7463:
712:
3266:. The information content of a black hole appears to be lost when it dissipates, as under these models the Hawking radiation is random (it has no relation to the original information). A number of solutions to this problem have been proposed, including suggestions that Hawking radiation is perturbed to contain the missing information, that the Hawking evaporation leaves some form of remnant particle containing the missing information, and that information is allowed to be lost under these conditions.
42:
3125:
929:
6960:
3334:, that photon's frequency stays regular only if the mode is extended back into the past region where no observer can go. That region seems to be unobservable and is physically suspect, so Hawking used a black hole solution without a past region that forms at a finite time in the past. In that case, the source of all the outgoing photons can be identified: a microscopic point right at the moment that the black hole first formed.
725:
2839:
833:
1621:
7451:
2054:
3120:{\displaystyle t_{\mathrm {ev} }={\frac {5120\pi G^{2}M^{3}}{\hbar c^{4}}}={\frac {480c^{2}V}{\hbar G}}=5120\pi \,t_{\text{P}}\left({\frac {M}{m_{\text{P}}}}\right)^{3}\approx 3.396\times 10^{-16}\,\mathrm {s} \ \left({M \over \mathrm {kg} }\right)^{3}\approx 2.140\times 10^{67}\,{\text{years}}\ \left({\frac {M}{M_{\odot }}}\right)^{3},}
1301:
3378:(10 or 11), the values of Planck constants can be radically different, and the formulas for Hawking radiation have to be modified as well. In particular, the lifetime of a micro black hole with a radius below the scale of the extra dimensions is given by equation 9 in Cheung (2002) and equations 25 and 26 in Carr (2005).
1379:
3345:
solution. Matter that falls on the white hole accumulates on it, but has no future region into which it can go. Tracing the future of this matter, it is compressed onto the final singular endpoint of the white hole evolution, into a trans-Planckian region. The reason for these types of divergences is
3329:
of
Hawking radiation, if the mode is traced back in time, has a frequency that diverges from that which it has at great distance, as it gets closer to the horizon, which requires the wavelength of the photon to "scrunch up" infinitely at the horizon of the black hole. In a maximally extended external
3337:
The quantum fluctuations at that tiny point, in
Hawking's original calculation, contain all the outgoing radiation. The modes that eventually contain the outgoing radiation at long times are redshifted by such a huge amount by their long sojourn next to the event horizon that they start off as modes
920:
is compressed into a volume small enough that the escape velocity is greater than the speed of light. Nothing can travel that fast, so nothing within a certain distance, proportional to the mass of the black hole, can escape beyond that distance. The region beyond which not even light can escape is
2489:
Assuming that a small black hole has zero entropy, the integration constant is zero. Forming a black hole is the most efficient way to compress mass into a region, and this entropy is also a bound on the information content of any sphere in space time. The form of the result strongly suggests that
1094:
applied to black-hole horizons. Close to the event horizon of a black hole, a local observer must accelerate to keep from falling in. An accelerating observer sees a thermal bath of particles that pop out of the local acceleration horizon, turn around, and free-fall back in. The condition of local
3349:
There exist alternative physical pictures that give the
Hawking radiation in which the trans-Planckian problem is addressed. The key point is that similar trans-Planckian problems occur when the modes occupied with Unruh radiation are traced back in time. In the Unruh effect, the magnitude of the
975:
to show that in theory, instead of cancelling each other out normally, the antimatter and matter fields were disrupted by the black hole, causing antimatter and matter particles to "blip" into existence as a result of the imbalanced matter fields, and drawing energy from the disruptor itself: the
995:. This means that no information loss is expected in black holes (since the theory permits no such loss) and the radiation emitted by a black hole is probably the usual thermal radiation. If this is correct, then Hawking's original calculation should be corrected, though it is not known how (see
2552:
or larger. Writing in 1976, Page using the understanding of neutrinos at the time erroneously worked on the assumption that neutrinos have no mass and that only two neutrino flavors exist, and therefore his results of black hole lifetimes do not match the modern results which take into account
3633:
In
September 2010 an experimental set-up created a laboratory "white hole event horizon" that the experimenters claimed was shown to radiate an optical analog to Hawking radiation. However, the results remain unverified and debatable, and its status as a genuine confirmation remains in doubt.
