:α 5488:α 5480:ν 5477:μ 5467:α 5459:ν 5456:μ 5440:η 5437:− 5419:∫ 5410:π 5327:ν 5324:μ 5320:η 5314:ν 5311:μ 5277:ν 5274:μ 5236:ν 5233:μ 5214:− 5209:ν 5206:μ 5193:η 5177:π 5171:− 5163:δ 5155:β 5152:ν 5142:γ 5134:α 5131:μ 5121:δ 5118:γ 5114:η 5108:β 5105:α 5097:− 5092:ν 5089:μ 5079:η 5075:◻ 5032:ν 5024:δ 5021:γ 5011:μ 5003:β 5000:α 4981:− 4976:ν 4968:δ 4965:α 4955:μ 4947:γ 4944:α 4931:δ 4928:γ 4918:β 4915:α 4905:ν 4902:μ 4898:η 4892:η 4889:− 4870:∫ 4861:π 4800:φ 4791:∂ 4786:φ 4777:∂ 4770:χ 4767:− 4744:φ 4739:χ 4735:∂ 4730:φ 4725:α 4721:∂ 4714:φ 4711:− 4703:− 4700:φ 4695:α 4691:∂ 4686:φ 4681:α 4677:∂ 4670:φ 4667:− 4647:− 4634:χ 4628:φ 4599:φ 4571:χ 4543:φ 4534:∂ 4529:φ 4520:∂ 4513:φ 4490:φ 4485:α 4481:∂ 4476:φ 4471:α 4467:∂ 4460:φ 4457:− 4430:φ 4417:φ 4325:ψ 4321:− 4298:φ 4258:ψ 4238:φ 4212:φ 4201:∗ 4197:ρ 4193:π 4184:φ 4179:ν 4175:∂ 4169:μ 4165:∂ 4159:ν 4156:μ 4152:η 4068:φ 4051:− 4030:φ 4018:− 3971:φ 3942:φ 3897:ν 3893:∂ 3883:μ 3879:∂ 3867:φ 3861:− 3848:φ 3827:φ 3821:− 3811:ν 3808:μ 3804:η 3793:ν 3790:μ 3782:π 3773:φ 3770:◻ 3717:φ 3694:φ 3689:ν 3685:∂ 3680:φ 3675:μ 3671:∂ 3664:ν 3661:μ 3650:− 3644:φ 3636:φ 3593:φ 3580:− 3562:∫ 3553:π 3489:− 3483:α 3441:∞ 3433:φ 3420:α 3389:∞ 3381:φ 3341:∞ 3305:φ 3295:α 3277:φ 3253:φ 3217:φ 3211:− 3201:∞ 3159:φ 3154:− 3146:⁡ 3121:φ 3085:φ 3079:− 3069:∞ 3022:φ 2984:∞ 2942:φ 2924:− 2909:φ 2904:− 2896:⁡ 2871:φ 2834:∞ 2798:φ 2795:− 2789:⁡ 2762:φ 2730:φ 2685:φ 2629:φ 2616:∫ 2613:δ 1881:Nordtvedt 1872:Nordtvedt 1870:Hellings– 1859:Pressuron 1854:Chameleon 1846:Nordtvedt 1664:α 1659:ν 1656:σ 1652:Γ 1625:ν 1621:∇ 1593:ν 1590:μ 1559:σ 1556:μ 1546:ν 1541:ν 1538:σ 1534:Γ 1525:ν 1522:σ 1512:μ 1507:ν 1504:σ 1500:Γ 1491:ν 1481:ν 1478:μ 1463:ν 1460:μ 1450:ν 1446:∇ 1411:ν 1391:μ 1365:ν 1351:μ 1337:ν 1334:μ 1326:− 1313:τ 1295:signature 1278:ν 1275:μ 1213:∝ 1178:− 1127:− 1119:∫ 966:ν 963:μ 919:μ 911:μ 821:− 813:∫ 804:π 738:ν 735:μ 717:− 712:ν 709:μ 690:π 666:ν 663:μ 621:ν 618:μ 600:− 595:ν 592:μ 563:π 549:ν 546:μ 515:ν 501:μ 487:ν 484:μ 425:∫ 422:δ 382:μ 375:φ 353:φ 348:μ 344:∇ 316:μ 309:φ 287:φ 282:μ 278:∂ 261:signature 240:ν 237:μ 205:ν 202:μ 198:η 187:is used. 95:inflation 25018:Graviton 24828:F-theory 24821:M-theory 24397:Standard 24261:(1912). 24219:(1912). 24195:20220843 23221:22400725 23062:14791921 23054:10019545 22966:16615589 22958:10059316 22821:53600834 22731:phys.org 22659:17376981 22547:12305911 22494:15879285 22367:59248448 22297:26066423 22055:22400725 21993:17017857 21795:(1912). 21266:: 1059. 