5383:
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22:
1647:, although Krasnikov also notes that when the spacetime is not flat from the outset, a similar result could be achieved without tachyons by placing in advance some devices along the travel path and programming them to come into operation at preassigned moments and to operate in a preassigned manner. Some suggested methods avoid the problem of tachyonic motion, but would probably generate a
1635:. The need for exotic matter raises questions about whether one can distribute the matter in an initial spacetime that lacks a warp bubble in such a way that the bubble is created at a later time, although some physicists have proposed models of dynamical warp-drive spacetimes in which a warp bubble is formed in a previously flat space. Moreover, according to
660:
153:, and would not move within this bubble but instead be carried along as the region itself moves due to the actions of the drive. The local velocity relative to the deformed spacetime would be subluminal, but the speed at which a spacecraft could move would be superluminal, thereby rendering possible interstellar flight, such as a visit to
1776:(donut shape). However, as this less energetic warp bubble also thickens toward the interior region, it leaves less flat space to house the spacecraft, which has to be smaller. Furthermore, if the intensity of the space warp can be oscillated over time, the energy required is reduced even more. According to White, a modified
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the necessary infrastructure. The pilot inside the bubble is causally disconnected from its walls and cannot carry out any action outside the bubble: the bubble cannot be used for the first trip to a distant star because the pilot cannot place infrastructure ahead of the bubble while "in transit". For example, traveling to
649:
1855:, and Philip O'Byrne have argued that were an Alcubierre-driven ship to decelerate from superluminal speed, the particles that its bubble had gathered in transit would be released in energetic outbursts akin to the infinitely-blueshifted radiation hypothesized to occur at the inner event horizon of a
1809:
matter cannot be found or used, then a solution might be to arrange for masses along the path of the vessel to be set in motion in such a way that the required field was produced. But in this case, the
Alcubierre drive vessel can only travel routes that, like a railroad, have first been equipped with
1771:
spacecraft (c. 700 kg) or less, and stated their intent to perform small-scale experiments in constructing warp fields. White proposed to thicken the extremely thin wall of the warp bubble, so the energy is focused in a larger volume, but the overall peak energy density is actually smaller. In a
203:
The
Alcubierre drive remains a hypothetical concept with seemingly difficult problems, although the amount of energy required is no longer thought to be unobtainably large. Furthermore, Alexey Bobrick and Gianni Martire claim that, in principle, a class of subluminal, spherically symmetric warp drive
1747:
to a few milligrams. Van Den Broeck detailed this by saying that the total energy can be reduced dramatically by keeping the surface area of the warp bubble itself microscopically small, while at the same time expanding the spatial volume inside the bubble. However, Van Den Broeck concludes that the
1615:
to a certain family of inertial observers, but these observers are not really physically distinguished from other such families. Alcubierre interpreted his "warp bubble" in terms of a contraction of space ahead of the bubble and an expansion behind, but this interpretation could be misleading, since
187:
and inhabitants experience no proper acceleration. This method of transport does not involve objects in motion at faster-than-light speeds with respect to the contents of the warp bubble; that is, a light beam within the warp bubble would still always move more quickly than the ship. Because objects
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These results suggest that any ship using an
Alcubierre warp drive carrying people would need shielding to protect them from potential dangerously blueshifted particles during the journey, and any people at the destination would be gamma-ray and high energy particle blasted into oblivion due to the
1780:
could test the idea: one of the legs of the interferometer would appear to have a slightly different length when the test devices were energised. Alcubierre has expressed skepticism about the experiment, saying: "from my understanding there is no way it can be done, probably not for centuries if at
199:
An extension of the
Alcubierre metric that eliminates the expansion of the volume elements and instead relies on the change in distances along the direction of travel is that of mathematician José Natårio. In his metric, spacetime contracts towards the prow of the ship and expands in the direction
1904:
hypothesizes that in all cases where the classical theory of general relativity allows them, quantum effects would intervene to eliminate the possibility, making these spacetimes impossible to realize. A possible type of effect that would accomplish this is a buildup of vacuum fluctuations on the
1879:
meters. In
Alcubierre's original calculations, a bubble macroscopically large enough to enclose a ship of 200 meters would require a total amount of exotic matter greater than the mass of the observable universe, and straining the exotic matter to an extremely thin band of 10 meters is considered
1718:
conjectured by Ford and Roman hold, the energy requirements for some warp drives may be unfeasibly large as well as negative. For example, the energy equivalent of â10 kg might be required to transport a small spaceship across the Milky Wayâan amount orders of magnitude greater than the estimated
1592:, the Alcubierre metric has some apparently peculiar aspects. In particular, Alcubierre has shown that a ship using an Alcubierre drive travels on a free-fall geodesic even while the warp bubble is accelerating: its crew would be in free fall while accelerating without experiencing accelerational
1922:
and writes: "The conjecture has not been proven (it wouldn't be a conjecture if it had), but there are good arguments in its favor based on quantum field theory. The conjecture does not prohibit faster-than-light travel. It just states that if a method to travel faster than light exists, and one
1784:
In 2021, physicist Erik Lentz described a way warp drives sourced from known and familiar purely positive energy could existâwarp bubbles based on superluminal self-reinforcing "soliton" waves. The claim is controversial, with other physicists arguing that all physically reasonable warp drives
1734:
in
Belgium, in 1999, tried to address the potential issues. By contracting the 3+1-dimensional surface area of the bubble being transported by the drive, while at the same time expanding the three-dimensional volume contained inside, Van Den Broeck was able to reduce the total energy needed to
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1676:
A spaceship appropriately located with respect to the bubble trajectory could then choose to enter the bubble, rather like a passenger catching a passing trolley car, and thus make the superluminal journey ... as
Krasnikov points out, causality considerations do not prevent the crew of a
188:
within the bubble are not moving (locally) more quickly than light, the mathematical formulation of the
Alcubierre metric is consistent with the conventional claims of the laws of relativity (namely, that an object with mass cannot attain or exceed the speed of light) and conventional
1467:
1917:
Alcubierre briefly discusses some of these issues in a series of lecture slides posted online, where he writes: "beware: in relativity, any method to travel faster than light can in principle be used to travel back in time (a time machine)". In the next slide, he brings up the
1004:{\displaystyle {\begin{aligned}v_{s}(t)&={\frac {dx_{s}(t)}{dt}},\\r_{s}(t)&={\sqrt {{\big (}x-x_{s}(t){\big )}^{2}+y^{2}+z^{2}}},\\f(r_{s})&={\frac {\tanh {\big (}\sigma (r_{s}+R){\big )}-\tanh {\big (}\sigma (r_{s}-R){\big )}}{2\tanh(\sigma R)}},\end{aligned}}}
414:
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As Farnes' theory allows a positive mass (i.e. a ship) to reach a speed equal to the speed of light, it has been dubbed "controversial". If the theory is correct, which has been highly debated in the scientific literature, it would explain dark energy, dark matter, allow
1659:
does not mean that
Alcubierre bubbles, if it were possible to create them, could not be used as a means of superluminal travel. It only means that the actions required to change the metric and create the bubble must be taken beforehand by some observer whose forward
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appear to support the conjecture, including a calculation dealing specifically with quantum effects in warp-drive spacetimes that suggested that warp bubbles would be semiclassically unstable, but ultimately the conjecture can only be decided by a full theory of
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of the intended path of a craft must be placed at superluminal speedâthat constructing an
Alcubierre drive requires an Alcubierre drive even if the metric that allows it is physically meaningful. Coule further argues that an analogous objection will apply to
1941:
television series and films use the term "warp drive" to describe their method of faster-than-light travel. Neither the Alcubierre theory, nor anything similar, existed when the series was conceivedâthe term "warp drive" and general concept originated with
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to travel more quickly than the speed of light. The existence of exotic matter is not theoretically ruled out; however, generating and sustaining enough exotic matter to perform feats such as faster-than-light travel (and to keep open the "throat" of a
451:
1842:
would destroy anything inside the bubble at superluminal velocities and destabilize the bubble itself; the article also argues that these problems are absent if the bubble velocity is subluminal, although the drive still requires exotic matter.
1600:, however, would be present near the edges of the flat-space volume because of the large space curvature there, but a suitable specification of the metric would keep the tidal forces very small within the volume occupied by the ship.