2580:
Some pre-1998 calculations, using outdated assumptions about neutrinos, were as follows: If black holes evaporate under
Hawking radiation, a solar mass black hole will evaporate over 10 years which is vastly longer than the age of the universe. A supermassive black hole with a mass of 10 (100
1309:
The field theory is defined by a local path integral, so if the boundary conditions at the horizon are determined, the state of the field outside will be specified. To find the appropriate boundary conditions, consider a stationary observer just outside the horizon at position
1836:
1817:
1829:
The gravitational redshift is given by the square root of the time component of the metric. So for the field theory state to consistently extend, there must be a thermal background everywhere with the local temperature redshift-matched to the near horizon temperature:
2521:, the life span of a black hole can be shown to scale as the cube of its initial mass, and Hawking estimated that any black hole formed in the early universe with a mass of less than approximately 10 kg would have evaporated completely by the present day.
1108:
976:
black holes (to escape), effectively draining energy from the black hole. In addition, not all of the particles were close to the event horizon, and the ones that were could not escape. In effect, this energy acted as if the black hole itself was slowly
3482:
2603:
during the collapse of superclusters of galaxies. Even these would evaporate over a timescale of up to 2 Ă 10 years. Post-1998 science modifies these results slightly; for example, the modern estimate of a solar-mass black hole lifetime is 10 years.
1691:
The horizon is not a special boundary, and objects can fall in. So the local observer should feel accelerated in ordinary
Minkowski space by the principle of equivalence. The near-horizon observer must see the field excited at a local temperature
1095:
thermal equilibrium implies that the consistent extension of this local thermal bath has a finite temperature at infinity, which implies that some of these particles emitted by the horizon are not reabsorbed and become outgoing
Hawking radiation.
2544:-dependent manner as frequency decreases, especially when the wavelength becomes comparable to the size of the event horizon. Page concluded that primordial black holes could survive to the present day only if their initial mass were roughly
5633:
Belgiorno, Francesco D.; Cacciatori, Sergio Luigi; Clerici, Matteo; Gorini, Vittorio; Ortenzi, Giovanni; Rizzi, Luca; Rubino, Eleonora; Sala, Vera Giulia; Faccio, Daniele (2010). "Hawking radiation from ultrashort laser pulse filaments".
1616:{\displaystyle (\mathrm {d} s)^{2}=-\left({\frac {\rho }{4M}}\right)^{2}\,(\mathrm {d} t)^{2}+(\mathrm {d} \rho )^{2}+(\mathrm {d} X_{\perp })^{2}=-\rho ^{2}\,(\mathrm {d} \tau )^{2}+(\mathrm {d} \rho )^{2}+(\mathrm {d} X_{\perp })^{2},}
3346:
that modes that end at the horizon from the point of view of outside coordinates are singular in frequency there. The only way to determine what happens classically is to extend in some other coordinates that cross the horizon.
3242:
Unlike most objects, a black hole's temperature increases as it radiates away mass. The rate of temperature increase is exponential, with the most likely endpoint being the dissolution of the black hole in a violent burst of
2712:
2337:
2422:
803:
and rotational energy of black holes and is therefore also theorized to cause black hole evaporation. Because of this, black holes that do not gain mass through other means are expected to shrink and ultimately vanish.
2536:. The time for the event horizon or entropy of a black hole to halve is known as the Page time. The calculations are complicated by the fact that a black hole, being of finite size, is not a perfect black body; the
113:
2717:
The
BekensteinâHawking luminosity of a black hole, under the assumption of pure photon emission (i.e. that no other particles are emitted) and under the assumption that the horizon is the radiating surface is:
3362:
The formulas from the previous section are applicable only if the laws of gravity are approximately valid all the way down to the Planck scale. In particular, for black holes with masses below the Planck mass
1074:
ought to create and emit particles. Hawking would find aspects of both of these arguments true once he did the calculation himself. Due to
Bekenstein's contribution to black hole entropy, it is also known as
2789:
2127:
2049:{\displaystyle T(r')={\frac {1}{4\pi {\sqrt {2Mr\left(1-{\frac {2M}{r}}\right)}}}}{\sqrt {\frac {1-{\frac {2M}{r}}}{1-{\frac {2M}{r'}}}}}={\frac {1}{4\pi {\sqrt {2Mr\left(1-{\frac {2M}{r'}}\right)}}}}.}
1698:
3860:
Physically, the
GullstrandâPainlevĂ© metric describes space falling into the Schwarzschild black hole at the Newtonian escape velocity. ... At the horizon, the velocity equals the speed of light.
