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1844:"Consequently, he ends up with inequalities of the type... Except that one may look at the actual equations of Matrix theory and see that none of these commutators is nonzero... The last displayed inequality above obviously can't be a consequence of quantum gravity because it doesn't depend on G at all! However, in the Gâ0 limit, one must reproduce non-gravitational physics in the flat Euclidean background spacetime. Hogan's rules don't have the right limit so they can't be right." â
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450:; it is those light rays that are just barely unable to escape. If neighboring geodesics start moving toward each other they eventually collide, at which point their extension is inside the black hole. So the geodesics are always moving apart, and the number of geodesics which generate the boundary, the area of the horizon, always increases. Hawking's result was called the second law of
641:
that this field makes a logarithmic tent-pole shaped bump on the horizon of a black hole, and like a shadow, the bump is an alternative description of the particle's location and mass. For a four-dimensional spherical uncharged black hole, the deformation of the horizon is similar to the type of deformation which describes the emission and absorption of particles on a string-theory
436:, this prevents falling objects from crossing the event horizon no matter how close they get to it. Since any change in quantum state requires time to flow, all objects and their quantum information state stay imprinted on the event horizon. Bekenstein concluded that from the perspective of any remote observer, the black hole entropy is directly proportional to the area of the
242:
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arrangement" of matter and energy. The only salient difference between the thermodynamic entropy of physics and
Shannon's entropy of information is in the units of measure; the former is expressed in units of energy divided by temperature, the latter in essentially dimensionless "bits" of information.
761:
of a particle are the product of all the degrees of freedom of its sub-particles, were a particle to have infinite subdivisions into lower-level particles, the degrees of freedom of the original particle would be infinite, violating the maximal limit of entropy density. The holographic principle thus
648:
This idea was made more precise by
Leonard Susskind, who had also been developing holography, largely independently. Susskind argued that the oscillation of the horizon of a black hole is a complete description of both the infalling and outgoing matter, because the world-sheet theory of string theory
461:
At first, Hawking did not take the analogy too seriously. He argued that the black hole must have zero temperature, since black holes do not radiate and therefore cannot be in thermal equilibrium with any black body of positive temperature. Then he discovered that black holes do radiate. When heat is
652:
This work showed that the black hole information paradox is resolved when quantum gravity is described in an unusual string-theoretic way assuming the string-theoretical description is complete, unambiguous and non-redundant. The space-time in quantum gravity would emerge as an effective description
588:, the enumerated ways a system can be configured microscopically while leaving the macroscopic description unchanged. Black hole entropy is deeply puzzling â it says that the logarithm of the number of states of a black hole is proportional to the area of the horizon, not the volume in the interior.
307:
quantum field theories. Much of the usefulness of the duality results from a strong-weak duality: when the fields of the quantum field theory are strongly interacting, the ones in the gravitational theory are weakly interacting and thus more mathematically tractable. This fact has been used to study
214:
titled "Information in the
Holographic Universe", Bekenstein summarizes that "Thermodynamic entropy and Shannon entropy are conceptually equivalent: the number of arrangements that are counted by Boltzmann entropy reflects the amount of Shannon information one would need to implement any particular
793:
This plot shows the sensitivity of various experiments to fluctuations in space and time. Horizontal axis is the log of apparatus size (or duration time the speed of light), in meters; vertical axis is the log of the rms fluctuation amplitude in the same units. The lower left corner represents the
640:
would deform the horizon of the black hole, and the deformed horizon could produce different outgoing particles than the undeformed horizon. When a particle falls into a black hole, it is boosted relative to an outside observer, and its gravitational field assumes a universal form. 't Hooft showed
399:
Given a fixed volume, a black hole whose event horizon encompasses that volume should be the object with the highest amount of entropy. Otherwise, imagine something with a larger entropy, then by throwing more mass into that something, we obtain a black hole with less entropy, violating the second
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Hawking's calculation suggested that the radiation which black holes emit is not related in any way to the matter that they absorb. The outgoing light rays start exactly at the edge of the black hole and spend a long time near the horizon, while the infalling matter only reaches the horizon much
407:
The illustration demonstrates the way of thinking of the entropic gravity, holographic principle, entropy distribution, and derivation of
Einstein General Relativity equations from these considerations. The Einstein equation takes the form of the first law of thermodynamics when Bekenstein and
197:
described it more precisely in terms of the number of distinct microscopic states that the particles composing a macroscopic "chunk" of matter could be in, while still "looking" like the same macroscopic "chunk". As an example, for the air in a room, its thermodynamic entropy would equal the
560:
If black holes have a finite entropy, they should also have a finite temperature. In particular, they would come to equilibrium with a thermal gas of photons. This means that black holes would not only absorb photons, but they would also have to emit them in the right amount to maintain
645:. Since the deformations on the surface are the only imprint of the incoming particle, and since these deformations would have to completely determine the outgoing particles, 't Hooft believed that the correct description of the black hole would be by some form of string theory.
649:
was just such a holographic description. While short strings have zero entropy, he could identify long highly excited string states with ordinary black holes. This was a deep advance because it revealed that strings have a classical interpretation in terms of black holes.
568:
Time-independent solutions to field equations do not emit radiation, because a time-independent background conserves energy. Based on this principle, Hawking set out to show that black holes do not radiate. But, to his surprise, a careful analysis convinced him that
794:
Planck length or time. In these units, the size of the observable universe is about 26. Various physical systems and experiments are plotted. The "holographic noise" line represents the rms transverse holographic fluctuation amplitude on a given scale.
70:. Susskind said, "The three-dimensional world of ordinary experienceâthe universe filled with galaxies, stars, planets, houses, boulders, and peopleâis a hologram, an image of reality coded on a distant two-dimensional surface." As pointed out by
629:. This would mean that quantum mechanics would have to be modified because, in quantum mechanics, states which are superpositions with probability amplitudes never become states which are probabilistic mixtures of different possibilities.
392:, the entropy would disappear. The random properties of the gas would no longer be seen once the black hole had absorbed the gas and settled down. One way of salvaging the second law is if black holes are in fact random objects with an
1010:"Is Our Universe a Hologram? Physicists Debate Famous Idea on Its 25th Anniversary â The Ads/CFT duality conjecture suggests our universe is a hologram, enabling significant discoveries in the 25 years since it was first proposed"
696:. The later authors reinterpreted the same matrix models as a description of the dynamics of point black holes in particular limits. Holography allowed them to conclude that the dynamics of these black holes give a complete
573:, and in just the right way to come to equilibrium with a gas at a finite temperature. Hawking's calculation fixed the constant of proportionality at 1/4; the entropy of a black hole is one quarter its horizon area in
806:
claims that the holographic principle would imply quantum fluctuations in spatial position that would lead to apparent background noise or "holographic noise" measurable at gravitational wave detectors, in particular
653:
of the theory of oscillations of a lower-dimensional black-hole horizon, and suggest that any black hole with appropriate properties, not just strings, would serve as a basis for a description of string theory.
121:
bags of gold". The existence of such solutions conflicts with the holographic interpretation, and their effects in a quantum theory of gravity including the holographic principle are not yet fully understood.
750:) about the whereabouts of all the particles which compose matter in that volume. In particular, a given volume has an upper limit of information it can contain, at which it will collapse into a black hole.