20450:16578082 20319:(1923). 20290:(1922). 19985:28179848 19933:(1): 4. 18331:Rastall 17418:GW170817 16860:, where 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14296:) 14293:W 14290:( 14287:R 14283:[ 14277:g 14269:= 14264:R 14260:L 14233:M 14229:L 14202:M 14198:L 14194:+ 14189:R 14185:L 14181:= 14178:L 14145:g 14106:. 14097:4 14093:k 14088:+ 14082:K 14076:2 14072:2 14067:= 14062:1 14055:G 14031:1 14028:= 14023:n 14020:a 14017:i 14014:n 14011:o 14008:t 14005:w 14002:e 13999:N 13995:G 13991:= 13988:c 13957:1 13946:2 13942:) 13938:K 13932:2 13929:( 13920:0 13912:4 13908:e 13904:) 13901:4 13898:+ 13895:K 13892:( 13889:G 13886:2 13874:K 13868:2 13863:G 13860:6 13854:= 13845:2 13833:8 13826:) 13822:8 13819:+ 13812:0 13804:4 13800:e 13789:0 13781:4 13774:e 13770:) 13767:1 13761:K 13758:2 13755:( 13751:( 13745:K 13741:G 13738:4 13732:= 13723:1 13689:1 13686:= 13651:1 13644:2 13640:) 13636:2 13627:( 13622:2 13609:4 13606:3 13601:= 13598:) 13592:( 13589:F 13576:F 13560:n 13557:o 13554:t 13551:w 13548:e 13545:N 13541:G 13530:G 13501:g 13487:L 13451:] 13445:, 13439:[ 13435:U 13414:K 13411:, 13408:k 13386:) 13380:2 13377:( 13362:U 13352:U 13348:2 13345:+ 13333:g 13324:2 13320:e 13316:= 13298:g 13267:U 13257:U 13241:g 13237:= 13225:h 13194:x 13189:4 13185:d 13178:g 13169:) 13162:, 13148:| 13143:f 13139:, 13130:f 13126:, 13108:g 13100:( 13096:L 13090:= 13081:m 13077:S 13069:x 13064:4 13060:d 13053:g 13044:] 13039:) 13035:1 13032:+ 13023:U 13013:U 13000:g 12995:( 12989:K 12982:2 12971:] 12965:, 12959:[ 12955:U 12949:] 12943:, 12937:[ 12933:U 12920:g 12907:g 12902:[ 12892:G 12882:K 12874:= 12865:v 12861:S 12853:x 12848:4 12844:d 12837:g 12828:] 12824:) 12819:2 12811:G 12808:k 12805:( 12802:F 12797:4 12787:2 12779:0 12771:G 12766:2 12763:1 12758:+ 12750:, 12737:, 12720:h 12714:2 12705:[ 12696:2 12693:1 12685:= 12676:s 12672:S 12639:m 12635:S 12631:+ 12626:v 12622:S 12618:+ 12613:s 12609:S 12605:+ 12600:g 12596:S 12592:= 12589:S 12560:U 12486:0 12482:a 12477:/ 12471:2 12467:c 12463:= 12458:0 12454:l 12427:f 12404:f 12380:) 12339:g 12333:2 12328:0 12319:( 12309:f 12300:G 12294:8 12288:2 12283:0 12279:a 12270:= 12267:L 12231:] 12224:2 12219:0 12215:a 12208:2 12203:| 12191:| 12184:[ 12180:f 12174:G 12168:8 12162:2 12157:0 12153:a 12144:= 12141:L 12062:) 12049:C 12045:+ 12028:T 12024:+ 12019:+ 12007:T 12002:( 11994:4 11990:c 11985:G 11979:8 11973:= 11961:g 11957:R 11952:2 11949:1 11932:R 11847:g 11837:K 11827:K 11798:) 11792:( 11763:m 11759:S 11755:+ 