3604:
Under experimentally achievable conditions for gravitational systems, this effect is too small to be observed directly. It was predicted that Hawking radiation could be studied by analogy using
3220:, in order for the black hole to dissipate, the black hole must have a temperature greater than that of the present-day blackbody radiation of the universe of 2.7 K. A study suggests that
4386:
Since we have assumed a maximum scale of gravitational binding â for instance, superclusters of galaxies â black hole formation eventually comes to an end in our model, with masses of up to 10
2254:
815:
are predicted to be larger emitters of radiation than larger black holes and should dissipate faster per their mass. As such, if small black holes exist such as permitted by the hypothesis of
483:
2197:
1368:
1296:{\displaystyle (\mathrm {d} s)^{2}=-\left(1-{\frac {2M}{r}}\right)\,(\mathrm {d} t)^{2}+{\frac {1}{\left(1-{\frac {2M}{r}}\right)}}\,(\mathrm {d} r)^{2}+r^{2}\,(\mathrm {d} \Omega )^{2}.}
2484:
3318:
that change frequency relative to other coordinates that are regular across the horizon. This is necessarily so, since to stay outside a horizon requires acceleration that constantly
7418:
7142:
3384:
756:
792:, who developed a theoretical argument for its existence in 1974. Hawking radiation is predicted to be extremely faint and is many orders of magnitude below the current best
3338:
with a wavelength much shorter than the Planck length. Since the laws of physics at such short distances are unknown, some find Hawking's original calculation unconvincing.
1062:'s attention, leading him to think about radiation due to this formalism. Hawking's subsequent theory and report followed a visit to Moscow in 1973, where Soviet scientists
948:
in general relativity, one can conceptualize the event horizon as the region beyond which space is infalling faster than the speed of light. (Although nothing can travel
5839:
135:
3500:
is the number of large extra dimensions. This formula is now consistent with black holes as light as a few TeV, with lifetimes on the order of the "new Planck time" ~
936:. Outside/inside the horizon (red), the infalling speed is less/greater than the speed of light. At the event horizon, the infalling speed equals the speed of light.
819:, they ought to lose mass more rapidly as they shrink, leading to a final cataclysm of high energy radiation alone. Such radiation bursts have not yet been detected.
7110:
3341:
The trans-Planckian problem is nowadays mostly considered a mathematical artifact of horizon calculations. The same effect occurs for regular matter falling onto a
3296:
near the black hole's horizon. This is due to the peculiar behavior there, where time stops as measured from far away. A particle emitted from a black hole with a
340:
7094:
7055:
4443:
6429:â studies the deviation of a loop quantized black hole from Hawking radiation. A novel observable quantum effect of black hole quantization is introduced.
3543:
Based on the fluctuations of the horizon area, a quantum black hole exhibits deviations from the Hawking radiation spectrum that would be observable were
952:
space faster than light, space itself can infall at any speed.) Once matter is inside the event horizon, all of the matter inside falls inevitably into a
693:
503:
345:
458:
6997:
6548:
6097:
5352:
7065:
2640:
2273:
6689:
972:
749:
5158:
Fermi-LAT collaboration (January 31, 2018). "Search for Gamma-Ray Emission from Local Primordial Black Holes with the Fermi Large Area Telescope".
2348:
7340:
3551:
to be observed. The quantum effects are centered at a set of discrete and unblended frequencies highly pronounced on top of the Hawking spectrum.
6654:
945:
933:
7356:
7201:
6329:
4179:
371:
205:
7462:
711:
7324:
6450:
4909:
Carr, Bernard J. (2005). "Primordial Black Holes â Recent Developments". In Pisin Chen; Elliott Bloom; Greg Madejski; Vahe Patrosian (eds.).
3217:
1024:
410:
48:
6235:
Ida, Daisuke; Oda, Kin'ya; Park, Seong-chan (2006). "Rotating Black Holes at Future Colliders. III. Determination of Black Hole Evolution".
956:, a place of infinite curvature and zero size, leaving behind a warped spacetime devoid of any matter; a classical black hole is pure empty
7428:
7364:
7304:
6045:
Barrau, AurĂ©lien; Grain, Julien; Alexeyev, Stanislav O. (2004). "GaussâBonnet black holes at the LHC: beyond the dimensionality of space".
4013:
3674:
2562:
5979:
Barrau, Aurélien; Féron, Chloé; Grain, Julien (2005). "Astrophysical Production of Microscopic Black Holes in a Low-Planck-Scale World".
963:
Our current understanding of quantum physics can be used to investigate what may happen in the region around the event horizon. In 1974,
3780:
2502:
When particles escape, the black hole loses a small amount of its energy and therefore some of its mass (mass and energy are related by
742:
6186:
Ida, Daisuke; Oda, Kin'ya; Park, Seong-chan (2005). "Rotating black holes at future colliders. II. Anisotropic scalar field emission".
7413:
7174:
5350:
BarcelĂł, Carlos; Liberati, Stefano; Visser, Matt (2003). "Towards the observation of Hawking radiation in BoseâEinstein condensates".