106:. If exotic matter with the correct properties cannot exist, then the drive cannot be constructed. At the close of his original article, however, Alcubierre argued (following an argument developed by physicists analyzing traversable
1837:
A 2009 article by Carlos BarcelĂł, Stefano Finazzi, and Stefano Liberati uses quantum theory to argue that the Alcubierre drive at faster-than-light velocities is impossible mostly because extremely high temperatures caused by
1672:(2,600 light-years away) and arrive less than 2,600 years in the future according to external clocks, it would be required that someone had already begun work on warping the space from Earth to Deneb at least 2,600 years ago:
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93:
Although the metric proposed by Alcubierre is consistent with the Einstein field equations, construction of such a drive is not necessarily possible. The proposed mechanism of the Alcubierre drive implies a negative
1905:
border of the region of spacetime where time travel would first become possible, causing the energy density to become high enough to destroy the system that would otherwise become a time machine. Some results in
2373:
Alcubierre, following the lead of wormhole theorists, argues that quantum field theory permits the existence of regions of negative energy density under special circumstances, and cites the Casimir effect as an
1298:
1814:(which is 25 light-years from Earth) requires arranging everything so that the bubble moving toward Vega with a superluminal velocity would appear; such arrangements will always take more than 25 years.
242:
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1619:
In general relativity, one often first specifies a plausible distribution of matter and energy, and then finds the geometry of the spacetime associated with it; but it is also possible to run the
665:
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1884:. Chris Van den Broeck constructed a modification of Alcubierre's model that requires much less exotic matter but places the ship in a curved spacetime "bottle" whose neck is about 10 meters.
1834:
An article by José Natårio (2002) argues that crew members could not control, steer or stop the ship in its warp bubble because the ship could not send signals to the front of the bubble.
86:; instead, the Alcubierre drive shifts space around an object so that the object would arrive at its destination more quickly than light would in normal space without breaking any
644:{\displaystyle {\begin{aligned}\alpha &=1,\\\beta ^{x}&=-v_{s}(t)f{\big (}r_{s}(t){\big )},\\\beta ^{y}&=\beta ^{z}=0,\\\gamma _{ij}&=\delta _{ij},\end{aligned}}}
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With this particular form of the metric, it can be shown that the energy density measured by observers whose 4-velocity is normal to the hypersurfaces is given by:
2053:
1607:, which is often used in discussing the initial-value formulation of general relativity. This might explain the widespread misconception that this spacetime is a
1681:
from Earth to a distant star and back in an arbitrarily short time, as measured by clocks on Earth, by altering the metric along the path of their outbound trip.
1723:. Counterarguments to these apparent problems have also been offered, although the energy requirements still generally require a Type III civilization on the
3880:
Visser, Matt (December 1997). "The reliability horizon for semi-classical quantum gravity: Metric fluctuations are often more important than back-reaction".
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that behave identically to the physics of the Alcubierre drive, providing a natural solution for the current "crisis in cosmology" due to a time-variable
25:
Two-dimensional visualization of an Alcubierre drive, showing the opposing regions of expanding and contracting spacetime that displace the central region
1282:{\displaystyle ds^{2}=\left(v_{s}(t)^{2}f{\big (}r_{s}(t){\big )}^{2}-1\right)\,dt^{2}-2v_{s}(t)f{\big (}r_{s}(t){\big )}\,dx\,dt+dx^{2}+dy^{2}+dz^{2}.}
4397:
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183:, allows a warp bubble to appear in previously flat spacetime and move away at effectively faster-than-light speed. The interior of the bubble is an
1643:
faster-than-light trip requires forcing the exotic matter to move at local faster-than-light speeds, something that would require the existence of
3348:
2098:
4139:
2707:
Farnes, J. S. (2018). "A Unifying Theory of Dark Energy and Dark Matter: Negative Masses and Matter Creation within a Modified ÎCDM Framework".
117:
Another possible issue is that, although the Alcubierre metric is consistent with Einstein's equations, general relativity does not incorporate
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that his theory was directly inspired by the term used in the show and cites the "'warp drive' of science fiction" in his 1994 article. A USS
3965:
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Krasnikov (2003), p. 13, "Moreover, by analogy with the Casimir effect, it is reasonable to assume that Ï in such a wormhole will be large (~
1699:. Nevertheless, an Alcubierre-type warp drive might be realized by exploiting certain experimentally verified quantum phenomena, such as the
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hold that a warp bubble traveling at 10-times the speed of light must have a wall thickness of no more than 10 metersâclose to the limiting
125:(which would incorporate both theories) would eliminate those solutions in general relativity that allow for backward time travel (see the
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1462:{\displaystyle -{\frac {c^{4}}{8\pi G}}{\frac {v_{s}^{2}\left(y^{2}+z^{2}\right)}{4g^{2}r_{s}^{2}}}\left({\frac {df}{dr_{s}}}\right)^{2},}
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1492:) is thought to be impractical. According to writer Robert Low, within the context of general relativity it is impossible to construct a
3371:
3151:
Ford and Roman (1995), p.5, "...the Casimir effect may be useful as an illustration. Here one has a constant negative energy density..."
1923:
tries to use it to build a time machine, something will go wrong: the energy accumulated will explode, or it will create a black hole."
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3428:
1985:
series have made closer use of the theory behind the Alcubierre Drive incorporating warp bubbles/fields into the in-universe science.
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associated with it, and this is what Alcubierre did in building his metric. This practice means that the solution can violate various
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68:
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BarcelĂł, Carlos; Finazzi, Stefano; Liberati, Stefano (2010). "On the impossibility of superluminal travel: the warp drive lesson".
1859:; forward-facing particles would thereby be energetic enough to destroy anything at the destination directly in front of the ship.
409:{\displaystyle ds^{2}=-\left(\alpha ^{2}-\beta _{i}\beta ^{i}\right)\,dt^{2}+2\beta _{i}\,dx^{i}\,dt+\gamma _{ij}\,dx^{i}\,dx^{j},}
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Pfenning, Michael John (1998). "Quantum Inequality Restrictions on Negative Energy Densities in Curved Spacetimes". p. 1692.
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perpendicular to the motion, meaning that the bubble actually "slides" through space, roughly speaking by "pushing space aside".
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Agnew, J. (16 August 2019). "An Examination of Warp Theory and Technology to Determine the State of the Art and Feasibility".
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to contract and the space behind it to expand. The ship would then ride this wave inside a region of flat space, known as a
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4005:
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McMonigal, Brendan; Lewis, Geraint F.; O'Byrne, Philip (20 March 2012). "Alcubierre warp drive: On the matter of matter".
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the contraction and expansion actually refer to the relative motion of nearby members of the family of ADM observers.
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The metric of this form has significant difficulties because all known warp-drive spacetime theories violate various
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2183:
Finazzi, Stefano; Liberati, Stefano; BarcelĂł, Carlos (2009). "Semiclassical instability of dynamical warp drives".
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travel by contracting space in front of it and expanding space behind it, under the assumption that a configurable
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spacetimes can be constructed based on physical principles presently known to humanity, such as positive energy.
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flat 2D representation, the ring of positive and negative energy, initially very thin, becomes a larger, fuzzy
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The amount of negative energy required for such a propulsion is not yet known. Pfenning and Allen Everett of
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energy densities required are still unachievable, as are the small size (a few orders of magnitude above the
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Coule has argued that schemes, such as the one proposed by Alcubierre, are infeasible because matter placed
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could reduce the massâenergy requirements for a macroscopic space ship from the equivalent of the planet
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4006:"Star Trek Adventures: A Star Beyond the Stars â Modiphius | Star Trek Adventures | DriveThruRPG.com"
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Ford, L. H.; Roman, T. A. (1996). "Quantum field theory constrains traversable wormhole geometries".
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had explored the idea of gravitationally repulsive negative masses while developing the equations of
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1900:. While it is possible that the fundamental laws of physics might allow closed timelike curves, the
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Lobo, Francisco S. N.; Visser, Matt (2004). "Fundamental limitations on 'warp drive' spacetimes".
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between parallel plates could fulfill the negative-energy requirement for the Alcubierre drive.
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Van Den Broeck, Chris (1999). "A 'warp drive' with more reasonable total energy requirements".
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in general relativity, meaning that the theory predicts that they could be used for backwards
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2688:"Bringing balance to the universe: New theory could explain missing 95 percent of the cosmos"
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at the front of the bubble. Allen Everett and Thomas Roman comment on Krasnikov's finding (
1515:
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is the shift vector that relates the spatial coordinate systems on different hypersurfaces,
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Alcubierre, Miguel (1994). "The warp drive: hyper-fast travel within general relativity".