11746:L 11739:g 11730:x 11725:4 11721:d 11711:G 11701:1 11696:= 11693:S 11663:L 11641:) 11635:( 11590:) 11584:( 11553:) 11537:g 11533:+ 11530:R 11518:g 11512:2 11509:1 11492:R 11487:( 11480:G 11474:8 11470:1 11465:= 11453:T 11424:) 11420:R 11408:g 11402:2 11399:1 11382:R 11377:( 11370:G 11364:8 11360:1 11355:= 11343:T 11313:m 11309:S 11305:+ 11301:x 11296:4 11292:d 11285:g 11277:) 11271:2 11265:R 11262:( 11253:G 11243:1 11238:= 11235:S 11206:m 11202:S 11198:+ 11194:x 11189:4 11185:d 11178:g 11170:R 11161:G 11151:1 11146:= 11143:S 11117:; 11114:G 11102:4 11099:= 11094:2 11090:c 11081:2 11078:1 11073:+ 11065:2 11034:; 11031:G 11019:4 11016:= 11008:2 10976:0 10973:= 10829:) 10802:g 10771:g 10740:g 10736:( 10730:G 10720:1 10715:= 10703:T 10668:g 10644:g 10636:= 10519:x 10497:= 10484:x 10458:+ 10440:d 10437:= 10386:x 10376:x 10363:g 10341:G 10331:1 10326:= 10319:L 10253:0 10250:= 10244:= 10238:= 10232:= 10203:2 10197:= 10190:; 10187:1 10184:= 10177:; 10174:0 10171:= 10142:1 10139:= 10132:; 10129:0 10126:= 10120:= 10114:= 10096:) 10084:. 10075:K 10045:T 10024:. 10016:; 10009:K 9997:; 9990:K 9986:= 9974:F 9947:, 9941:, 9935:, 9907:m 9903:S 9899:+ 9895:] 9886:; 9879:K 9870:; 9863:K 9856:+ 9844:F 9831:F 9812:R 9802:K 9792:K 9785:+ 9782:R 9773:K 9763:K 9756:+ 9753:R 9749:[ 9743:g 9735:x 9730:4 9726:d 9716:G 9706:1 9701:= 9698:S 9675:. 9666:K 9594:) 9588:( 9559:2 9550:2 9542:3 9536:4 9530:= 9527:) 9521:( 9487:2 9480:] 9476:) 9470:( 9467:f 9464:q 9461:) 9458:r 9452:1 9449:( 9446:+ 9443:r 9440:[ 9437:] 9434:1 9428:) 9422:( 9419:f 9416:q 9413:) 9410:q 9407:6 9401:1 9398:( 9395:[ 9392:) 9386:( 9383:f 9378:4 9375:1 9364:2 9361:3 9352:= 9349:) 9343:( 9316:f 9293:r 9286:) 9279:( 9276:f 9273:] 9270:) 9264:( 9261:f 9258:q 9252:1 9249:[ 9246:= 9222:q 9201:r 9127:0 9124:= 9094:G 9071:N 9067:G 9045:) 9039:( 9015:) 9009:( 8971:g 8960:m 8956:S 8942:g 8937:2 8924:f 8921:e 8918:d 8912:= 8893:T 8866:m 8862:L 8856:N 8852:G 8845:g 8839:x 8834:4 8830:d 8823:= 8818:m 8814:S 8789:) 8783:( 8774:2 8771:+ 8731:g 8721:) 8715:( 8703:R 8697:= 8688:L 8661:m 8657:S 8653:+ 8644:L 8638:g 8630:x 8625:4 8621:d 8611:G 8601:1 8596:= 8593:S 8563:L 8541:S 8467:, 8464:) 8461:) 8456:3 8452:R 8448:( 8443:O 8436:3 8428:+ 8424:) 8411:R 8398:R 8394:4 8373:R 8354:R 8350:+ 8345:2 8341:R 8336:( 8330:2 8322:+ 8319:R 8314:1 8306:+ 8301:0 8293:( 8285:g 8277:= 8272:L 8233:1 8225:s 8221:M 8198:s 8194:M 8171:s 8167:M 8143:, 8140:0 8137:= 8133:) 8126:2 8121:s 8117:M 8108:( 8102:3 8098:f 8094:2 8091:+ 8087:) 8080:2 8075:s 8071:M 8062:( 8056:2 8052:f 8048:+ 8044:) 8037:2 8032:s 8028:M 8019:( 8013:1 8009:f 8005:2 7979:. 