4078:
850:
122:
7134:
6963:
4783:
Brout, Robert; Massar, Serge; Parentani, Renaud; Spindel, Philippe (1995). "Hawking radiation without trans-Planckian frequencies".
4149:
4052:
3947:
3824:
872:
148:
6576:
6145:
Ida, Daisuke; Oda, Kin'ya; Park, Seong-chan (2003). "Rotating black holes at future colliders: Greybody factors for brane fields".
897:
began to mount half a century later, and these objects are of current interest primarily because of their compact size and immense
2724:
428:
7498:
7209:
7166:
7035:
6679:
2069:
1812:{\displaystyle T={\frac {\alpha }{2\pi }}={\frac {1}{2\pi \rho }}={\frac {1}{4\pi {\sqrt {2Mr\left(1-{\frac {2M}{r}}\right)}}}},}
41:
4393:... the timescale for black holes to radiate away all their energy ranges from to 10 years for black holes of one solar mass ...
7503:
7225:
5603:
3875:, World Scientific (2005). The tunneling process is described on pp.26â28, and described as Black Hole Evaporation on pp.48â49.
3569:
335:
2611:
emitted by a black hole in the form of Hawking radiation can be estimated for the simplest case of a nonrotating, non-charged
7423:
7280:
6869:
6737:
4645:
3644:
3263:
854:
6664:
6626:
4993:
Ashtekar, Abhay; Baez, John Carlos; Corichi, Alejandro; Krasnov, Kirill (1998). "Quantum Geometry and Black Hole Entropy".
4911:
Proceedings of the 22nd Texas Symposium on Relativistic Astrophysics at Stanford, Stanford California, December 13â17, 2004
3596:
may be able to create micro black holes and observe their evaporation. No such micro black hole has been observed at CERN.
468:
7488:
7332:
6990:
6752:
6541:
4405:
Page, Don N. (1976). "Particle emission rates from a black hole: Massless particles from an uncharged, nonrotating hole".
2826:
is the mass of the black hole. It is worth mentioning that the above formula has not yet been derived in the framework of
2627:
of blackbody radiation, the above formula for the temperature of the radiation, and the formula for the surface area of a
422:
130:
7441:
3659:
3627:
488:
7118:
6757:
3701:
6835:
6636:
2208:
7508:
2528:
refined this estimate by calculating the power produced, and the time to evaporation, for a non-rotating, non-charged
1657:. The metric describes a frame that is accelerating to keep from falling into the black hole. The local acceleration,
729:
220:
140:
7045:
7040:
6285:
Nicolaevici, Nistor (2003). "Blackbody spectrum from accelerated mirrors with asymptotically inertial trajectories".
5932:
5883:
4555:
3669:
2149:
1058:
developed a theory and reported that the black holes should have an entropy. Bekenstein's theory and report came to
7126:
6732:
4033:
For an alternative derivation and more detailed discussion of Hawking radiation as a form of Unruh radiation, see:
1316:
633:
181:
7050:
843:
433:
7372:
7025:
6845:
6822:
6772:
6742:
5981:
3649:
3236:
2437:
953:
785:
245:
7060:
6853:
3536:
is set to cancel out various constants such that the BekensteinâHawking entropy formula is reproduced. However,
2624:
508:
7493:
7233:
7150:
6983:
6899:
6534:
6515:
3618:
3371:). This is normally seen as an indication that the Planck mass is the lower limit on the mass of a black hole.
2612:
2537:
2529:
1099:
898:
668:
658:
325:
6699:
6591:
2202:
Thus a field theory defined on a black-hole background is in a thermal state whose temperature at infinity is
387:
5797:(1976). "Particle emission rates from a black hole: Massless particles from an uncharged, nonrotating hole".
4547:
4100:(1976). "Particle emission rates from a black hole: Massless particles from an uncharged, nonrotating hole".
925:; an observer outside it cannot observe, become aware of, or be affected by events within the event horizon.
7217:
7158:
7102:
6889:
6631:
5636:
5239:
5182:; Thomas, Scott (2002). "High energy colliders as black hole factories: The end of short distance physics".
4995:
4848:
4481:
4035:
de Witt, Bryce (1980). "Quantum gravity: the new synthesis". In Hawking, Stephen W.; Israel, Werner (eds.).
3937:
3281:
2803:
928:
653:
5698:
3477:{\displaystyle \tau \sim {\frac {1}{M_{*}}}\left({\frac {M_{\text{BH}}}{M_{*}}}\right)^{\frac {n+3}{n+1}},}
453:
6571:
6467:
5539:"Observation of stationary spontaneous Hawking radiation and the time evolution of an analogue black hole"
3548:
3375:
3210:
2819:
984:
906:
816:
807:
For all except the smallest black holes, this happens extremely slowly. The radiation temperature, called
623:
608:
215:
7182:
6797:
6709:
6606:
6596:
3593:
3585:
3573:
2827:
2491:
1091:
598:
166:
4283:
MacGibbon, Jane H.; Carr, B. J.; Page, Don N. (2008). "Do Evaporating Black Holes Form Photospheres?".