534:
1626:
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The holographic principle states that the entropy of ordinary mass (not just black holes) is also proportional to surface area and not volume; that volume itself is illusory and the universe is really a
74:, Thorn observed in 1978, that string theory admits a lower-dimensional description in which gravity emerges from it in what would now be called a holographic way. The prime example of holography is the
826:, shows that Craig Hogan's noise is absent down to a scale of 10 meters, as opposed to the scale of 10 meters predicted by Hogan, and the scale of 10 meters found in measurements of the
746:
used in classical physics. Applying this definition to a physical system leads to the conclusion that, for a given energy in a given volume, there is an upper limit to the density of information (the
174:. As an objective measure of the quantity of information, Shannon entropy has been enormously useful, as the design of all modern communications and data storage devices, from cellular phones to
162:
Bekenstein's topical overview "A Tale of Two
Entropies" describes potentially profound implications of Wheeler's trend, in part by noting a previously unexpected connection between the world of
614:
later. The infalling and outgoing mass/energy interact only when they cross. It is implausible that the outgoing state would be completely determined by some tiny residual scattering.
424:
on the entropy in a region of space, and the bound was proportional to the area of the region. He concluded that the black hole entropy is directly proportional to the area of the
952:, or internal quantum state is not information that is implied to be preserved in the surface fluctuations of the event horizon. (See however "path integral quantization")
117:
that allow values of the entropy larger than those allowed by an area law (radius squared), hence in principle larger than those of a black hole. These are the so-called "
4103:
811:. However these claims have not been widely accepted, or cited, among quantum gravity researchers and appear to be in direct conflict with string theory calculations.
206:
Shannon's efforts to find a way to quantify the information contained in, for example, a telegraph message, led him unexpectedly to a formula with the same form as
1009:
982:"Black Holes May Hide a Mind-Bending Secret About Our Universe â Take gravity, add quantum mechanics, stir. What do you get? Just maybe, a holographic cosmos"
446:
had shown earlier that the total horizon area of a collection of black holes always increases with time. The horizon is a boundary defined by light-like
636:
in more detail. He noted that when
Hawking radiation escapes, there is a way in which incoming particles can modify the outgoing particles. Their
198:
logarithm of the count of all the ways that the individual gas molecules could be distributed in the room, and all the ways they could be moving.
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1313:"Information in the Holographic Universe â Theoretical results about black holes suggest that the universe could be like a gigantic hologram"
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is microscopically random, like a hot gas. A known configuration of classical fields has zero entropy: there is nothing random about
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719:. These developments simultaneously explained how string theory is related to some forms of supersymmetric quantum field theories.
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and classical physics. This connection was first described shortly after the seminal 1948 papers of
American applied mathematician
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The
Bekenstein-Hawking entropy of a black hole is proportional to the surface area of the black hole as expressed in Planck units.
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of a system is the expected value of the system's information content. This definition of entropy is equivalent to the standard
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The duality represents a major advance in understanding of string theory and quantum gravity. This is because it provides a
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is substituted for the thermal energy added to the system, generally by non-integrable random processes, in contrast to d
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is defined as the logarithm of the reciprocal of the probability that a system is in a specific microstate, and the
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This suggests that matter itself cannot be subdivided infinitely many times and there must be an ultimate level of
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1718:"Central charges in the canonical realization of asymptotic symmetries: an example from three-dimensional gravity"
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causes time, from the perspective of a remote observer, to stop at the event horizon. Due to the natural limit on
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Bekenstein, Jacob D. (January 1981). "Universal upper bound on the entropy-to-energy ratio for bounded systems".
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The physical universe is widely seen to be composed of "matter" and "energy". In his 2003 article published in
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of all the objects that have fallen into the hole might be entirely contained in surface fluctuations of the
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Hawking interpreted this to mean that when black holes absorb some photons in a pure state described by a
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by translating problems in those subjects into more mathematically tractable problems in string theory.
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had rigorously proved in 1986, that the asymptotic symmetry of 2+1 dimensional gravity gives rise to a
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420:; when there is too much energy, the gas collapses into a black hole. Bekenstein used this to put an
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claimed to have found a way to test the holographic principle with a tabletop photon experiment.
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UC Berkeley's
Raphael Bousso gives an introductory lecture on the holographic principle â Video.
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The Black Hole War â My Battle with
Stephen Hawking to Make the World Safe for Quantum Mechanics
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189:(the branch of physics dealing with heat), entropy is popularly described as a measure of the "
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gave the first holographic descriptions of a higher-dimensional object, the 3+1-dimensional
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Physics inside a bounded region is fully captured by physics at the boundary of the region
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1292:"Information in the Holographic Universe by Jacob D. Bekenstein [July 14, 2003]"
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680:. The matrix theory they proposed was first suggested as a description of two branes in
261:, is a conjectured relationship between two kinds of physical theories. On one side are
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within the framework of string theory. However, there exist classical solutions to the
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in late 1997. Important aspects of the correspondence were elaborated in articles by
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memorably penned, 'see a world in a grain of sand', or is that idea no more than '
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except in the case of measurements, which the black hole should not be performing
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introduced today's most widely used measure of information content, now known as
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and because it is the most successful realization of the holographic principle.
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Susskind, Leonard (February 2003). "The Anthropic landscape of string theory".
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1098:. International A.D. Sakharov Conference on Physics. Moscow. pp. 447â54.
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using a holographic description in terms of charged point black holes, the D0
388:. If one throws a hot gas with entropy into a black hole, once it crosses the
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2022:, pedagogical lecture. For the holographic principle: see especially Fig. 1.
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Hogan, Craig J. (2008). "Measurement of quantum fluctuations in geometry".
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Majumdar, Parthasarathi (1998). "Black Hole Entropy and Quantum Gravity".
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that increases by an amount greater than the entropy of the consumed gas.
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1337:"The large $ N$ limit of superconformal field theories and supergravity"
803:
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193:" in a physical system of matter and energy. In 1877, Austrian physicist
143:
146:, with energy and matter as incidentals". Bekenstein asks "Could we, as
19:"Holographic universe" redirects here. For the Scar Symmetry album, see
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1988:'t Hooft, Gerard (1993). "Dimensional Reduction in Quantum Gravity".
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added to a thermal system, the change in entropy is the increase in
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instrument. Research continued at Fermilab under Hogan as of 2013.
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Troubled by this paradox, Gerard 't Hooft analyzed the emission of
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The most rigorous realization of the holographic principle is the
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529:{\displaystyle {\rm {d}}S={\frac {{\rm {\delta }}M\ c^{2}}{T}}.}
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to the information "inscribed" on the surface of its boundary.
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and a few additional state variables, such as the pressure.)
43:
62:, it was given a precise string theoretic interpretation by
97:, rather than cubed as might be expected. In the case of a
1889:"Frequently Asked Questions for the Holometer at Fermilab"
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Bousso, Raphael (1999). "A Covariant Entropy Conjecture".
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Bardeen, J. M.; Carter, B.; Hawking, S. W. (1 June 1973).
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implies that the subdivisions must stop at some level.
1912:"Single photon could detect quantum-scale black holes"
1941:
Bousso, Raphael (2002). "The holographic principle".
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Bousso, Raphael (2002). "The Holographic Principle".
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Susskind, Leonard (1995). "The World as a Hologram".
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article on holographic principle by Jacob Bekenstein
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Analyses in 2011 of measurements of gamma ray burst
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anti-de Sitter/conformal field theory correspondence
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speculatively summarized a current trend started by
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can be thought of as encoded on a lower-dimensional
2056:from the original on 11 December 2021 – via
1096:Reformulating string theory with the 1/N expansion
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602:
319:The AdS/CFT correspondence was first proposed by
303:It also provides a powerful toolkit for studying
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1341:Advances in Theoretical and Mathematical Physics
42:that states that the description of a volume of
1413:"Top Cited Articles of All Time (2014 edition)"
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277:. On the other side of the correspondence are
81:The holographic principle was inspired by the
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1863:"Integral challenges physics beyond Einstein"
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377:, they were thought not to have any entropy.