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is the lapse function that gives the interval of proper time between nearby hypersurfaces,
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Calculations by physicist Allen Everett show that warp bubbles could be used to create
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Hiscock, William A. (1997). "Quantum effects in the Alcubierre warp drive spacetime".
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Van den Broeck, Christian (2000). "Alcubierre's warp drive: Problems and prospects".
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Krasnikov, S. (2003). "The quantum inequalities do not forbid spacetime shortcuts".
2099:"Scientists Are Starting to Take Warp Drives Seriously, Especially This One Concept"
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Pfenning, Michael J.; Ford, L. H. (1997). "The unphysical nature of 'Warp Drive'".
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Everett, Allen; Roman, Thomas (1997). "A Superluminal Subway: The Krasnikov Tube".
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3518:"Breaking the warp barrier: hyper-fast solitons in EinsteinâMaxwell-plasma theory"
3142:), which would relieve one of having to seek additional sources of exotic matter."
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3465:"Spacecraft in a 'warp bubble' could travel faster than light, claims physicist"
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has equal amounts of positive and negative qualities. Farnes' theory relies on
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would not apply as they would with conventional motion at near-light speeds.
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3492:"There's light-speed travel in 'Star Wars' and 'Star Trek.' Is it possible?"
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The original warp-drive metric and simple variants of it happen to have the
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2761:"Astrophysicist claims "dark fluid" fills the missing 95% of the Universe"
2443:. Fundamental Theories of Physics. Vol. 189. Cham. pp. 257â279.
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has proposed a theory, published in the peer-reviewed scientific journal
103:
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Van den Broeck, Chris (1999). "On the (im)possibility of warp bubbles".
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Alcubierre, Miguel; Lobo, Francisco S. N. (2017). "Warp Drive Basics".
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2002:(for more on the sense in which the Alcubierre spacetime is a solution)
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in the other direction, first specifying a metric and then finding the
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With regard to certain specific effects of special relativity, such as
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121:. Some physicists have presented arguments to suggest that a theory of
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4455:
4351:
4243:
2765:
2549:
1937:
1768:
1611:
of the field equation of general relativity. Metrics in ADM form are
225:
221:
172:
83:
2782:"Can a negative-mass cosmology explain dark matter and dark energy?"
1887:
1572:), and suggest that an Alcubierre drive is physically possible with
5298:
4648:
4450:
3660:
3642:
Jessica Santiago; Sebastian Schuster; Mark Visser (15 March 2022).
3534:
2798:
2721:
2585:
2449:
1644:
1489:
146:
145:
by creating a wave that would cause the fabric of space ahead of a
107:
3865:
3738:
2303:
2199:
1739:. Later in 2003, by slightly modifying the Van den Broeck metric,
4177:
A short video clip of the hypothetical effects of the warp drive.
2900:
Krasnikov, S. (1998). "Hyper-fast travel in general relativity".
1994:
1806:
1764:
1593:
1028:. Alcubierre's specific form of the metric can thus be written:
4978:
1711:, when described in the context of the quantum field theories.
1549:
1477:
52:
4256:
4188:
GonzĂĄlez-DĂaz, Pedro (14 July 2000). "Warp Drive Space-Time".
3364:"Nasa physicist says warp drive is more feasible than thought"
2546:"Warp Drive May Be More Feasible Than Thought, Scientists Say"
1677:
spaceship from arranging, by their own actions, to complete a
82:
Objects cannot accelerate to the speed of light within normal
4539:
4161:"Can We Travel Faster Than Light? with Dr. Miguel Alcubierre"
2632:
Low, Robert J. (1999). "Speed Limits in General Relativity".
1773:
1669:
21:
1548:, an idea which leads to a "beautiful" hypothesis where the
1499:
43:
idea according to which a spacecraft could achieve apparent
4959:
1811:
1759:
and collaborators announced that modifying the geometry of
445:
The particular form that Alcubierre studied is defined by:
441:
is a positive-definite metric on each of the hypersurfaces.
1707:
that also violate the energy conditions, such as negative
3964:
J. Gardiner, "Warp Drive â From Imagination to Reality",
3723:
3343:
2306:"Wormholes, Time Machines, and the Weak Energy Condition"
3617:"Breaking the warp barrier for faster-than-light travel"
2842:
Natario, Jose (2002). "Warp drive with zero expansion".
1483:
Thus, because the energy density is negative, one needs
63:
in 1994, the Alcubierre drive is based on a solution of
3644:"Generic warp drives violate the null energy condition"
3447:"2013 Starship Congress: Warp Field Physics, an Update"
1639:, generating a bubble in a previously flat space for a
59:) could be created. Proposed by theoretical physicist
2388:
1826:
proposed method of constructing an Alcubierre drive.
1301:
1037:
663:
454:
245:
236:, with the metric taking the following general form:
3045:
2304:
Thorne, Kip; Michael Morris; Ulvi Yurtsever (1988).
3223:
1926:
3378:
2567:Bobrick, Alexey; Martire, Gianni (20 April 2021).
1829:
1461:
1281:
1003:
643:
408:
3099:
3097:
2539:
2537:
2535:
2533:
1888:Causality violation and semiclassical instability
1846:
5397:
4244:"Skeptoid #922: Testing Alcubierre's Warp Drive"
3339:"How NASA might build its very first warp drive"
2895:
2893:
16:Hypothetical FTL transportation by warping space
2389:Fil'chenkov, M.; Laptev, Yu. (1 October 2017).
2116:
2114:
2112:
2054:AIAA Propulsion and Energy Forum and Exposition
2046:
2044:
4182:Marcelo B. Ribeiro's Page on Warp Drive Theory
3426:Miguel Alcubierre's Twitter feed, 29 July 2013
3278:
3103:
3094:
3041:
3039:
2959:
2566:
2530:
2438:
1536:, and which is expected to be testable by the
129:) and thus make the Alcubierre drive invalid.
75:, the Alcubierre drive is also referred to as
4555:
4272:
4187:
3966:Journal of the British Interplanetary Society
3701:"Warp Drives May Come With a Killer Downside"
3590:"Star Trek's Warp Drive Leads to New Physics"
3457:
3394:Journal of the British Interplanetary Society
2890:
2779:
2092:
2090:
1664:contains the entire trajectory of the bubble.
1209:
1183:
1117:
1090:
963:
931:
915:
883:
800:
767:
549:
523:
2503:
2441:Wormholes, Warp Drives and Energy Conditions
2244:
2242:
2240:
2238:
2236:
2234:
2109:
2041:
3769:extreme blueshifts for P+ region particles.
3036:
2680:
2391:"Galaxy travel via Alcubierre's warp drive"
4562:
4548:
4279:
4265:
4156:It describes the concept in laymans terms.
4140:"Ideas Based on What We'd Like To Achieve"
4082:
2489:: CS1 maint: location missing publisher (
2248:
2087:
1880:impractical. Similar constraints apply to
1690:
4205:
4098:
4049:
3893:
3864:
3786:
3737:
3659:
3533:
3294:
3239:
3176:
3160:
3061:
2965:
2955:
2953:
2951:
2915:
2899:
2857:
2815:
2797:
2720:
2647:
2584:
2543:
2448:
2264:
2231:
2198:
2178:
2176:
2174:
2172:
2136:
2120:
1735:transport small atoms to less than three
1500:Connection to dark energy and dark matter
1221:
1214:
1139:
389:
375:
352:
338:
308:
3780:
2979:
2977:
2700:
2371:from the original on 21 September 2012.
2096:
1668:For example, if one wanted to travel to
20:
4238:
4033:
3852:
3801:
3438:
3336:
2841:
2753:
179:that, if interpreted in the context of
5398:
3879:
3713:from the original on 10 December 2012.
3489:
3453:from the original on 20 November 2013.
3332:
3330:
2948:
2706:
2544:Moskowitz, Clara (17 September 2012).
2514:10.7208/chicago/9780226225005.001.0001
2504:Everett, Allen; Roman, Thomas (2011).
2362:
2352:from the original on 23 February 2011.
2169:
1800:
1752:) of the spacetime structures needed.
1743:reduced the necessary total amount of
5436:Exact solutions in general relativity
4543:
4260:
3848:from the original on 12 October 2013.
3698:
3515:
3509:
3444:
3384:
3351:from the original on 10 January 2013.
2983:
2974:
2837:
2835:
2556:from the original on 13 January 2013.
2050:
2000:Exact solutions in general relativity
34:
3587:
3483:
3415:from the original on 9 October 2022.