5322:
7483:
6830:
6476:
6404:
6369:
6344:
6296:
6287:
6256:
6207:
6166:
6116:
6066:
6000:
5951:
5902:
5858:
5808:
5794:
5765:
5726:
5655:
5560:
5487:
5430:
5371:
5258:
5203:
5124:
5069:
5014:
4965:
4924:
4867:
4804:
4749:
4712:
4664:
4573:
4520:
4505:
4416:
4353:
4304:
4241:
4188:
4111:
4097:
3986:
3735:
3517:
3331:
2620:
2525:
2518:
988:
773:
418:
6360:
3964:
960:, and the simplest (nonrotating and uncharged) is characterized just by its mass and event horizon.
7296:
7288:
6442:
5731:
3795:
3654:
3186:
1627:
1071:
613:
593:
583:
578:
563:
330:
473:
6884:
6812:
6767:
6420:
6394:
6380:
6373:
6312:
6272:
6246:
6223:
6197:
6156:
6132:
6106:
6082:
6056:
6030:
6016:
5990:
5967:
5941:
5918:
5892:
5848:
5781:
5679:
5645:
5584:
5550:
5537:
Kolobov, Victor I.; Golubkov, Katrine; Muñoz de Nova, Juan Ramón; Steinhauer, Jeff (March 2021).
5519:
5477:
5446:
5420:
5387:
5361:
5282:
5248:
5219:
5193:
5159:
5140:
5114:
5085:
5059:
5030:
5004:
4955:
4914:
4891:
4857:
4828:
4794:
4680:
4654:
4623:
4597:
4563:
4448:
4377:
4320:
4294:
4265:
4231:
4204:
3976:
3902:
3759:
3521:
2503:
1067:
902:
890:
663:
548:
320:
225:
210:
171:
33:
4698:
4340:
See page 596: table 1 and the "black hole decay" section and previous sentence on that page in
3540:
corrections to the entropy and radiation of black holes have been computed based on the theory.
5464:
Muñoz de Nova, Juan Ramón; Golubkov, Katrine; Kolobov, Victor I.; Steinhauer, Jeff (May 2019).
4044:
7348:
6929:
6924:
6669:
6446:
6385:
6237:
6188:
6147:
6047:
5799:
5671:
5576:
5511:
5503:
5274:
5184:
5105:
5050:
4883:
4820:
4785:
4765:
4740:
4703:
4407:
4369:
4344:
4285:
4257:
4155:
4145:
4102:
4074:
4048:
3943:
3820:
3751:
3533:
3351:
2596:. Some monster black holes in the universe are predicted to continue to grow up to perhaps 10
543:
493:
268:
7455:
7258:
7030:
6747:
6494:
6484:
6434:
6412:
6352:
6304:
6264:
6215:
6174:
6124:
6074:
6008:
5959:
5955:
5930:
Barrau, Aurélien; et al. (2003). "Antideuterons as a probe of primordial black holes".
5910:
5906:
5866:
5816:
5773:
5756:
5703:
5663:
5568:
5495:
5438:
5379:
5266:
5211:
5132:
5077:
5022:
4973:
4875:
4812:
4757:
4720:
4672:
4589:
4581:
4577:
4528:
4424:
4361:
4312:
4249:
4196:
4119:
4036:
3994:
3894:
3743:
3623:
3605:
3525:
1055:
812:
638:
618:
573:
553:
498:
17:
6029:
Barrau, Aurélien; Boudoul, Gaëlle (2002). "Some aspects of primordial black hole physics".
5301:
2259:
From the black-hole temperature, it is straightforward to calculate the black-hole entropy
7006:
6934:
6557:
6095:
Kanti, Panagiota (2004). "Black Holes in Theories with Large Extra Dimensions: a Review".