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154:'?", referring to the holographic principle.
1987:
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656:In 1995, Susskind, along with collaborators
384:noted that this leads to a violation of the
210:. In an article in the August 2003 issue of
970:
373:. Since black holes are exact solutions of
202:Energy, matter, and information equivalence
4255:
4241:
3841:Magnetospheric eternally collapsing object
3282:
3268:
2087:
2073:
2038:
2012:Introduction to the AdS/CFT correspondence
1436:
1307:
1148:. Little, Brown and Company. p. 410.
1001:
822:space observatory launched in 2002 by the
296:formulation of string theory with certain
1993:
1954:
1779:
1692:
1585:
1548:
1370:
1352:
1334:
1298:
1240:
1184:
1103:
1054:
109:. The holographic principle resolves the
1716:Brown, J. D. & Henneaux, M. (1986).
1682:
1624:
1534:
1217:
1139:
1040:
788:
726:
625:in a thermal mixed state described by a
402:
240:
157:
1850:Hogan's holographic noise doesn't exist
1651:
1482:"The four laws of black hole mechanics"
1405:
1280:Information in the Holographic Universe
1008:Ananthaswamy, Anil (14 February 2023).
976:
4684:
1940:
1722:Communications in Mathematical Physics
1571:
1486:Communications in Mathematical Physics
1227:(2009). "Black Holes, AdS, and CFTs".
1223:
1168:
4236:
3263:
2068:
1909:
1818:
1763:
1685:The Davis Meeting on Cosmic Inflation
1625:Anderson, Rupert W. (31 March 2015).
1330:
1328:
1093:
920:"Complete description" means all the
784:
668:, presented a formulation of the new
346:
125:
93:in any region scales with the radius
89:, which conjectures that the maximum
4217:
2485:Bogomol'nyiâPrasadâSommerfield bound
2044:"The Holographic Universe Explained"
1658:. New York: Back Bay Books. p.
1094:Thorn, Charles B. (27â31 May 1991).
289:that describe elementary particles.
285:, including theories similar to the
265:(AdS) which are used in theories of
4262:
1821:"Our world may be a giant hologram"
580:The entropy is proportional to the
245:Conjectured relationship of adS/CFT
13:
1628:The Cosmic Compendium: Black Holes
1325:
1229:General Relativity and Gravitation
480:
14:
4718:
4670:Template:Quantum mechanics topics
2094:
2004:
1819:Chown, Marcus (15 January 2009).
4665:
4664:
4386:Topological quantum field theory
4216:
4207:
4206:
3505:TolmanâOppenheimerâVolkoff limit
3376:
4371:Jackiw–Teitelboim gravity
3622:Innermost stable circular orbit
3289:
2682:Eleven-dimensional supergravity
1910:Cowen, Ron (22 November 2012).
1903:
1881:
1855:
1838:
1812:
1757:
1709:
1676:
1645:
1618:
1565:
1528:
1473:
1430:
1396:
1043:Journal of Mathematical Physics
914:
905:
682:eleven-dimensional supergravity
357:An object with relatively high
4576:Causal dynamical triangulation
4444:Black hole information paradox
4048:Timeline of black hole physics
1574:Journal of High Energy Physics
1335:Maldacena, Juan (March 1998).
1284:
1273:
1162:
1087:
773:. However, J. David Brown and
609:Black hole information paradox
603:Black hole information paradox
597:covariant version of the bound
408:Hawking equations are applied.
111:black hole information paradox
1:
4542:Wheeler–DeWitt equation
3816:Nonsingular black hole models
2130:Second superstring revolution
1604:10.1088/1126-6708/1999/07/004
1402:Klebanov and Maldacena. 2009.
959:
934:size, shape, motion, number,
877:Implicate and explicate order
4464:Cosmic censorship hypothesis
4283:BatalinâVilkovisky formalism
2624:Generalized complex manifold
2125:First superstring revolution
2000:. 't Hooft's original paper.
882:Quantum speed limit theorems
723:Limit on information density
386:second law of thermodynamics
333:Alexander Markovich Polyakov
21:Holographic Universe (album)
7:
4702:Quantum information science
4038:Rossi X-ray Timing Explorer
4003:Hypercompact stellar system
3993:Gamma-ray burst progenitors
1537:Indian Journal of Physics B
839:
430:Gravitational time dilation
182:, rely on Shannon entropy.
101:, the insight was that the
38:and a supposed property of
23:. For the Epica album, see
10:
4723:
4560:Hartle–Hawking state
4459:Bousso's holographic bound
4439:Black hole complementarity
3724:Black hole complementarity
3691:Bousso's holographic bound
3676:Quasi-periodic oscillation
3374:
3368:MalamentâHogarth spacetime
2222:Non-critical string theory
1798:10.1103/PhysRevD.77.104031
1393:de Haro et al. 2013, p. 2.
1372:10.4310/ATMP.1998.v2.n2.a1
1140:Susskind, Leonard (2008).
857:Bousso's holographic bound
606:
350:
234:
231:The AdS/CFT correspondence
50:to the region â such as a
18:
4656:
4623:
4568:
4552:Euclidean quantum gravity
4550:
4529:Canonical quantum gravity
4527:
4494:
4487:
4479:Gravitational singularity
4449:Black-hole thermodynamics
4429:
4394:
4351:
4333:RyuâTakayanagi conjecture
4270:
4202:
4076:
3928:
3890:
3869:
3808:
3767:
3716:
3595:Gravitational singularity
3582:
3475:
3385:
3310:
3297:
2766:
2743:
2720:
2667:
2552:
2460:
2402:
2334:
2283:
2250:
2145:
2102:
1973:10.1103/RevModPhys.74.825
1943:Reviews of Modern Physics
1259:10.1007/s10714-008-0749-7
1203:10.1103/RevModPhys.74.825
1172:Reviews of Modern Physics
932:) determined these to be
924:qualities. For example,
452:black hole thermodynamics
353:Black hole thermodynamics
269:, formulated in terms of
87:black hole thermodynamics
25:The Holographic Principle
4606:Superfluid vacuum theory
4361:2+1D topological gravity
4179:PSO J030947.49+271757.31
4104:SDSS J150243.09+111557.3
3637:BlandfordâZnajek process
2758:Introduction to M-theory
2452:WessâZuminoâWitten model
2394:HananyâWitten transition
2120:History of string theory
1652:Dennett, Daniel (1991).
898:
599:based upon null sheets.
466:divided by temperature:
314:condensed matter physics
279:conformal field theories
178:to hard disk drives and
4596:Noncommutative geometry
4343:WeinbergâWitten theorem
4338:Trans-Planckian problem
3435:Active galactic nucleus
2437:Vertex operator algebra
2137:String theory landscape
1655:Consciousness Explained
1459:10.1103/PhysRevD.23.287
456:law of entropy increase
434:maximum speed of motion
4278:AdS/CFT correspondence
4063:Tidal disruption event
4033:Supermassive dark star
3951:Black holes in fiction
3936:Outline of black holes
3569:Supermassive dark star
3488:Gravitational collapse
2735:AdS/CFT correspondence
2490:Exceptional Lie groups
2432:Superconformal algebra
2404:Conformal field theory
2275:MontonenâOlive duality
2227:Non-linear sigma model
795:
767:AdS/CFT correspondence
732:
678:type IIA string theory
530:
454:, by analogy with the
412:In a sphere of radius
409:
283:quantum field theories
246:
237:AdS/CFT correspondence
140:John Archibald Wheeler
76:AdS/CFT correspondence
4504:Bosonic string theory
4416:Semiclassical gravity
4313:Holographic principle
4303:Gravitational anomaly
3941:Black Hole Initiative
3754:Holographic principle
2730:Holographic principle
2697:Type IIB supergravity
2692:Type IIA supergravity
2544:-form electrodynamics
2163:Bosonic string theory
1867:European Space Agency
824:European Space Agency
792:
755:fundamental particles
730:
531:
406:
263:anti-de Sitter spaces
259:gauge/gravity duality
244:
158:Unexpected connection
56:gravitational horizon
32:holographic principle
4537:Loop quantum gravity
4396:Quantum field theory
3744:Final parsec problem
3703:Schwarzschild radius
2649:HoĹavaâWitten theory
2596:Hyperkähler manifold
2284:Particles and fields
2232:Tachyon condensation
2217:Matrix string theory
2010:Alfonso V. Ramallo:
1309:Bekenstein, Jacob D.