3361:
3337:Dvorsky, George (26 November 2012).
2434:
2432:
2384:
2382:
162:
5134:TolmanâOppenheimerâVolkoff equation
5087:FriedmannâLemaĂźtreâRobertsonâWalker
3977:
3327:
2631:
1952:. Alcubierre stated in an email to
141:proposed a method for changing the
13:
4312:Novikov self-consistency principle
3802:Everett, Allen E. (15 June 1996).
3621:Georg-August-UniversitÀt Göttingen
3374:from the original on 8 April 2016.
2832:
2773:
2569:"Introducing physical warp drives"
14:
5447:
4904:HamiltonâJacobiâEinstein equation
4132:
3699:Major, Jason (29 February 2012).
2780:Socas-Navarro, H. (30 May 2019).
2429:
2379:
2363:Cramer, John G. (15 April 1996).
1862:
1496:in the absence of exotic matter.
1476:is the determinant of the metric
5382:
5381:
4322:Quantum mechanics of time travel
4302:Chronology protection conjecture
3445:White, Harold (17 August 2013).
1920:chronology protection conjecture
1902:chronology protection conjecture
127:chronology protection conjecture
4286:
3998:
3971:
3958:
3926:
3873:
3795:
3774:
3717:
3692:
3635:
3609:
3581:
3516:Lentz, Erik W. (9 March 2021).
3419:
3355:
3272:
3217:
3154:
3145:
3132:
2625:
2560:
2508:. University of Chicago Press.
2497:
2415:10.1016/j.actaastro.2017.07.011
2097:Williams, Matt (1 March 2020).
1882:Krasnikov's superluminal subway
1830:Survivability inside the bubble
1778:MichelsonâMorley interferometer
1721:mass of the observable universe
1685:
1540:around 2030. Farnes found that
4711:Massâenergy equivalence (E=mc)
4569:
3968:, vol. 61, pp. 353â357 (2008).
3490:Dunham, Will (11 March 2021).
2356:
2297:
1975:Star Trek: The Original Series
1946:'s 1931 science fiction novel
1847:Damaging effect on destination
1732:Katholieke Universiteit Leuven
1204:
1198:
1175:
1169:
1111:
1105:
1076:
1069:
988:
979:
958:
939:
910:
891:
862:
849:
794:
788:
753:
747:
716:
710:
684:
678:
544:
538:
515:
509:
207:
1:
4418:Parallel universes in fiction
4167:. Event Horizon. 6 June 2019.
4086:Classical and Quantum Gravity
4037:Classical and Quantum Gravity
4027:
3912:10.1016/S0370-2693(97)01226-4
3588:Gast, Robert (October 2021).
3522:Classical and Quantum Gravity
3282:Classical and Quantum Gravity
3227:Classical and Quantum Gravity
2994:Classical and Quantum Gravity
2845:Classical and Quantum Gravity
2635:Classical and Quantum Gravity
2573:Classical and Quantum Gravity
2252:Classical and Quantum Gravity
4428:Philosophy of space and time
2786:Astronomy & Astrophysics
2709:Astronomy & Astrophysics
2467:10.1007/978-3-319-55182-1_11
1730:Chris Van Den Broeck of the
1521:Astronomy & Astrophysics
232:of constant coordinate time
7:
4726:Relativistic Doppler effect
4117:10.1088/0264-9381/21/24/011
4068:10.1088/0264-9381/14/11/002
3980:"The Physics of Warp Drive"
3678:10.1103/PhysRevD.105.064038
3313:10.1088/0264-9381/16/12/314
2817:10.1051/0004-6361/201935317
2739:10.1051/0004-6361/201832898
2506:Time Travel and Warp Drives
2365:"The Alcubierre Warp Drive"
2335:10.1103/PhysRevLett.61.1446
1988:
1805:Krasnikov proposed that if
10:
5452:
5197:In computational physics:
4721:Relativity of simultaneity
4408:Many-worlds interpretation
4295:General terms and concepts
4224:10.1103/PhysRevD.62.044005
3804:"Warp drive and causality"
3756:10.1103/PhysRevD.85.064024
3387:"Warp Field Mechanics 101"
3258:10.1088/0264-9381/14/7/011
3106:AIP Conference Proceedings
3015:10.1088/0264-9381/15/8/026
2876:10.1088/0264-9381/19/6/308
2666:10.1088/0264-9381/16/2/016
2283:10.1088/0264-9381/11/5/001
2217:10.1103/PhysRevD.79.124017
2155:10.1103/PhysRevD.67.104013
1579:
1503:
1014:with arbitrary parameters
132:
65:Einstein's field equations
5379:
5211:
5076:
5048:
5034:LenseâThirring precession
4917:
4866:
4828:
4807:
4796:
4754:
4698:
4682:
4624:
4616:Doubly special relativity
4588:
4577:
4469:
4426:
4390:
4367:
4330:
4294:
4198:American Physical Society
51:field lower than that of
4894:Post-Newtonian formalism
4884:Einstein field equations
4820:Mathematical formulation
4644:Hyperbolic orthogonality
4317:Self-fulfilling prophecy
3831:10.1103/PhysRevD.53.7365
3552:10.1088/1361-6382/abe692
3195:10.1103/PhysRevD.53.5496
3080:10.1103/PhysRevD.56.2100
2934:10.1103/PhysRevD.57.4760
2603:10.1088/1361-6382/abdf6e
2034:
1621:Einstein field equations
185:inertial reference frame
5426:Hypothetical technology
4605:Galilean transformation
4596:Principle of relativity
3449:. Icarus Interstellar.
2808:2019A&A...626A...5S
2731:2018A&A...620A..92F
2314:Physical Review Letters
2014:Quantum vacuum thruster
1972:. Since the release of
1691:Massâenergy requirement
171:defines the warp-drive
98:and therefore requires
5421:Science fiction themes
4690:Lorentz transformation
4481:closed timelike curves
4332:Time travel in fiction
4142:. NASA. Archived from
3431:9 January 2014 at the
3385:White, Harold (2013).
1894:closed timelike curves
1789:, as well as both the
1683:
1666:
1625:energyâmomentum tensor
1566:closed timelike curves
1538:Square Kilometre Array
1463:
1283:
1005:
645:
410:
26:
5158:WeylâLewisâPapapetrou
4899:Raychaudhuri equation
4838:Equivalence principle
4529:Traversable wormholes
4307:Closed timelike curve
2984:Coule, D. H. (1998).
2024:Spacecraft propulsion
1907:semiclassical gravity
1787:weak energy condition
1705:stressâenergy tensors
1674:
1657:
1464:
1284:
1006:
646:
411:
24:
5416:Lorentzian manifolds
5199:Numerical relativity
5040:pulsar timing arrays
4340:Timelines in fiction
4010:www.drivethrurpg.com
3654:(6) 064038: 064038.
1969:Star Trek Adventures
1716:quantum inequalities
1516:University of Oxford
1299:
1035:
661:
452:
243:
36:[alkuËÎČjere]
5406:Interstellar travel
5091:Friedmann equations
4985:HulseâTaylor binary
4947:Gravitational waves
4843:Riemannian geometry
4669:Proper acceleration
4654:Maxwell's equations
4600:Galilean relativity
4377:Grandfather paradox
4242:(6 February 2024).
4216:2000PhRvD..62d4005G
4171:John Michael Godier
4109:2004CQGra..21.5871L
4060:1997CQGra..14L.183H
3934:"Faster than light"
3904:1997PhLB..415....8V
3823:1996PhRvD..53.7365E
3748:2012PhRvD..85f4024M
3670:2022PhRvD.105f4038S
3595:Scientific American
3544:2021CQGra..38g5015L
3406:2013JBIS...66..242W
3305:1999CQGra..16.3973V
3250:1997CQGra..14.1743P
3187:1996PhRvD..53.5496F
3118:2000AIPC..504.1105V
3072:1997PhRvD..56.2100E
3007:1998CQGra..15.2523C
2926:1998PhRvD..57.4760K
2868:2002CQGra..19.1157N
2658:1999CQGra..16..543L
2595:2021CQGra..38j5009B
2459:2017FTP...189..257A
2407:2017AcAau.139..254F
2327:1988PhRvL..61.1446M
2275:1994CQGra..11L..73A
2209:2009PhRvD..79l4017F
2147:2003PhRvD..67j4013K
2063:10.2514/6.2019-4288
1851:Brendan McMonigal,
1801:Placement of matter
1797:energy conditions.