7975:] 7956:R 7951:) 7944:2 7939:s 7935:M 7926:( 7920:3 7916:f 7897:R 7893:+ 7881:R 7876:) 7869:2 7864:s 7860:M 7851:( 7845:2 7841:f 7828:R 7824:+ 7821:R 7817:) 7810:2 7805:s 7801:M 7792:( 7786:1 7782:f 7778:R 7775:+ 7772:R 7767:2 7762:p 7758:M 7753:[ 7747:g 7739:= 7734:L 7698:) 7695:R 7692:( 7689:f 7666:) 7663:R 7660:( 7657:f 7652:g 7644:= 7639:L 7606:. 7602:] 7583:R 7564:R 7558:3 7554:f 7550:+ 7538:R 7525:R 7519:2 7515:f 7511:+ 7506:2 7502:R 7496:1 7492:f 7488:+ 7485:R 7481:[ 7475:g 7467:= 7462:L 7425:. 7421:] 7402:R 7383:R 7379:+ 7367:R 7354:R 7350:4 7342:2 7338:R 7334:+ 7331:R 7327:[ 7321:g 7313:= 7308:L 7275:M 7247:] 7238:2 7234:M 7230:6 7224:2 7220:R 7214:+ 7211:R 7207:[ 7201:g 7193:= 7188:L 7096:h 7064:m 7060:S 7056:+ 7052:] 7042:| 7031:h 7021:| 7010:h 6997:| 6984:h 6969:| 6961:h 6957:+ 6943:| 6935:h 6917:| 6912:h 6908:2 6896:| 6883:h 6865:| 6860:h 6856:2 6852:[ 6838:x 6833:4 6829:d 6819:G 6809:1 6804:= 6801:S 6765:h 6761:+ 6745:= 6733:g 6699:h 6661:x 6657:d 6647:x 6643:d 6626:= 6617:2 6609:d 6602:, 6593:d 6582:x 6578:d 6572:= 6569:) 6560:u 6556:( 6552:, 6543:) 6533:u 6529:( 6520:) 6510:y 6506:( 6503:= 6490:w 6482:, 6479:0 6476:= 6467:) 6457:y 6453:( 6444:) 6434:y 6430:( 6426:, 6417:) 6407:x 6403:( 6391:x 6387:= 6374:) 6364:y 6360:( 6326:x 6274:] 6260:d 6250:u 6241:g 6232:[ 6222:3 6218:) 6208:w 6204:( 6188:y 6173:y 6149:2 6130:= 6127:) 6118:x 6114:( 6102:g 6052:g 6013:K 5982:T 5951:K 5941:K 5928:g 5924:= 5921:N 5898:N 5895:+ 5892:2 5888:N 5880:= 5877:) 5874:N 5871:( 5868:F 5840:m 5836:S 5832:+ 5824:; 5817:K 5808:; 5801:K 5797:) 5794:N 5791:( 5788:F 5783:g 5774:x 5769:4 5765:d 5755:G 5745:1 5740:= 5737:S 5710:) 5695:B 5677:g 5667:( 5654:T 5643:/ 5639:g 5634:G 5628:4 5622:= 5619:B 5593:f 5590:+ 5578:B 5564:a 5536:m 5532:S 5528:+ 5525:) 5517:, 5513:B 5504:, 5500:B 5496:f 5493:+ 5484:| 5473:B 5463:| 5452:B 5448:a 5445:( 5432:x 5427:4 5423:d 5413:G 5403:1 5398:= 5395:S 5371:f 5350:a 5307:B 5303:= 5300:B 5270:B 5244:) 5241:T 5229:g 5223:2 5220:1 5202:T 5198:( 5189:/ 5185:g 5180:G 5168:= 5159:| 5148:g 5138:| 5127:g 5101:g 5085:g 5048:m 5044:S 5040:+ 5037:) 5028:| 5017:g 5007:| 4996:g 4990:2 4987:1 4972:| 4961:g 4951:| 4940:g 4936:( 4924:g 4911:g 4883:x 4878:4 4874:d 4864:G 4854:1 4849:= 4846:S 4804:) 4795:0 4781:0 4763:e 4756:2 4753:3 4747:+ 4707:e 4663:e 4656:2 4653:1 4643:( 4637:) 4631:+ 4625:3 4622:( 