946:color, aroma, taste
475:
375:Einstein's equations
58:. First proposed by
4692:Theoretical physics
4406:BunchâDavies vacuum
4398:in curved spacetime
4298:FaddeevâPopov ghost
4043:Superluminal motion
4018:Population III star
3988:Gravitational waves
3946:Black hole starship
3729:Information paradox
2687:Type I supergravity
2591:CalabiâYau manifold
2586:Ricci-flat manifold
2565:KaluzaâKlein theory
2306:RamondâRamond field
2212:String field theory
2032:Scientific American
1965:2002RvMP...74..825B
1790:2008PhRvD..77j4031H
1734:1986CMaPh.104..207B
1703:2003dmci.confE..26S
1596:1999JHEP...07..004B
1559:1999InJPB..73..147M
1498:1973CMaPh..31..161B
1451:1981PhRvD..23..287B
1363:1998AdTMP...2..231M
1318:Scientific American
1251:2009GReGr..41..903M
1195:2002RvMP...74..825B
1114:1994hep.th....5069T
1065:1995JMP....36.6377S
1015:Scientific American
980:(10 October 2022).
740:information entropy
736:Information content
638:gravitational field
621:, they re-emit new
371:gravitational waves
341:high energy physics
298:boundary conditions
287:YangâMills theories
253:, sometimes called
212:Scientific American
132:Scientific American
103:information content
4591:Group field theory
4519:Superstring theory
4474:Firewall (physics)
3877:Optical black hole
3790:ReissnerâNordstrĂśm
3749:Firewall (physics)
3654:Gravitational lens
2654:K-theory (physics)
2531:ADE classification
2168:Superstring theory
1852:, 7 February 2012.
1742:10.1007/BF01211590
1506:10.1007/BF01645742
987:The New York Times
887:Physical cosmology
852:Beyond black holes
796:
785:Experimental tests
759:degrees of freedom
733:
526:
410:
347:Black hole entropy
247:
164:information theory
126:High-level summary
115:Einstein equations
4679:
4678:
4636:Eternal inflation
4631:Quantum cosmology
4619:
4618:
4411:Hawking radiation
4376:Liouville gravity
4230:
4229:
4023:Supermassive star
4013:Naked singularity
4008:Membrane paradigm
3734:Cosmic censorship
3708:Spaghettification
3696:Immirzi parameter
3649:Hawking radiation
3590:Astrophysical jet
3559:Supermassive star
3549:Binary black hole
3483:Stellar evolution
3425:Intermediate-mass
3257:
3256:
3039:van Nieuwenhuizen
2575:Why 10 dimensions
2480:ChernâSimons form
2447:KacâMoody algebra
2427:Conformal algebra
2422:Conformal anomaly
2316:Magnetic monopole
2311:KalbâRamond field
2153:NambuâGoto action
2042:(10 April 2019).
1767:Physical Review D
1669:978-0-316-18066-5
1439:Physical Review D
1123:978-1-56072-073-7
1049:(11): 6377â6396.
942:secondary quality
634:Hawking radiation
584:of the number of
521:
506:
255:Maldacena duality
34:is a property of
4714:
4668:
4667:
4492:
4491:
4454:Bekenstein bound
4271:Central concepts
4257:
4250:
4243:
4234:
4233:
4220:
4219:
4210:
4209:
3882:Sonic black hole
3831:Dark-energy star
3686:Bekenstein bound
3671:Mâsigma relation
3600:Ring singularity
3380:
3284:
3277:
3270:
3261:
3260:
2767:String theorists
2707:Lie superalgebra
2659:Twisted K-theory
2617:Spin(7)-manifold
2570:Compactification
2412:Virasoro algebra
2195:Heterotic string
2089:
2082:
2075:
2066:
2065:
2061:
1999:
1997:
1984:
1958:
1929:
1928:
1926:
1924:
1907:
1901:
1900:
1898:
1896:
1885:
1879:
1878:
1876:
1874:
1859:
1853:
1842:
1836:
1835:
1833:
1831:
1816:
1810:
1809:
1783:
1761:
1755:
1753:
1713:
1707:
1706:
1696:
1680:
1674:
1673:
1649:
1643:
1642:
1622:
1616:
1615:
1589:
1569:
1563:
1562:
1552:
1532:
1526:
1525:
1477:
1471:
1470:
1445:(215): 287â298.
1434:
1428:
1427:
1425:
1423:
1409:
1403:
1400:
1394:
1391:
1385:
1384:
1374:
1356:
1332:
1323:
1322:
1305:
1296:
1295:
1288:
1282:
1277:
1271:
1270:
1244:
1221:
1215:
1214:
1188:
1166:
1160:
1159:
1147:
1137:
1128:
1127:
1107:
1091:
1085:
1084:
1073:10.1063/1.531249
1058:
1038:
1027:
1026:
1024:
1022:
1005:
999:
998:
996:
994:
974:
953:
928:(and before him
918:
912:
909:
872:Entropic gravity
847:Bekenstein bound
834:Jacob Bekenstein
779:Virasoro algebra
748:Bekenstein bound
698:non-perturbative
563:detailed balance
535:
533:
532:
527:
522:
517:
516:
515:
504:
500:
499:
492:
484:
483:
382:Jacob Bekenstein
308:many aspects of
305:strongly coupled
294:non-perturbative
281:(CFT) which are
257:(after ref.) or
195:Ludwig Boltzmann
136:Jacob Bekenstein
83:Bekenstein bound
64:Leonard Susskind
54:boundary like a
4722:
4721:
4717:
4716:
4715:
4713:
4712:
4711:
4682:
4681:
4680:
4675:
4674:
4652:
4641:FRW/CFT duality
4615:
4564:
4546:
4523:
4483:
4425:
4397:
4390:
4347:
4266:
4264:Quantum gravity
4261:
4231:
4226:
4198:
4174:ULAS J1342+0928
4134:SDSS J0849+1114
4119:Phoenix Cluster
4072:
3924:
3886:
3865:
3804:
3763:
3759:No-hair theorem
3712:
3666:Bondi accretion
3632:Penrose process
3578:
3544:Gamma-ray burst
3471:
3381:
3372:
3358:Direct collapse
3306:
3293:
3288:
3258:
3253:
2762:
2739:
2716:
2663:
2611:
2581:Kähler manifold
2548:
2525:
2518:
2511:
2504:
2497:
2456:
2417:Mirror symmetry
2398:
2384:Brane cosmology
2330:
2279:
2246:
2202:N=2 superstring
2188:Type IIB string
2183:Type IIA string
2158:Polyakov action
2141:
2098:
2093:
2007:
1932:
1922:
1920:
1908:
1904:
1894:
1892:
1887:
1886:
1882:
1872:
1870:
1861:
1860:
1856:
1843:
1839:
1829:
1827:
1817:
1813:
1762:
1758:
1714:
1710:
1681:
1677:
1670:
1650:
1646:
1639:
1623:
1619:
1570:
1566:
1533:
1529:
1478:
1474:
1435:
1431:
1421:
1419:
1411:
1410:
1406:
1401:
1397:
1392:
1388:
1333:
1326:
1311:(August 2003).