1755:In 2012, physicist
1586:Lorentz contraction
1410:
1347:
177:Lorentzian manifold
159:within a few days.
102:or manipulation of
39:) is a speculative
5431:1994 introductions
5140:ReissnerâNordström
5058:BransâDicke theory
4889:Linearized gravity
4716:Length contraction
4634:Frame of reference
4611:Special relativity
4475:general relativity
4398:Alternative future
4391:Parallel timelines
4369:Temporal paradoxes
4345:in science fiction
2769:. 29 October 2019.
2696:. 5 December 2018.
2019:Reactionless drive
1546:general relativity
1459:
1396:
1333:
1279:
1001:
999:
641:
639:
406:
224:is described by a
218:general relativity
181:general relativity
27:
5411:Warp drive theory
5393:
5392:
5207:
5206:
5186:OzsvĂĄthâSchĂŒcking
4792:
4791:
4774:Minkowski diagram
4731:Thomas precession
4674:Relativistic mass
4537:
4536:
4489:Alcubierre metric
4403:Alternate history
4190:Physical Review D
4093:(24): 5871â5892.
4044:(11): L183âL188.
3882:Physics Letters B
3817:(12): 7365â7368.
3811:Physical Review D
3726:Physical Review D
3648:Physical Review D
3289:(12): 3973â3979.
3171:(10): 5496â5507.
3164:Physical Review D
3126:10.1063/1.1290913
3049:Physical Review D
2903:Physical Review D
2523:978-0-226-04548-1
2476:978-3-319-55181-4
2395:Acta Astronautica
2321:(13): 1446â1449.
2186:Physical Review D
2124:Physical Review D
2072:978-1-62410-590-6
1840:Hawking radiation
1741:Serguei Krasnikov
1697:energy conditions
1649:naked singularity
1637:Serguei Krasnikov
1629:energy conditions
1444:
1412:
1328:
992:
837:
728:
163:Alcubierre metric
143:geometry of space
139:Miguel Alcubierre
119:quantum mechanics
77:Alcubierre metric
61:Miguel Alcubierre
45:faster-than-light
5443:
5385:
5384:
5168:van Stockum dust
4940:Two-body problem
4858:Mach's principle
4805:
4804:
4746:Terrell rotation
4586:
4585:
4564:
4557:
4550:
4541:
4540:
4524:van Stockum dust
4436:Butterfly effect
4281:
4274:
4267:
4258:
4257:
4253:
4235:
4209:
4168:
4155:
4153:
4151:
4128:
4102:
4079:
4053:
4021:
4020:
4018:
4016:
4002:
3996:
3995:
3993:
3991:
3986:on 24 April 2013
3982:. Archived from
3975:
3969:
3962:
3956:
3955:
3953:
3951:
3946:on 18 March 2016
3945:
3939:. Archived from
3938:
3930:
3924:
3923:
3897:
3877:
3871:
3870:
3868:
3856:
3850:
3849:
3847:
3808:
3799:
3793:
3792:
3790:
3778:
3772:
3771:
3741:
3721:
3715:
3714:
3696:
3690:
3689:
3663:
3639:
3633:
3632:
3630:
3628:
3613:
3607:
3606:
3604:
3602:
3585:
3579:
3578:
3576:
3574:
3537:
3513:
3507:
3506:
3504:
3502:
3487:
3481:
3480:
3478:
3476:
3461:
3455:
3454:
3442:
3436:
3423:
3417:
3416:
3414:
3391:
3382:
3376:
3375:
3359:
3353:
3352:
3334:
3325:
3324:
3298:
3276:
3270:
3269:
3243:
3234:(7): 1743â1751.
3221:
3215:
3214:
3180:
3158:
3152:
3149:
3143:
3136:
3130:
3129:
3101:
3092:
3091:
3065:
3056:(4): 2100â2108.
3043:
3034:
3033:
3032:on 27 June 2007.
3031:
3025:. Archived from
3001:(8): 2523â2537.
2990:
2981:
2972:
2971:
2969:
2957:
2946:
2945:
2919:
2910:(8): 4760â4766.
2897:
2888:
2887:
2861:
2852:(6): 1157â1166.
2839:
2830:
2829:
2819:
2801:
2777:
2771:
2770:
2757:
2751:
2750:
2724:
2704:
2698:
2697:
2684:
2678:
2677:
2651:
2629:
2623:
2622:
2588:
2564:
2558:
2557:
2541:
2528:
2527:
2501:
2495:
2494:
2488:
2480:
2452:
2436:
2427:
2426:
2386:
2377:
2376:
2360:
2354:
2353:
2351:
2310:
2301:
2295:
2294:
2268:
2246:
2229:
2228:
2202:
2180:
2167:
2166:
2140:
2118:
2107:
2106:
2103:ScienceAlert.com
2094:
2085:
2084:
2048:
1949:Islands of Space
1944:John W. Campbell
1878:
1853:Geraint F. Lewis
1558:Hubble parameter
1475:
1468:
1466:
1465:
1460:
1455:
1454:
1449:
1445:
1443:
1442:
1441:
1428:
1420:
1413:
1411:
1409:
1404:
1395:
1394:
1381:
1380:
1376:
1375:
1374:
1362:
1361:
1346:
1341:
1331:
1329:
1327:
1316:
1315:
1306:
1288:
1286:
1285:
1280:
1275:
1274:
1259:
1258:
1243:
1242:
1213:
1212:
1197:
1196:
1187:
1186:
1168:
1167:
1152:
1151:
1138:
1134:
1127:
1126:
1121:
1120:
1104:
1103:
1094:
1093:
1084:
1083:
1068:
1067:
1050:
1049:
1027:
1020:
1010:
1008:
1007:
1002:
1000:
993:
991:
968:
967:
966:
951:
950:
935:
934:
919:
918:
903:
902:
887:
886:
873:
861:
860:
838:
836:
835:
823:
822:
810:
809:
804:
803:
787:
786:
771:
770:
764:
746:
745:
729:
727:
719:
709:
708:
695:
677:
676:
650:
648:
647:
642:
640:
633:
632:
613:
612:
587:
586:
570:
569:
553:
552:
537:
536:
527:
526:
508:
507:
488:
487:
440:
431:
425:
415:
413:
412:
407:
402:
401:
388:
387:
374:
373:
351:
350:
337:
336:
321:
320:
307:
303:
302:
301:
292:
291:
279:
278:
258:
257:
235:
192:effects such as
156:Proxima Centauri
38:
31:Alcubierre drive
5451:
5450:
5446:
5445:
5444:
5442:
5441:
5440:
5396:
5395:
5394:
5389:
5375:
5203:
5107:BKL singularity
5097:LemaĂźtreâTolman
5072:
5068:Quantum gravity
5050:
5044:
5030:geodetic effect
5004:(together with
4974:LISA Pathfinder
4913:
4862:
4848:Penrose diagram
4830:
4824:
4799:
4788:
4784:Minkowski space
4750:
4694:
4678:
4626:
4620:
4580:
4573:
4568:
4538:
4533:
4519:Tipler cylinder
4478:
4465:
4422:
4386:
4363:
4326:
4290:
4285:
4159:
4149:
4147:
4146:on 9 April 2013
4138:
4135:
4030:
4025:
4024:
4014:
4012:
4004:
4003:
3999:
3989:
3987:
3978:Shapiro, Alan.
3976:
3972:
3963:
3959:
3949:
3947:
3943:
3936:
3932:
3931:
3927:
3878:
3874:
3857:
3853:
3845:
3806:
3800:
3796:
3779:
3775:
3722:
3718:
3697:
3693:
3640:
3636:
3626:
3624:
3615:
3614:
3610:
3600:
3598:
3586:
3582:
3572:
3570:
3514:
3510:
3500:
3498:
3488:
3484:
3474:
3472:
3471:. 19 March 2021
3463:
3462:
3458:
3443:
3439:
3433:Wayback Machine
3424:
3420:
3412:
3389:
3383:
3379:
3362:Steadman, Ian.