5830:
5751:
5179:
3933:
3920:
3844:
3663:
3537:
3529:
3248:
2608:
1063:
1059:
968:
789:
673:
648:
533:
528:
392:
273:
235:
6523:
A. Barrau & J. Grain explain how the Hawking radiation could be detected at colliders
6520:
6489:
6462:
6435:
5407:"Observation of quantum Hawking radiation and its entanglement in an analogue black hole"
443:
6480:
6463:"Focus on Classical and Quantum Analogs for Gravitational Phenomena and Related Effects"
6408:
6348:
6300:
6260:
6211:
6170:
6120:
6070:
6004:
5862:
5812:
5769:
5659:
5564:
5491:
5466:"Observation of thermal Hawking radiation and its temperature in an analogue black hole"
5434:
5375:
5262:
5207:
5128:
5073:
5018:
4969:
4928:
4871:
4808:
4753:
4716:
4668:
4524:
4420:
4357:
4308:
4245:
4192:
4115:
3990:
3739:
1046:
across) would be in equilibrium at 2.7 K, absorbing as much radiation as it emits.
987:), black holes in certain cases (and perhaps in general) are equivalent to solutions of
7467:
7070:
6904:
6372:
about gravity in small scales including the deviation from Hawking radiation effect by
5411:
5237:
Dimopoulos, Savas; Landsberg, Greg (2001). "Black Holes at the Large Hadron Collider".
2811:
2558:
2541:
964:
716:
683:
678:
366:
230:
6308:
5727:"Artificial event horizon emits laboratory analog to theoretical black hole radiation"
5103:
Ansari, Mohammad H. (2008). "Generic degeneracy and entropy in loop quantum gravity".
3612:
are analogous to light in a gravitational black hole and the flow of an approximately
7477:
6879:
6789:
6316:
5588:
5538:
5523:
5450:
5286:
5144:
4724:
4676:
4601:
4324:
4037:
3906:
3613:
3513:
3319:
3293:
3256:
922:
781:
643:
603:
558:
538:
463:
361:
240:
6416:
6321:â consistent derivation of the Hawking radiation in the FullingâDavies mirror model.
6227:
6136:
6086:
5922:
5611:
5465:
5136:
5081:
5034:
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4208:
7396:
7390:
6807:
6714:
6621:
6616:
6611:
6586:
6424:
6276:
6078:
6025:â experimental searches for primordial black holes thanks to the emitted antimatter
6020:
5971:
5785:
5683:
5667:
5391:
5306:
5223:
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4453:
4269:
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and the Hawking effect both talk about field modes in the superficially stationary
3311:
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1823:
1087:
588:
568:
5270:
4879:
4585:
3572:, which is searching for the terminal gamma-ray flashes expected from evaporating
5963:
5914:
5881:
Barrau, Aurélien; et al. (2002). "Antiprotons from primordial black holes".
4365:
4174:
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5406:
4253:
4137:
3252:
2507:
992:
977:
894:
832:
478:
448:
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6219:
6178:
5572:
5215:
5048:
Ansari, Mohammad H. (2007). "Spectroscopy of a canonically quantized horizon".
5026:
4316:
2707:{\displaystyle T_{\mathrm {H} }={\frac {\hbar c^{3}}{8\pi GMk_{\mathrm {B} }}}}
2332:{\displaystyle \mathrm {d} S={\frac {\mathrm {d} Q}{T}}=8\pi M\,\mathrm {d} Q.}
983:
However, according to the conjectured gauge-gravity duality (also known as the
788:
is inside the event horizon, it cannot escape. It is named after the physicist
6939:
6724:
6659:
6581:
6325:
6128:
5871:
5834:
5499:
5383:
4738:
Jacobson, Theodore (1991). "Black-hole evaporation and ultrashort distances".
3998:
3342:
3289:
3161:
1042:
1007:
1003:
777:
688:
250:
176:
27:
Thermal radiation believed to be emitted by black holes due to quantum effects
5580:
5507:
4816:
4761:
4622:
Kapusta, Joseph (1999). "The Last Eight Minutes of a Primordial Black Hole".
4159:
4067:
For an accessible discussion of the Unruh effect and Hawking radiation, see:
3755:
3709:
2417:{\displaystyle \mathrm {d} S=8\pi M\,\mathrm {d} M=\mathrm {d} (4\pi M^{2}).}
6894:
6762:
6674:
6646:
6437:
Black Holes, White Dwarfs, and Neutron Stars: The Physics of Compact Objects
5820:
5327:
4978:
4943:
4846:
Cheung, Kingman (2002). "Black Hole Production and Large Extra Dimensions".
4428:
4123:
3873:
An Introduction to Black Holes. Information and the String Theory Revolution
3796:"Black Hole Entropy and 2D Conformal Field Theory - Towards Quantum Gravity"
3315:
3300:
3244:
3239:
by showing how black holes interact thermally with the rest of the universe.