1306:
1299:
1290:
1289:
1285:
1278:
1274:
1222:
1218:
1167:
1163:
1156:
1138:
1131:
1124:
1092:
1088:
1039:
1030:
1020:
1018:
1006:
1002:
992:
990:
978:Overbye, Dennis
975:
971:
962:
957:
956:
944:information as
919:
915:
910:
906:
901:
896:
867:Digital physics
862:Brane cosmology
842:
818:in 2004 by the
787:
725:
700:formulation of
694:Hermann Nicolai
666:Stephen Shenker
611:
605:
595:came up with a
541:(Here the term
511:
507:
495:
494:
493:
491:
479:
478:
476:
473:
472:
444:Stephen Hawking
367:magnetic fields
355:
349:
267:quantum gravity
239:
233:
204:
172:Shannon entropy
160:
128:
60:Gerard 't Hooft
40:quantum gravity
36:string theories
28:
17:
12:
11:
5:
4720:
4710:
4709:
4704:
4699:
4694:
4677:
4676:
4673:
4672:
4658:
4657:
4654:
4653:
4651:
4650:
4649:
4648:
4643:
4638:
4627:
4625:
4621:
4620:
4617:
4616:
4614:
4613:
4611:Twistor theory
4608:
4603:
4598:
4593:
4588:
4583:
4578:
4572:
4570:
4566:
4565:
4563:
4562:
4556:
4554:
4548:
4547:
4545:
4544:
4539:
4533:
4531:
4525:
4524:
4522:
4521:
4516:
4511:
4506:
4500:
4498:
4489:
4485:
4484:
4482:
4481:
4476:
4471:
4466:
4461:
4456:
4451:
4446:
4441:
4435:
4433:
4427:
4426:
4424:
4423:
4418:
4413:
4408:
4402:
4400:
4392:
4391:
4389:
4388:
4383:
4378:
4373:
4368:
4363:
4357:
4355:
4349:
4348:
4346:
4345:
4340:
4335:
4330:
4325:
4320:
4315:
4310:
4305:
4300:
4295:
4290:
4285:
4280:
4274:
4272:
4268:
4267:
4260:
4259:
4252:
4245:
4237:
4228:
4227:
4225:
4224:
4214:
4203:
4200:
4199:
4197:
4196:
4194:Swift J1644+57
4191:
4186:
4181:
4176:
4171:
4166:
4161:
4156:
4151:
4146:
4144:MS 0735.6+7421
4141:
4136:
4131:
4126:
4121:
4116:
4111:
4109:Sagittarius A*
4106:
4101:
4096:
4091:
4086:
4080:
4078:
4074:
4073:
4071:
4070:
4065:
4060:
4055:
4050:
4045:
4040:
4035:
4030:
4025:
4020:
4015:
4010:
4005:
4000:
3995:
3990:
3985:
3984:
3983:
3978:
3968:
3963:
3958:
3953:
3948:
3943:
3938:
3932:
3930:
3926:
3925:
3923:
3922:
3917:
3912:
3907:
3902:
3896:
3894:
3888:
3887:
3885:
3884:
3879:
3873:
3871:
3867:
3866:
3864:
3863:
3858:
3853:
3848:
3843:
3838:
3833:
3828:
3823:
3818:
3812:
3810:
3806:
3805:
3803:
3802:
3797:
3792:
3787:
3782:
3771:
3769:
3765:
3764:
3762:
3761:
3756:
3751:
3746:
3741:
3736:
3731:
3726:
3720:
3718:
3714:
3713:
3711:
3710:
3705:
3700:
3699:
3698:
3688:
3683:
3681:Thermodynamics
3678:
3673:
3668:
3663:
3662:
3661:
3651:
3646:
3644:Accretion disk
3641:
3640:
3639:
3634:
3624:
3619:
3614:
3609:
3608:
3607:
3602:
3592:
3586:
3584:
3580:
3579:
3577:
3576:
3571:
3566:
3561:
3556:
3551:
3546:
3541:
3540:
3539:
3534:
3529:
3519:
3518:
3517:
3507:
3502:
3501:
3500:
3490:
3485:
3479:
3477:
3473:
3472:
3470:
3469:
3468:
3467:
3462:
3457:
3452:
3447:
3442:
3437:
3427:
3422:
3421:
3420:
3410:
3409:
3408:
3405:
3400:
3389:
3387:
3383:
3382:
3375:
3373:
3371:
3370:
3365:
3360:
3355:
3350:
3345:
3340:
3335:
3330:
3325:
3320:
3318:BTZ black hole
3314:
3312:
3308:
3307:
3305:
3304:
3298:
3295:
3294:
3287:
3286:
3279:
3272:
3264:
3255:
3254:
3252:
3251:
3246:
3241:
3236:
3231:
3226:
3221:
3216:
3211:
3206:
3201:
3196:
3191:
3186:
3181:
3176:
3171:
3166:
3161:
3156:
3151:
3146:
3141:
3136:
3131:
3126:
3121:
3116:
3111:
3106:
3101:
3096:
3091:
3089:Randjbar-Daemi
3086:
3081:
3076:
3071:
3066:
3061:
3056:
3051:
3046:
3041:
3036:
3031:
3026:
3021:
3016:
3011:
3006:
3001:
2996:
2991:
2986:
2981:
2976:
2971:
2966:
2961:
2956:
2951:
2946:
2941:
2936:
2931:
2926:
2921:
2916:
2911:
2906:
2901:
2896:
2891:
2886:
2881:
2876:
2871:
2866:
2861:
2856:
2851:
2846:
2841:
2836:
2831:
2826:
2821:
2816:
2811:
2806:
2801:
2796:
2791:
2786:
2781:
2776:
2770:
2768:
2764:
2763:
2761:
2760:
2755:
2749:
2747:
2741:
2740:
2738:
2737:
2732:
2726:
2724:
2718:
2717:
2715:
2714:
2712:Lie supergroup
2709:
2704:
2699:
2694:
2689:
2684:
2679:
2673:
2671:
2665:
2664:
2662:
2661:
2656:
2651:
2646:
2641:
2636:
2631:
2626:
2621:
2620:
2619:
2614:
2609:
2605:
2604:
2603:
2593:
2583:
2578:
2572:
2567:
2562:
2556:
2554:
2550:
2549:
2547:
2546:
2538:
2533:
2528:
2523:
2516:
2509:
2502:
2495:
2487:
2482:
2477:
2472:
2466:
2464:
2458:
2457:
2455:
2454:
2449:
2444:
2439:
2434:
2429:
2424:
2419:
2414:
2408:
2406:
2400:
2399:
2397:
2396:
2391:
2389:Quiver diagram
2386:
2381:
2376:
2371:
2366:
2361:
2356:
2351:
2346:
2340:
2338:
2332:
2331:
2329:
2328:
2323:
2318:
2313:
2308:
2303:
2298:
2293:
2287:
2285:
2281:
2280:
2278:
2277:
2272:
2267:
2262:
2256:
2254:
2252:String duality
2248:
2247:
2245:
2244:
2239:
2234:
2229:
2224:
2219:
2214:
2209:
2204:
2199:
2198:
2197:
2192:
2191:
2190:
2185:
2178:Type II string
2175:
2165:
2160:
2155:
2149:
2147:
2143:
2142:
2140:
2139:
2134:
2133:
2132:
2127:
2117:
2115:Cosmic strings
2112:
2106:
2104:
2100:
2099:
2092:
2091:
2084:
2077:
2069:
2063:
2062:
2049:PBS Space Time
2036:
2028:
2023:
2006:
2005:External links
2003:
2002:
2001:
1985:
1956:hep-th/0203101
1949:(3): 825â874.