3360:
3356:
3335:
3328:
3277:
3273:
3222:
3218:
3159:
3155:
3150:
3146:
3137:
3133:
3102:
3095:
3044:
3037:
3029:
2988:
2986:"No warp drive"
2982:
2975:
2958:
2949:
2898:
2891:
2840:
2833:
2778:
2774:
2759:
2758:
2754:
2705:
2701:
2686:
2685:
2681:
2630:
2626:
2565:
2561:
2542:
2531:
2524:
2502:
2498:
2482:
2481:
2477:
2437:
2430:
2387:
2380:
2361:
2357:
2349:
2308:
2302:
2298:
2247:
2232:
2181:
2170:
2119:
2110:
2095:
2088:
2073:
2049:
2042:
2037:
1991:
1960:appears in the
1954:William Shatner
1933:
1912:quantum gravity
1890:
1876:
1865:
1857:Kerr black hole
1849:
1832:
1803:
1767:to that of the
1725:Kardashev scale
1703:, that lead to
1693:
1688:
1582:
1554:negative masses
1542:Albert Einstein
1524:, that unifies
1510:Astrophysicist
1508:
1502:
1473:
1450:
1437:
1433:
1429:
1421:
1419:
1415:
1414:
1405:
1400:
1390:
1386:
1382:
1370:
1366:
1357:
1353:
1352:
1348:
1342:
1337:
1332:
1330:
1317:
1311:
1307:
1305:
1300:
1297:
1296:
1270:
1266:
1254:
1250:
1238:
1234:
1208:
1207:
1192:
1188:
1182:
1181:
1163:
1159:
1147:
1143:
1122:
1116:
1115:
1114:
1099:
1095:
1089:
1088:
1079:
1075:
1063:
1059:
1058:
1054:
1045:
1041:
1036:
1033:
1032:
1022:
1015:
998:
997:
969:
962:
961:
946:
942:
930:
929:
914:
913:
898:
894:
882:
881:
874:
872:
865:
856:
852:
843:
842:
831:
827:
818:
814:
805:
799:
798:
797:
782:
778:
766:
765:
763:
756:
741:
737:
734:
733:
720:
704:
700:
696:
694:
687:
672:
668:
664:
662:
659:
658:
638:
637:
625:
621:
614:
605:
601:
598:
597:
582:
578:
571:
565:
561:
558:
557:
548:
547:
532:
528:
522:
521:
503:
499:
489:
483:
479:
476:
475:
462:
455:
453:
450:
449:
439:
435:
429:
423:
397:
393:
383:
379:
366:
362:
346:
342:
332:
328:
316:
312:
297:
293:
287:
283:
274:
270:
269:
265:
253:
249:
244:
241:
240:
233:
210:
167:The Alcubierre
165:
135:
123:quantum gravity
17:
12:
11:
5:
5449:
5439:
5438:
5433:
5428:
5423:
5418:
5413:
5408:
5391:
5390:
5380:
5377:
5376:
5374:
5373:
5366:
5361:
5356:
5351:
5346:
5341:
5336:
5331:
5326:
5321:
5316:
5311:
5306:
5301:
5296:
5294:Choquet-Bruhat
5291:
5286:
5281:
5276:
5271:
5266:
5261:
5256:
5251:
5246:
5241:
5236:
5231:
5226:
5221:
5215:
5213:
5209:
5208:
5205:
5204:
5202:
5201:
5194:
5193:
5188:
5183:
5176:
5175:
5170:
5165:
5160:
5155:
5146:Axisymmetric:
5143:
5142:
5137:
5131:
5120:
5119:
5114:
5109:
5104:
5099:
5094:
5085:Cosmological:
5082:
5080:
5074:
5073:
5071:
5070:
5065:
5060:
5054:
5052:
5046:
5045:
5043:
5042:
5037:
5026:frame-dragging
5023:
5018:
5013:
5010:Einstein rings
5006:Einstein cross
4999:
4988:
4987:
4982:
4976:
4971:
4966:
4953:
4943:
4942:
4937:
4932:
4927:
4921:
4919:
4915:
4914:
4912:
4911:
4909:Ernst equation
4906:
4901:
4896:
4891:
4886:
4881:
4879:BSSN formalism
4876:
4870:
4868:
4864:
4863:
4861:
4860:
4855:
4850:
4845:
4840:
4834:
4832:
4826:
4825:
4823:
4822:
4817:
4811:
4809:
4802:
4794:
4793:
4790:
4789:
4787:
4786:
4781:
4776:
4771:
4766:
4760:
4758:
4752:
4751:
4749:
4748:
4743:
4738:
4736:Ladder paradox
4733:
4728:
4723:
4718:
4713:
4708:
4702:
4700:
4696:
4695:
4693:
4692:
4686:
4684:
4680:
4679:
4677:
4676:
4671:
4666:
4661:
4656:
4651:
4646:
4641:
4639:Speed of light
4636:
4630:
4628:
4622:
4621:
4619:
4618:
4613:
4608:
4602:
4592:
4590:
4583:
4575:
4574:
4567:
4566:
4559:
4552:
4544:
4535:
4534:
4532:
4531:
4526:
4521:
4516:
4511:
4509:Krasnikov tube
4506:
4501:
4496:
4494:BTZ black hole
4491:
4485:
4483:
4467:
4466:
4464:
4463:
4461:Predestination
4458:
4453:
4448:
4443:
4438:
4432:
4430:
4424:
4423:
4421:
4420:
4415:
4410:
4405:
4400:
4394:
4392:
4388:
4387:
4385:
4384:
4379:
4373:
4371:
4365:
4364:
4362:
4361:
4360:
4359:
4349:
4348:
4347:
4336:
4334:
4328:
4327:
4325:
4324:
4319:
4314:
4309:
4304:
4298:
4296:
4292:
4291:
4284:
4283:
4276:
4269:
4261:
4255:
4254:
4240:Dunning, Brian
4236:
4185:
4179:
4174:
4157:
4134:
4133:External links
4131:
4130:
4129:
4080:
4029:
4026:
4023:
4022:
3997:
3970:
3957:
3925:
3872:
3851:
3794:
3773:
3716:
3706:Universe Today
3691:
3634:
3623:. 9 March 2021
3608:
3580:
3508:
3482:
3456:
3437:
3418:
3377:
3354:
3326:
3271:
3216:
3153:
3144:
3131:
3093:
3035:
2973:
2947:
2889:
2831:
2772:
2752:
2699:
2679:
2642:(2): 543â549.
2624:
2579:(10): 105009.
2559:
2529:
2522:
2496:
2475:
2428:
2378:
2355:
2296:
2259:(5): L73âL77.
2230:
2193:(12): 124017.
2168:
2131:(10): 104013.