957:
793:
259:
5675:
5515:
5278:
4887:
4824:
4769:
4373:
4261:
2517:). Consequently, an evaporating black hole will have a finite lifespan. By
6802:
6601:
6035:
5995:
5946:
5897:
4919:
4628:
3304:
2554:
886:
628:
438:
278:
6091:â searches for new physics (quantum gravity) with primordial black holes
5323:"Stephen Hawkings 50 bet on the world the universe and the God particle"
4593:
3781:"John Michell: Country Parson Described Black Holes in 1783 | AMNH"
3297:
6399:
6251:
6202:
6161:
6111:
6061:
5253:
5198:
5064:
4862:
4799:
4236:
4222:
Page, Don N. (6 December 1993). "Information in Black Hole Radiation".
4200:
4073:. Princeton, New Jersey: Princeton University Press. pp. 154â162.
3898:
3285:
1306:
The black hole is the background spacetime for a quantum field theory.
934:
infalling into a Schwarzschild black hole at the Newtonian escape speed
857: in this section. Unsourced material may be challenged and removed.
108:{\displaystyle G_{\mu \nu }+\Lambda g_{\mu \nu }={\kappa }T_{\mu \nu }}
6499:
6356:
5442:
5366:
5119:
5009:
4659:
4532:
4142:
Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics
2431:, so the entropy of a black hole is proportional to its surface area:
5777:
3747:
3609:
3326:
2628:
1020:
917:
913:
3209:. This is why some astronomers are searching for signs of exploding
2631:(the black hole's event horizon), several equations can be derived.
6012:
5555:
5482:
5425:
5164:
4960:
4568:
901:. Early research into black holes were done by individuals such as
6975:
6526:
5853:
5650:
4299:
3981:
3544:
3225:
2342:
The heat energy that enters serves to increase the total mass, so
1016:
927:
4944:"Black Hole Evaporation: A Perspective from Loop Quantum Gravity"
3496:
is the low-energy scale, which could be as low as a few TeV, and
3247:. A complete description of this dissolution requires a model of
3965:"Effective Temperature, Hawking Radiation and Quasinormal Modes"
3589:
3565:
3251:, however, as it occurs when the black hole's mass approaches 1
1036:
800:
6979:
6530:
4475:
4473:
4471:
3367:), they result in impossible lifetimes below the Planck time (~
4342:
Frautschi, Steven (1982). "Entropy in an Expanding Universe".
826:
5877:â links between primordial black holes and the early universe
4611:– via The University of Manchester's Research Explorer.
4499:
4497:
4495:
4014:"Hawking-Bekenstein radiation and the shifting of a paradigm"
3231:
Black hole evaporation has several significant consequences:
3702:"A conversation with Dr. Stephen Hawking & Lucy Hawking"
2784:{\displaystyle P={\frac {\hbar c^{6}}{15360\pi G^{2}M^{2}}}}
6383:(2007). "Spectroscopy of a canonically quantized horizon".
4012:
Nature, Research Communities by Springer (March 14, 2018).
3142:
are the mass and (Schwarzschild) volume of the black hole,
2565:
figure for the age of the universe yielded a mass bound of
2122:{\displaystyle T(\infty )={\frac {1}{4\pi {\sqrt {2Mr}}}},}
3284:
is the issue that Hawking's original calculation includes
3262:
The simplest models of black hole evaporation lead to the
3235:
Black hole evaporation produces a more consistent view of
6281:â determination of black hole's life and extra dimensions
5602:
Emerging Technology from the arXiv (September 27, 2010).
3885:
Bekenstein, A. (1972). "Black holes and the second law".
3512:
A detailed study of the quantum geometry of a black hole
811:, is inversely proportional to the black hole's mass, so
6461:
Leonhardt, Ulf; Maia, Clovis; Schuetzhold, Ralf (2010).
2490:
the physical description of a gravitating theory can be
6368:
consists of the recent developments and predictions of
3726:
Hawking, S. W. (1974-03-01). "Black hole explosions?".
3622:). Observations of Hawking radiation were reported, in
3307:
frequency, and therefore a trans-Planckian wavelength.
2557:. A 2008 calculation using the particle content of the
3520:. Loop-quantization does not reproduce the result for
7439:
5825:â first detailed studies of the evaporation mechanism
5699:"Ultrafast Laser Pulse Makes Desktop Black Hole Glow"
3387:
3160:
are Planck mass and Planck time. A black hole of one
2842:
2727:
2643:
2440:
2351:
2276:
2211:
2152:
2072:
1839:
1701:
1382:
1319:
1111:
51:
4701:(1985). "On the quantum structure of a black hole".