1937:
1936:
1931:
1930:
1902:
1880:
1869:. 30 June 2011
1854:
1837:
1811:
1774:(10): 104031.
1756:
1728:(2): 207â226.
1708:
1694:hep-th/0302219
1675:
1668:
1644:
1637:
1617:
1587:hep-th/9905177
1564:
1527:
1492:(2): 161â170.
1472:
1429:
1404:
1395:
1386:
1354:hep-th/9711200
1347:(2): 231â252.
1324:
1297:
1283:
1272:
1225:Marolf, Donald
1216:
1186:hep-th/0203101
1179:(3): 825â874.
1161:
1154:
1129:
1122:
1105:hep-th/9405069
1086:
1056:hep-th/9409089
1028:
1000:
968:
967:
966:
961:
958:
955:
954:
913:
903:
902:
900:
897:
895:
894:
889:
884:
879:
874:
869:
864:
859:
854:
849:
843:
841:
838:
786:
783:
771:Juan Maldacena
724:
721:
706:Juan Maldacena
686:Bernard de Wit
662:Willy Fischler
627:density matrix
607:Main article:
604:
601:
593:Raphael Bousso
539:
538:
537:
536:
525:
520:
514:
510:
503:
498:
490:
487:
482:
351:Main article:
348:
345:
321:Juan Maldacena
235:Main article:
232:
229:
203:
200:
187:thermodynamics
168:Claude Shannon
159:
156:
152:poetic license
127:
124:
96:
72:Raphael Bousso
15:
9:
6:
4:
3:
2:
4719:
4708:
4705:
4703:
4700:
4698:
4695:
4693:
4690:
4689:
4687:
4671:
4663:
4660:
4659:
4655:
4647:
4644:
4642:
4639:
4637:
4634:
4633:
4632:
4629:
4628:
4626:
4622:
4612:
4609:
4607:
4604:
4602:
4599:
4597:
4594:
4592:
4589:
4587:
4586:Dual graviton
4584:
4582:
4579:
4577:
4574:
4573:
4571:
4567:
4561:
4558:
4557:
4555:
4553:
4549:
4543:
4540:
4538:
4535:
4534:
4532:
4530:
4526:
4520:
4517:
4515:
4512:
4510:
4507:
4505:
4502:
4501:
4499:
4497:
4496:String theory
4493:
4490:
4486:
4480:
4477:
4475:
4472:
4470:
4467:
4465:
4462:
4460:
4457:
4455:
4452:
4450:
4447:
4445:
4442:
4440:
4437:
4436:
4434:
4432:
4428:
4422:
4419:
4417:
4414:
4412:
4409:
4407:
4404:
4403:
4401:
4399:
4393:
4387:
4384:
4382:
4379:
4377:
4374:
4372:
4369:
4367:
4364:
4362:
4359:
4358:
4356:
4354:
4350:
4344:
4341:
4339:
4336:
4334:
4331:
4329:
4326:
4324:
4321:
4319:
4316:
4314:
4311:
4309:
4306:
4304:
4301:
4299:
4296:
4294:
4291:
4289:
4286:
4284:
4281:
4279:
4276:
4275:
4273:
4269:
4265:
4258:
4253:
4251:
4246:
4244:
4239:
4238:
4235:
4223:
4215:
4213:
4205:
4204:
4201:
4195:
4192:
4190:
4187:
4185:
4182:
4180:
4177:
4175:
4172:
4170:
4169:Markarian 501
4167:
4165:
4162:
4160:
4157:
4155:
4152:
4150:
4147:
4145:
4142:
4140:
4137:
4135:
4132:
4130:
4127:
4125:
4122:
4120:
4117:
4115:
4112:
4110:
4107:
4105:
4102:
4100:
4097:
4095:
4094:XTE J1118+480
4092:
4090:
4089:XTE J1650-500
4087:
4085:
4082:
4081:
4079:
4075:
4069:
4066:
4064:
4061:
4059:
4056:
4054:
4051:
4049:
4046:
4044:
4041:
4039:
4036:
4034:
4031:
4029:
4026:
4024:
4021:
4019:
4016:
4014:
4011:
4009:
4006:
4004:
4001:
3999:
3996:
3994:
3991:
3989:
3986:
3982:
3979:
3977:
3974:
3973:
3972:
3969:
3967:
3964:
3962:
3959:
3957:
3954:
3952:
3949:
3947:
3944:
3942:
3939:
3937:
3934:
3933:
3931:
3927:
3921:
3918:
3916:
3913:
3911:
3908:
3906:
3903:
3901:
3898:
3897:
3895:
3893:
3889:
3883:
3880:
3878:
3875:
3874:
3872:
3868:
3862:
3859:
3857:
3854:
3852:
3849:
3847:
3844:
3842:
3839:
3837:
3834:
3832:
3829:
3827:
3824:
3822:
3819:
3817:
3814:
3813:
3811:
3807:
3801:
3798:
3796:
3793:
3791:
3788:
3786:
3783:
3780:
3776:
3775:Schwarzschild
3773:
3772:
3770:
3766:
3760:
3757:
3755:
3752:
3750:
3747:
3745:
3742:
3740:
3737:
3735:
3732:
3730:
3727:
3725:
3722:
3721:
3719:
3715:
3709:
3706:
3704:
3701:
3697:
3694:
3693:
3692:
3689:
3687:
3684:
3682:
3679:
3677:
3674:
3672:
3669:
3667:
3664:
3660:
3657:
3656:
3655:
3652:
3650:
3647:
3645:
3642:
3638:
3635:
3633:
3630:
3629:
3628:
3625:
3623:
3620:
3618:
3617:Photon sphere
3615:
3613:
3612:Event horizon
3610:
3606:
3603:
3601:
3598:
3597:
3596:
3593:
3591:
3588:
3587:
3585:
3581:
3575:
3572:
3570:
3567:
3565:
3562:
3560:
3557:
3555:
3552:
3550:
3547:
3545:
3542:
3538:
3537:Related links
3535:
3533:
3530:
3528:
3525:
3524:
3523:
3520:
3516:
3515:Related links
3513:
3512:
3511:
3508:
3506:
3503:
3499:
3498:Related links
3496:
3495:
3494:
3491:
3489:
3486:
3484:
3481:
3480:
3478:
3474:
3466:
3463:
3461:
3458:
3456:
3453:
3451:
3448:
3446:
3443:
3441:
3438:
3436:
3433:
3432:
3431:
3428:
3426:
3423:
3419:
3416:
3415:
3414:
3411:
3406:
3404:
3401:
3399:
3396:
3395:
3394:
3391:
3390:
3388:
3384:
3379:
3369:
3366:
3364:
3361:
3359:
3356:
3354:
3351:
3349:
3346:
3344:
3341:
3339:
3336:
3334:
3331:
3329:
3326:
3324:
3323:Schwarzschild
3321:
3319:
3316:
3315:
3313:
3309:
3303:
3300:
3299:
3296:
3292:
3285:
3280:
3278:
3273:
3271:
3266:
3265:
3262:
3250:
3247:
3245:
3242:
3240:
3237:
3235:
3234:Zamolodchikov
3232:
3230:
3229:Zamolodchikov
3227:
3225:
3222:
3220:
3217:
3215:
3212:
3210:
3207:
3205:
3202:
3200:
3197:
3195:
3192:
3190:
3187:
3185:
3182:
3180:
3177:
3175:
3172:
3170:
3167:
3165:
3162:
3160:
3157:
3155:
3152:
3150:
3147:
3145:
3142:
3140:
3137:
3135:
3132:
3130:
3127:
3125:
3122:
3120:
3117:
3115:
3112:
3110:
3107:
3105:
3102:
3100:
3097:
3095:
3092:
3090:
3087:
3085:
3082:
3080:
3077:
3075:
3072:
3070:
3067:
3065:
3062:
3060:
3057:
3055:
3052:
3050:
3047:
3045:
3042:
3040:
3037:
3035:
3032:
3030:
3027:
3025:
3022:
3020:
3017:
3015:
3012:
3010:
3007:
3005:
3002:
3000:
2997:
2995:
2992:
2990:
2987:
2985:
2982:
2980:
2977:
2975:
2972:
2970:
2967:
2965:
2962:
2960:
2957:
2955:
2952:
2950:
2947:
2945:
2942:
2940:
2937:
2935:
2932:
2930:
2927:
2925:
2922:
2920:
2917:
2915:
2912:
2910:
2907:
2905:
2902:
2900:
2897:
2895:
2892:
2890:
2887:
2885:
2882:
2880:
2877:
2875:
2872:
2870:
2867:
2865:
2862:
2860:
2857:
2855:
2852:
2850:
2847:
2845:
2842:
2840:
2837:
2835:
2832:
2830:
2827:
2825:
2822:
2820:
2817:
2815:
2812:
2810:
2807:
2805:
2802:
2800:
2797:
2795:
2792:
2790:
2787:
2785:
2782:
2780:
2777:
2775:
2772:
2771:
2769:
2765:
2759:
2756:
2754:
2753:Matrix theory
2751:
2750:
2748:
2746:
2742:
2736:
2733:
2731:
2728:
2727:
2725:
2723:
2719:
2713:
2710:
2708:
2705:
2703:
2700:
2698:
2695:
2693:
2690:
2688:
2685:
2683:
2680:
2678:
2675:
2674:
2672:
2670:
2669:Supersymmetry
2666:
2660:
2657:
2655:
2652:
2650:
2647:
2645:
2642:
2640:
2637:
2635:
2632:
2630:
2627:
2625:
2622:
2618:
2615:
2613:
2606:
2602:
2599:
2598:
2597:
2594:
2592:
2589:
2588:
2587:
2584:
2582:
2579:
2576:
2573:
2571:
2568:
2566:
2563:
2561:
2558:
2557:
2555:
2551:
2545:
2543:
2539:
2537:
2534:
2532:
2529:
2526:
2519:
2512:
2505:
2498:
2491:
2488:
2486:
2483:
2481:
2478:
2476:
2473:
2471:
2468:
2467:
2465:
2463:
2459:
2453:
2450:
2448:
2445:
2443:
2440:
2438:
2435:
2433:
2430:
2428:
2425:
2423:
2420:
2418:
2415:
2413:
2410:
2409:
2407:
2405:
2401:
2395:
2392:
2390:
2387:
2385:
2382:
2380:
2377:
2375:
2372:
2370:
2367:
2365:
2362:
2360:
2357:
2355:
2352:
2350:
2347:
2345:
2342:
2341:
2339:
2337:
2333:
2327:
2324:
2322:
2321:Dual graviton
2319:
2317:
2314:
2312:
2309:
2307:
2304:
2302:
2299:
2297:
2294:
2292:
2289:
2288:
2286:
2282:
2276:
2273:
2271:
2268:
2266:
2263:
2261:
2258:
2257:
2255:
2253:
2249:
2243:
2240:
2238:
2237:RNS formalism
2235:
2233:
2230:
2228:
2225:
2223:
2220:
2218:
2215:
2213:
2210:
2208:
2205:
2203:
2200:
2196:
2193:
2189:
2186:
2184:
2181:
2180:
2179:
2176:
2174:
2173:Type I string
2171:
2170:
2169:
2166:
2164:
2161:
2159:
2156:
2154:
2151:
2150:
2148:
2144:
2138:
2135:
2131:
2128:
2126:
2123:
2122:
2121:
2118:
2116:
2113:
2111:
2108:
2107:
2105:
2101:
2097:
2096:String theory
2090:
2085:
2083:
2078:
2076:
2071:
2070:
2067:
2059:
2055:
2051:
2050:
2045:
2041:
2037:
2035:
2033:
2029:
2027:
2024:
2021:
2017:
2013:
2009:
2008:
1996:
1995:gr-qc/9310026
1991:
1986:
1982:
1978:
1974:
1970:
1966:
1962:
1957:
1952:
1948:
1944:
1939:
1938:
1934:
1933:
1919:
1918:
1913:
1906:
1891:. 6 July 2013
1890:
1884:
1868:
1864:
1858:
1851:
1847:
1841:
1826:
1822:
1815:
1807:
1803:
1799:
1795:
1791:
1787:
1782:
1777:
1773:
1769:
1768:
1760:
1751:
1747:
1743:
1739:
1735:
1731:
1727:
1723:
1719:
1712:
1704:
1700:
1695:
1690:
1686:
1679:
1671:
1665:
1661:
1657:
1656:
1648:
1640:
1638:9781329024588
1634:
1630:
1629:
1621:
1613:
1609:
1605:
1601:
1597:
1593:
1588:
1583:
1579:
1575:
1568:
1560:
1556:
1551:
1550:gr-qc/9807045
1546:
1542:
1538:
1531:
1523:
1519:
1515:
1511:
1507:
1503:
1499:
1495:
1491:
1487:
1483:
1476:
1468:
1464:
1460:
1456:
1452:
1448:
1444:
1440:
1433:
1418:
1414:
1408:
1399:
1390:
1382:
1378:
1373:
1368:
1364:
1360:
1355:
1350:
1346:
1342:
1338:
1331:
1329:
1321:. p. 59.
1320:
1319:
1314:
1310:
1304:
1302:
1293:
1287:
1281:
1276:
1268:
1264:
1260:
1256:
1252:
1248:
1243:
1238:
1235:(4): 903â17.
1234:
1230:
1226:
1220:
1212:
1208:
1204:
1200:
1196:
1192:
1187:
1182:
1178:
1174:
1173:
1165:
1157:
1155:9780316016407
1151:
1146:
1145:
1136:
1134:
1125:
1119:
1115:
1111:
1106:
1101:
1097:
1090:
1082:
1078:
1074:
1070:
1066:
1062:
1057:
1052:
1048:
1044:
1037:
1035:
1033:
1017:
1016:
1011:
1004:
989:
988:
983:
979:
973:
969:
964:
963:
951:
947:
943:
939:
935:
931:
927:
923:
917:
908:
904:
893:
890:
888:
885:
883:
880:
878:
875:
873:
870:
868:
865:
863:
860:
858:
855:
853:
850:
848:
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4624:Applications
4514:Supergravity
4421:Unruh effect
4328:Quantum foam
4323:Planck units
4318:IR/UV mixing
4312:
4293:Causal patch
4124:PKS 1302-102
3998:Gravity well
3966:Compact star
3920:Microquasars
3905:Most massive
3809:Alternatives
3753:
3574:X-ray binary
3493:Neutron star
3430:Supermassive
3407:Hawking star
3348:Supermassive
2779:Arkani-Hamed
2729:
2677:Supergravity
2644:Moduli space
2541:
2536:Dirac string
2462:Gauge theory
2442:Loop algebra
2379:Black string
2242:GS formalism
2047:
2040:O'Dowd, Matt
2031:
2011:
1946:
1942:
1921:. Retrieved
1915:
1905:
1893:. Retrieved
1883:
1871:. Retrieved
1857:
1840:
1828:. Retrieved
1825:NewScientist
1824:
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1631:. Lulu.com.