2108:
2086:
2071:
2039:
2038:
2036:
2033:
2032:
2031:
2026:
2021:
2016:
2011:
2003:
1997:
1990:
1987:
1978:, more recent
1932:
1925:
1889:
1886:
1864:
1863:Wall thickness
1861:
1848:
1845:
1831:
1828:
1802:
1799:
1701:Casimir effect
1692:
1689:
1687:
1684:
1653:Krasnikov tube
1581:
1578:
1532:into a single
1501:
1498:
1470:
1469:
1458:
1453:
1448:
1440:
1436:
1432:
1427:
1424:
1418:
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1323:
1320:
1314:
1310:
1304:
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1269:
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1177:
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1012:
1011:
996:
990:
987:
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981:
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975:
972:
965:
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851:
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830:
826:
821:
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636:
631:
628:
624:
620:
617:
615:
611:
608:
604:
600:
599:
596:
593:
590:
585:
581:
577:
574:
572:
568:
564:
560:
559:
556:
551:
546:
543:
540:
535:
531:
525:
520:
517:
514:
511:
506:
502:
498:
495:
492:
490:
486:
482:
478:
477:
474:
471:
468:
465:
463:
461:
458:
457:
443:
442:
437:
433:
427:
417:
416:
405:
400:
396:
392:
386:
382:
378:
372:
369:
365:
361:
358:
355:
349:
345:
341:
335:
331:
327:
324:
319:
315:
311:
306:
300:
296:
290:
286:
282:
277:
273:
268:
264:
261:
256:
252:
248:
228:of space-like
209:
206:
164:
161:
134:
131:
112:Casimir vacuum
96:energy density
73:metric tensors
67:. Since those
49:energy-density
15:
9:
6:
4:
3:
2:
5448:
5437:
5434:
5432:
5429:
5427:
5424:
5422:
5419:
5417:
5414:
5412:
5409:
5407:
5404:
5403:
5401:
5388:
5378:
5372:
5371:
5367:
5365:
5362:
5360:
5357:
5355:
5352:
5350:
5347:
5345:
5342:
5340:
5337:
5335:
5332:
5330:
5327:
5325:
5322:
5320:
5317:
5315:
5312:
5310:
5307:
5305:
5302:
5300:
5297:
5295:
5292:
5290:
5287:
5285:
5282:
5280:
5279:Chandrasekhar
5277:
5275:
5272:
5270:
5267:
5265:
5262:
5260:
5257:
5255:
5252:
5250:
5247:
5245:
5242:
5240:
5239:Schwarzschild
5237:
5235:
5232:
5230:
5227:
5225:
5222:
5220:
5217:
5216:
5214:
5210:
5200:
5196:
5195:
5192:
5189:
5187:
5184:
5182:
5178:
5177:
5174:
5171:
5169:
5166:
5164:
5161:
5159:
5156:
5153:
5149:
5145:
5144:
5141:
5138:
5135:
5132:
5130:
5126:
5125:Schwarzschild
5122:
5121:
5118:
5115:
5113:
5110:
5108:
5105:
5103:
5100:
5098:
5095:
5092:
5088:
5084:
5083:
5081:
5079:
5075:
5069:
5066:
5064:
5061:
5059:
5056:
5055:
5053:
5047:
5041:
5038:
5035:
5031:
5027:
5024:
5022:
5021:Shapiro delay
5019:
5017:
5014:
5011:
5007:
5003:
5000:
4997:
4993:
4990:
4989:
4986:
4983:
4980:
4977:
4975:
4972:
4970:
4967:
4965:
4964:collaboration
4961:
4957:
4954:
4952:
4948:
4945:
4944:
4941:
4938:
4936:
4933:
4931:
4930:Event horizon
4928:
4926:
4923:
4922:
4920:
4916:
4910:
4907:
4905:
4902:
4900:
4897:
4895:
4892:
4890:
4887:
4885:
4882:
4880:
4877:
4875:
4874:ADM formalism
4872:
4871:
4869:
4865:
4859:
4856:
4854:
4851:
4849:
4846:
4844:
4841:
4839:
4836:
4835:
4833:
4827:
4821:
4818:
4816:
4813:
4812:
4810:
4806:
4803:
4801:
4795:
4785:
4782:
4780:
4779:Biquaternions
4777:
4775:
4772:
4770:
4767:
4765:
4762:
4761:
4759:
4757:
4753:
4747:
4744:
4742:
4739:
4737:
4734:
4732:
4729:
4727:
4724:
4722:
4719:
4717:
4714:
4712:
4709:
4707:
4706:Time dilation
4704:
4703:
4701:
4697:
4691:
4688:
4687:
4685:
4681:
4675:
4672:
4670:
4667:
4665:
4662:
4660:
4659:Proper length
4657:
4655:
4652:
4650:
4647:
4645:
4642:
4640:
4637:
4635:
4632:
4631:
4629:
4623:
4617:
4614:
4612:
4609:
4606:
4603:
4601:
4597:
4594:
4593:
4591:
4587:
4584:
4582:
4576:
4572:
4565:
4560:
4558:
4553:
4551:
4546:
4545:
4542:
4530:
4527:
4525:
4522:
4520:
4517:
4515:
4512:
4510:
4507:
4505:
4502:
4500:
4497:
4495:
4492:
4490:
4487:
4486:
4484:
4482:
4476:
4472:
4468:
4462:
4459:
4457:
4454:
4452:
4449:
4447:
4444:
4442:
4439:
4437:
4434:
4433:
4431:
4429:
4425:
4419:
4416:
4414:
4411:
4409:
4406:
4404:
4401:
4399:
4396:
4395:
4393:
4389:
4383:
4380:
4378:
4375:
4374:
4372:
4370:
4366:
4358:
4355:
4354:
4353:
4350:
4346:
4343:
4342:
4341:
4338:
4337:
4335:
4333:
4329:
4323:
4320:
4318:
4315:
4313:
4310:
4308:
4305:
4303:
4300:
4299:
4297:
4293:
4289:
4282:
4277:
4275:
4270:
4268:
4263:
4262:
4259:
4251:
4250:
4245:
4241:
4237:
4233:
4229:
4225:
4221:
4217:
4213:
4208:
4207:gr-qc/9907026
4203:
4199:
4195:
4191:
4186:
4183:
4180:
4178:
4175:
4172:
4166:
4162:
4158:
4145:
4141:
4137:
4136:
4126:
4122:
4118:
4114:
4110:
4106:
4101:
4100:gr-qc/0406083
4096:
4092:
4088:
4087:
4081:
4077:
4073:
4069:
4065:
4061:
4057:
4052:
4051:gr-qc/9707024
4047:
4043:
4039:
4038:
4032:
4031:
4011:
4007:
4001:
3985:
3981:
3974:
3967:
3961:
3942:
3935:
3929:
3921:
3917:
3913:
3909:
3905:
3901:
3896:
3895:gr-qc/9702041
3891:
3887:
3883:
3876:
3867:
3862:
3855:
3844:
3840:
3836:
3832:
3828:
3824:
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3469:Physics World
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3112:: 1105â1110.
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2967:gr-qc/9906050
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2917:gr-qc/9511068
2913:
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2859:gr-qc/0110086
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2649:gr-qc/9812067
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2138:gr-qc/0207057
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2100:
2093:
2091:
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2060:
2056:
2055:
2047:
2045:
2040:
2030:
2027:
2025:
2022:
2020:
2017:
2015:
2012:
2010:
2009:
2004:
2001:
1998:
1996:
1993:
1992:
1986:
1984:
1981:
1977:
1976:
1971:
1970:
1966:
1963:
1959:
1955:
1951:
1950:
1945:
1940:
1939:
1930:
1924:
1921:
1915:
1913:
1908:
1903:
1899:
1895:
1885:
1883:
1874:
1873:Planck length
1870:
1860:
1858:
1854:
1844:
1841:
1835:
1827:
1825:
1820:
1815:
1813:
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1762:
1761:exotic matter
1758:
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1745:negative mass
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1633:exotic matter
1630:
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1590:time dilation
1587:
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1574:exotic matter
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1506:Negative mass
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1485:exotic matter
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390:
384:
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329:
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288:
284:
280:
275:
271:
266:
262:
259:
254:
250:
246:
239:
238:
237:
231:
230:hypersurfaces
227:
223:
219:
215:
214:ADM formalism
205:
201:
197:
195:
194:time dilation
191:
186:
182:
178:
174:
170:
160:
158:
157:
152:
148:
144:
140:
130:
128:
124:
120:
115:
113:
109:
105:
101:
100:exotic matter
97:
91:
89:
88:physical laws
85:
80:
78:
74:
70:
66:
62:
58:
57:negative mass
54:
50:
46:
42:
37:
32:
23:
19:
5369:
5190:
5063:KaluzaâKlein
4815:Introduction
4741:Twin paradox
4514:Misner space
4499:Gödel metric
4488:
4479:can contain
4247:
4193:
4189:
4164:
4148:. Retrieved
4144:the original
4090:
4084:
4041:
4035:
4013:. Retrieved
4009:
4000:
3988:. Retrieved
3984:the original
3973:
3960:
3948:. Retrieved
3941:the original
3928:
3885:
3881:
3875:
3854:
3814:
3810:
3797:
3776:
3767:
3729:
3725:
3719:
3704:
3694:
3651:
3647:
3637:
3625:. Retrieved
3620:
3611:
3599:. Retrieved
3593:
3583:
3571:. Retrieved
3525:
3521:
3511:
3499:. Retrieved
3495:
3485:
3473:. Retrieved
3468:
3459:
3440:
3421:
3397:
3393:
3380:
3367:
3357:
3342:
3286:
3280:
3274:
3231:
3225:
3219:
3168:
3162:
3156:
3147:
3139:
3134:
3109:
3105:
3053:
3047:
3027:the original
2998:
2992:
2907:
2901:
2849:
2843:
2789:
2785:
2775:
2764:
2755:
2712:
2708:
2702:
2691:
2682:
2639:
2633:
2627:
2576:
2572:
2562:
2505:
2499:
2440:
2398:
2394:
2372:
2358:
2318:
2312:
2299:
2256:
2250:
2190:
2184:
2128:
2122:
2102:
2052:
2029:Unruh effect
2007:
1979:
1973:
1967:
1965:tabletop RPG
1961:
1957:
1947:
1936:
1934:
1928:
1927:Relation to
1916:
1891:
1866:
1850:
1836:
1833:
1823:
1818:
1816:
1804:
1785:violate the
1783:
1757:Harold White
1754:
1750:Planck scale
1737:solar masses
1729:
1713:
1694:
1686:Difficulties
1678:
1675:
1667:
1658:
1640:
1631:and require
1618:
1612:
1608:
1602:
1598:tidal forces
1583:
1562:
1519:
1512:Jamie Farnes
1509:
1482:
1471:
1291:
1023:
1016:
1013:
653:
444:
418:
211:
202:
198:
190:relativistic
166:
154:
150:
136:
116:
92:
81:
76:
30:
28:
18:
5152:KerrâNewman
5123:Spherical:
4992:Other tests
4935:Singularity
4867:Formulation
4829:Fundamental
4683:Formulation
4664:Proper time
4625:Fundamental
4504:Kerr metric
4441:Determinism
4382:Causal loop
4288:Time travel
4169:(hosted by
3888:(1): 8â14.