4617:2 4614:1 4608:e 4604:= 4595:L 4547:) 4538:0 4524:0 4509:e 4502:2 4499:3 4493:+ 4453:e 4446:2 4443:1 4436:( 4426:e 4422:= 4413:L 4385:] 4379:2 4375:z 4371:d 4368:+ 4363:2 4359:y 4355:d 4352:+ 4347:2 4343:x 4339:d 4335:[ 4329:2 4316:2 4312:t 4308:d 4302:2 4294:= 4289:2 4285:s 4281:d 4215:) 4209:( 4206:k 4190:4 4187:= 4127:] 4121:2 4117:z 4113:d 4110:+ 4105:2 4101:y 4097:d 4094:+ 4089:2 4085:x 4081:d 4077:[ 4071:) 4065:( 4062:f 4059:2 4055:e 4046:2 4042:t 4038:d 4033:) 4027:( 4024:f 4021:2 4014:e 4010:= 4005:2 4001:s 3997:d 3974:) 3968:( 3965:k 3945:) 3939:( 3936:f 3923:t 3906:] 3902:t 3888:t 3873:) 3864:2 3857:e 3853:+ 3845:2 3841:e 3836:( 3832:+ 3824:2 3817:e 3799:[ 3786:T 3779:4 3776:= 3745:m 3741:S 3720:R 3657:g 3653:2 3647:R 3641:= 3632:L 3606:m 3602:S 3598:+ 3589:L 3583:g 3575:x 3570:4 3566:d 3556:G 3546:1 3541:= 3538:S 3517:c 3500:2 3496:/ 3492:7 3486:= 3458:2 3453:) 3446:2 3437:c 3428:( 3423:) 3417:2 3414:+ 3408:( 3405:+ 3401:) 3394:2 3385:c 3376:( 3372:4 3369:+ 3366:1 3363:= 3356:2 3352:c 3346:2 3337:c 3330:, 3325:2 3320:) 3313:2 3309:c 3300:( 3292:+ 3285:2 3281:c 3272:= 3268:) 3261:2 3257:c 3248:( 3244:f 3214:2 3206:2 3197:c 3193:= 3188:2 3184:c 3179:, 3175:) 3167:2 3163:c 3150:( 3140:= 3136:) 3129:2 3125:c 3116:( 3112:f 3082:2 3074:2 3065:c 3061:= 3056:2 3052:c 3047:, 3044:1 3041:= 3037:) 3030:2 3026:c 3017:( 3013:f 2980:c 2976:= 2973:c 2968:) 2962:2 2956:2 2952:) 2946:2 2937:/ 2933:c 2930:( 2917:2 2913:c 2900:( 2890:= 2886:) 2879:2 2875:c 2866:( 2862:f 2830:c 2826:= 2823:c 2819:, 2816:) 2811:2 2807:c 2802:/ 2792:( 2783:= 2780:) 2775:2 2771:c 2766:/ 2759:( 2756:f 2720:c 2701:r 2697:M 2694:G 2688:= 2659:0 2656:= 2653:s 2650:d 2645:) 2637:2 2633:c 2623:( 2619:f 1965:. 1895:– 1879:– 1780:) 1719:– 1715:– 1586:T 1552:T 1530:+ 1518:T 1496:+ 1488:, 1474:T 1468:= 1456:T 1442:= 1439:0 1423:. 1361:x 1357:d 1347:x 1343:d 1330:g 1323:= 1318:2 1310:d 1271:g 1234:R 1217:R 1209:L 1181:1 1175:= 1172:g 1160:. 1148:x 1143:4 1138:d 1130:g 1122:L 1116:= 1113:S 1089:S 1068:L 997:m 993:S 971:) 959:g 955:( 949:= 946:g 907:R 903:= 900:R 879:G 853:m 849:S 845:+ 842:x 837:4 833:d 824:g 816:R 807:G 795:4 791:c 785:= 782:S 752:. 747:) 743:R 731:g 725:2 722:1 705:R 700:( 693:G 687:8 681:4 677:c 671:= 659:T 630:) 626:T 614:g 608:2 605:1 588:T 583:( 575:4 571:c 566:G 560:8 554:= 542:R 511:x 507:d 497:x 493:d 480:g 476:= 471:2 466:s 463:d 437:0 434:= 431:s 428:d 379:; 313:, 233:g 159:G 134:c

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