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1420:. Retrieved
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1089:
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1019:. Retrieved
1013:
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985:
972:
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937:
933:
930:Robert Boyle
921:
916:
907:
892:Quantum foam
832:
813:
797:
764:
752:
734:
717:gauge theory
655:
651:
647:
631:
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612:
590:
579:
575:Planck units
567:
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553:temperature
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129:
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4697:Black holes
4581:Causal sets
4431:Black holes
4114:Centaurus A
4068:Planet Nine
3971:Exotic star
3900:Black holes
3846:Planck star
3795:KerrâNewman
3510:White dwarf
3460:Radio-Quiet
3418:Microquasar
3291:Black holes
3139:Silverstein
2639:Orientifold
2374:Black holes
2369:Black brane
2326:Dual photon
1895:14 February
1422:26 December
1417:INSPIRE-HEP
1021:15 February
816:GRB 041219A
804:Craig Hogan
704:. In 1997,
643:world sheet
586:microstates
464:massâenergy
422:upper bound
208:Boltzmann's
144:information
4707:Holography
4686:Categories
4646:Multiverse
4488:Approaches
4366:CGHS model
4353:Toy models
4288:CA-duality
4164:Q0906+6930
4154:Hercules A
4084:Cygnus X-1
4053:White hole
4028:Quasi-star
3981:Preon star
3976:Quark star
3961:Big Bounce
3821:Black star
3779:Derivation
3627:Ergosphere
3583:Properties
3564:Quasi-star
3554:Quark star
3465:Radio-Loud
3353:Primordial
3343:Kugelblitz
3159:Strominger
3154:Steinhardt
3149:Staudacher
3064:Polchinski
3014:Nanopoulos
2974:Mandelstam
2954:Kontsevich
2794:Berenstein
2722:Holography
2702:Superspace
2601:K3 surface
2560:Worldsheet
2475:Instantons
2103:Background
1923:3 February
1873:3 February
1846:LuboĹĄ Motl
1580:(7): 004.
1543:(2): 147.
993:10 October
960:References
926:John Locke
802:physicist
690:Jens Hoppe
225:isomorphic
134:magazine,
99:black hole
52:light-like
4662:See also:
4601:Spin foam
4381:RST model
4189:AT2018hyz
3836:Gravastar
3826:Dark star
3659:Microlens
3532:Hypernova
3527:Micronova
3522:Supernova
3476:Formation
3194:Veneziano
3074:Rajaraman
2969:Maldacena
2859:Gopakumar
2809:Dijkgraaf
2804:Curtright
2470:Anomalies
2349:NS5-brane
2270:U-duality
2265:S-duality
2260:T-duality
2020:1310.4319
1806:119087922
1781:0712.3419
1514:1432-0916
1467:120643289
1381:1095-0753
1242:0810.4886
965:Citations
757:. As the
658:Tom Banks
582:logarithm
543:δM c
497:δ
448:geodesics
335:, and by
223:which is
119:Wheeler's
4509:M-theory
4469:ER = EPR
4308:Graviton
4212:Category
4099:A0620-00
4058:Wormhole
3956:Big Bang
3856:Fuzzball
3739:ER = EPR
3605:Theorems
3403:Electron
3398:Extremal
3328:Rotating
3249:Zwiebach
3204:Verlinde
3199:Verlinde
3174:Townsend
3169:Susskind
3104:Sagnotti
3069:Polyakov
3024:Nekrasov
2989:Minwalla
2984:Martinec
2949:Knizhnik
2944:Klebanov
2939:Kapustin
2904:'t Hooft
2839:Fischler
2774:AganagiÄ
2745:M-theory
2634:Conifold
2629:Orbifold
2612:manifold
2553:Geometry
2359:M5-brane
2354:M2-brane
2291:Graviton
2207:F-theory
2054:Archived
1981:55096624
1830:19 April
1750:55421933
1522:54690354
1267:55210840
1211:55096624
1081:17316840
938:solidity
840:See also
820:INTEGRAL
800:Fermilab
713:membrane
710:type IIB
702:M-theory
670:M-theory
363:electric
275:M-theory
221:hologram
191:disorder
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4222:Commons
4184:P172+18
4139:TON 618
4077:Notable
3929:Related
3915:Quasars
3910:Nearest
3870:Analogs
3800:Hayward
3768:Metrics
3413:Stellar
3338:Virtual
3333:Charged
3302:Outline
3179:Trivedi
3164:Sundrum
3129:Shenker
3119:Seiberg
3114:Schwarz
3084:Randall
3044:Novikov
3034:Nielsen
3019:NÄstase
2929:Kallosh
2914:Gibbons
2854:Gliozzi
2844:Friedan
2834:Ferrara
2819:Douglas
2814:Distler
2364:S-brane
2344:D-brane
2301:Tachyon
2296:Dilaton
2110:Strings
2058:YouTube
1961:Bibcode
1935:Sources
1786:Bibcode
1730:Bibcode
1699:Bibcode
1612:9545752
1592:Bibcode
1555:Bibcode
1494:Bibcode
1447:Bibcode
1359:Bibcode
1247:Bibcode
1191:Bibcode
1110:Bibcode
1061:Bibcode
940:. Such
922:primary
828:GEO 600
809:GEO 600
623:photons
591:Later,
571:they do
394:entropy
359:entropy
310:nuclear
95:squared
91:entropy
4569:Others
4159:3C 273
4149:NeVe 1
4129:OJ 287
3851:Q star
3717:Issues
3450:Blazar
3440:Quasar
3244:Zumino
3239:Zaslow
3224:Yoneya
3214:Witten
3134:Siegel
3109:Scherk
3079:Ramond
3054:Ooguri
2979:Marolf
2934:Kaluza
2919:Kachru
2909:HoĹava
2899:Harvey
2894:Hanson
2879:Gubser
2869:Greene
2799:Bousso
2784:Atiyah
2336:Branes
2146:Theory
1979:
1917:Nature
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1748:
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1635:
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1512:
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1152:
1120:
1079:
692:, and
674:branes
664:, and
551:Kelvin
505:
331:, and
176:modems
3892:Lists
3393:Micro
3363:Rogue
3311:Types
3184:Turok
3094:RoÄek
3059:Ovrut
3049:Olive
3029:Neveu
3009:Myers
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2994:Moore
2964:Linde
2959:Klein
2884:Gukov
2874:Gross
2864:Green
2849:Gates
2829:Dvali
2789:Banks
2016:arXiv
1990:arXiv
1977:S2CID
1951:arXiv
1802:S2CID
1776:arXiv
1746:S2CID
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1608:S2CID
1582:arXiv
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1463:S2CID
1349:arXiv
1263:S2CID
1237:arXiv
1207:S2CID
1181:arXiv
1100:arXiv
1077:S2CID
1051:arXiv
950:sound
899:Notes
400:law.
369:, or
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3861:Geon
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3386:Size
3209:Wess
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3099:Rohm
2999:Motl
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2889:Guth
2824:Duff
1925:2013
1897:2014
1875:2013
1832:2010
1664:ISBN
1633:ISBN
1578:1999
1510:ISSN
1424:2015
1377:ISSN
1150:ISBN
1118:ISBN
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798:The
380:But
365:and
312:and
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180:DVDs
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3124:Sen
1969:doi
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1738:doi
1726:104
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1455:doi
1367:doi
1255:doi
1199:doi
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