3627:23 December
3601:21 December
3400:: 242â247.
2693:EurekAlert!
2401:: 254â257.
1898:time travel
1714:If certain
1709:massâenergy
1596:. Enormous
1570:time travel
1530:dark matter
1526:dark energy
208:Mathematics
151:warp bubble
110:) that the
104:dark energy
5400:Categories
5304:Zel'dovich
5212:Scientists
5191:Alcubierre
4998:of Mercury
4996:precession
4925:Black hole
4808:Background
4800:relativity
4769:World line
4764:Light cone
4589:Background
4581:relativity
4571:Relativity
4471:Spacetimes
4446:Eternalism
4413:Multiverse
4200:: 044005.
4028:References
3950:25 January
3661:2105.03079
3535:2006.07125
2799:1902.08287
2722:1712.07962
2586:2102.06824
2450:2103.05610
2008:Enterprise
1958:Alcubierre
1931:warp drive
1679:round trip
1662:light cone
1534:dark fluid
1504:See also:
1494:warp drive
212:Using the
175:. It is a
147:spacecraft
55:(that is,
41:warp drive
5274:Robertson
5259:Friedmann
5254:Eddington
5244:de Sitter
5078:Solutions
4956:detectors
4951:astronomy
4918:Phenomena
4853:Geodesics
4756:Spacetime
4699:Phenomena
4456:Free will
4352:Time loop
4125:119010055
3920:118984236
3866:1001.4960
3739:1202.5708
3686:234095711
3568:219635854
3560:0264-9381
3023:250843331
2826:0004-6361
2766:Big Think
2619:231924903
2611:0264-9381
2550:Space.com
2485:cite book
2423:0094-5765
2200:0904.0141
2081:202443606
1980:Star Trek
1962:Star Trek
1938:Star Trek
1929:Star Trek
1807:tachyonic
1769:Voyager 1
1514:from the
1322:π
1303:−
1154:−
1129:−
983:σ
977:
953:−
937:σ
927:
921:−
889:σ
879:
776:−
623:δ
603:γ
580:β
563:β
497:−
481:β
460:α
364:γ
330:β
295:β
285:β
281:−
272:α
263:−
226:foliation
222:spacetime
173:spacetime
137:In 1994,
108:wormholes
84:spacetime
69:solutions
5387:Category
5264:LemaĂźtre
5229:Einstein
5219:Poincaré
5179:Others:
5163:TaubâNUT
5129:interior
5051:theories
5049:Advanced
5016:redshift
4831:concepts
4649:Rapidity
4627:concepts
4451:Fatalism
4249:Skeptoid
4232:59940462
4015:22 April
3843:Archived
3839:10020029
3711:Archived
3573:22 April
3501:22 April
3475:22 April
3451:Archived
3429:Archived
3410:Archived
3372:Archived
3368:Wired UK
3349:Archived
3321:15466313
3266:15279207
3211:18106362
3203:10019835
3088:19017879
2942:55825213
2884:15859984
2747:53600834
2554:Archived
2374:example.
2369:Archived
2347:Archived
2343:10038800
2225:59575856
2163:17498199
1989:See also
1983:spin-off
1877:1.6 Ă 10
1819:en route
1795:dominant
1645:tachyons
1609:solution
1605:ADM form
1594:g-forces
1490:wormhole
5329:Hawking
5324:Penrose
5309:Novikov
5289:Wheeler
5234:Hilbert
5224:Lorentz
5181:pp-wave
5002:lensing
4798:General
4579:Special
4357:in film
4212:Bibcode
4165:YouTube
4105:Bibcode
4076:1884428
4056:Bibcode
3900:Bibcode
3819:Bibcode
3764:3993148
3744:Bibcode
3666:Bibcode
3540:Bibcode
3496:Reuters
3402:Bibcode
3301:Bibcode
3246:Bibcode
3183:Bibcode
3114:Bibcode
3068:Bibcode
3003:Bibcode
2922:Bibcode
2864:Bibcode
2804:Bibcode
2727:Bibcode
2715:: A92.
2674:6540037
2654:Bibcode
2591:Bibcode
2455:Bibcode
2403:Bibcode
2323:Bibcode
2291:4797900
2271:Bibcode
2205:Bibcode
2143:Bibcode
1995:EmDrive
1765:Jupiter
1641:one-way
1613:adapted
1580:Physics
133:History
5370:others
5359:Thorne
5349:Misner
5334:Taylor
5319:Geroch
5314:Ehlers
5284:Zwicky
5102:Kasner
4230:
4150:2 July
4123:
4074:
3990:2 June
3918:
3837:
3762:
3684:
3566:
3558:
3319:
3264:
3209:
3201:
3086:
3021:
2940:
2882:
2824:
2792:: A5.
2745:
2672:
2617:
2609:
2520:
2473:
2421:
2341:
2289:
2223:
2161:
2079:
2069:
1791:strong
1781:all".
1550:cosmos
1478:tensor
1472:where
1026:> 0
1019:> 0
654:where
419:where
220:, the
169:metric
53:vacuum
5364:Weiss
5344:Bondi
5339:Hulse
5269:Milne
5173:discs
5117:Milne
5112:Gödel
4969:Virgo
4228:S2CID
4202:arXiv
4196:(4).
4121:S2CID
4095:arXiv
4072:S2CID
4046:arXiv
3944:(PDF)
3937:(PDF)
3916:S2CID
3890:arXiv
3861:arXiv
3846:(PDF)
3807:(PDF)
3783:arXiv
3760:S2CID
3734:arXiv
3682:S2CID
3656:arXiv
3564:S2CID
3530:arXiv
3413:(PDF)
3390:(PDF)
3317:S2CID
3291:arXiv
3262:S2CID
3236:arXiv
3207:S2CID
3173:arXiv
3084:S2CID
3058:arXiv
3030:(PDF)
3019:S2CID
2989:(PDF)
2962:arXiv
2938:S2CID
2912:arXiv
2880:S2CID
2854:arXiv
2794:arXiv
2743:S2CID
2717:arXiv
2670:S2CID
2644:arXiv
2615:S2CID
2581:arXiv
2445:arXiv
2350:(PDF)
2309:(PDF)
2287:S2CID
2261:arXiv
2221:S2CID
2195:arXiv
2159:S2CID
2133:arXiv
2077:S2CID
2035:Notes
1869:Tufts
1774:torus
1670:Deneb
1568:(see
5299:Kerr
5249:Weyl
5148:Kerr
5008:and
4962:and
4960:LIGO
4477:that
4152:2008
4017:2021
3992:2013
3952:2017
3835:PMID
3629:2021
3603:2021
3575:2021
3556:ISSN
3503:2021
3477:2021
3199:PMID
2822:ISSN
2607:ISSN
2518:ISBN
2491:link
2471:ISBN
2419:ISSN
2339:PMID
2067:ISBN
2006:IXS
1935:The
1812:Vega
1793:and
1588:and
1528:and
1021:and
974:tanh
924:tanh
876:tanh
71:are
29:The
5354:Yau
4979:GEO
4473:in
4220:doi
4113:doi
4064:doi
3908:doi
3886:415
3827:doi
3752:doi
3674:doi
3652:105
3548:doi
3344:io9
3309:doi
3254:doi
3191:doi
3122:doi
3110:504
3076:doi
3011:doi
2930:doi
2872:doi
2812:doi
2790:626
2735:doi
2713:620
2662:doi
2599:doi
2510:doi
2463:doi
2411:doi
2399:139
2331:doi
2279:doi
2213:doi
2151:doi
2059:doi
1824:any
1655:):
216:of
5402::
5028:/
4994::
4949::
4246:.
4226:.
4218:.
4210:.
4194:62
4192:.
4173:).
4163:.
4119:.
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