4548:"Planck 2015 results: XIII. Cosmological parameters"
2833:
The time that the black hole takes to dissipate is:
1023:); in fact, such a black hole would absorb far more
1015:) has a temperature of only 60 nanokelvins (60
7406:
7383:
7316:
7273:
7250:
7193:
7086:
7079:
7013:
6917:
6862:
6844:
6821:
6788:
6781:
6723:
6688:
6645:
6564:
6457:â Hawking radiation evaporation formula derivation.
4643:Helfer, Adam D. (2003). "Do black holes radiate?".
4444:"Ask Ethan: How Do Black Holes Actually Evaporate?"
3819:. New York: Alfred A. Knopf, Penguin Random House.
5840:Monthly Notices of the Royal Astronomical Society
3476:
3303:, if traced back to the horizon, must have had an
3119:
2783:
2706:
2478:
2416:
2331:
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2191:
2121:
2048:
1811:
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1362:
1295:
107:
5300:Barrau, Aurélien; Grain, Julien (November 2004).
3576:. As of Jan 1st, 2023, none have been detected.
2249:{\displaystyle T_{\text{H}}={\frac {1}{8\pi M}}.}
784:. This is counterintuitive because once ordinary
4039:General Relativity: An Einstein Centenary Survey
2427:The radius of a black hole is twice its mass in
2263:. The change in entropy when a quantity of heat
909:who modeled black holes as having zero entropy.
893:. Evidence for the astrophysical objects termed
7111:Black Holes and Baby Universes and Other Essays
6433:Shapiro, Stuart L.; Teukolsky, Saul A. (1983).
4482:"Viktor T. Toth - Hawking radiation calculator"
2192:{\displaystyle T(\infty )={\frac {1}{8\pi M}}.}
6141:â evaporating black holes and extra-dimensions
3721:
3719:
6991:
6542:
2798:is the luminosity, i.e., the radiated power,
1363:{\displaystyle r=2M+{\frac {\rho ^{2}}{8M}}.}
980:(although it actually came from outside it).
750:
8:
4336:
4334:
4069:Gubser, Steven S.; Pretorius, Frans (2017).
4029:
4027:
3810:
3808:
3350:temperature can be calculated from ordinary
996:
4092:
4090:
2479:{\displaystyle S=\pi R^{2}={\frac {A}{4}}.}
885:Modern black holes were first predicted by
7083:
6998:
6984:
6976:
6785:
6549:
6535:
6527:
3838:
3836:
3224:must be less than 0.8% of the mass of the
3185:to evaporateâmuch longer than the current
2555:3 flavors of neutrinos with nonzero masses
757:
743:
309:
199:
29:
6498:
6488:
6398:
6250:
6201:
6160:
6110:
6098:International Journal of Modern Physics A
6060:
6034:
5994:
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5896:
5870:
5852:
5649:
5554:
5481:
5424:
5365:
5353:International Journal of Modern Physics A
5252:
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5008:
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4658:
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4235:
3980:
3969:International Journal of Modern Physics D
3444:
3432:
3422:
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3403:
3394:
3386:
3216:However, since the universe contains the
3108:
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3006:
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2013:
1991:
1979:
1952:
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1249:
1237:
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1170:
1150:
1127:
1115:
1110:
873:Learn how and when to remove this message
96:
87:
75:
56:
50:
5604:"First Observation of Hawking Radiation"
3666:, other extractions of black-hole energy
3354:field theory, and is not controversial.
973:quantum field theory in curved spacetime
7446:
7341:Stephen Hawking: Master of the Universe
7095:The Large Scale Structure of SpaceâTime
6041:â cosmology with primordial black holes
4506:"Some Simple Black Hole Thermodynamics"
4018:Research Communities by Springer Nature
3692:
2932:
2892:
2737:
2662:
379:
353:
312:
258:
32:
7357:Into the Universe with Stephen Hawking
5790:â Hawking's first article on the topic
4180:Communications in Mathematical Physics
4043:. Cambridge University Press. p.
3845:"A Black Hole is a Waterfall of Space"
3775:
3773:
3547:from Hawking radiation of evaporating
3228:â approximately the mass of the Moon.
2634:The Hawking radiation temperature is:
2059:The inverse temperature redshifted to
1086:Hawking radiation is dependent on the
7325:God, the Universe and Everything Else
5697:Grossman, Lisa (September 29, 2010).
5321:Henderson, Mark (September 9, 2008).
4913:. Vol. 041213. pp. 89â100.
3963:Corda, Christian (October 29, 2012).
3218:cosmic microwave background radiation
1025:cosmic microwave background radiation
7:
7365:Brave New World with Stephen Hawking
7066:PenroseâHawking singularity theorems
3255:, its radius will also approach two
1373:The local metric to lowest order is
855:adding citations to reliable sources
7202:George's Secret Key to the Universe
5835:"Black holes in the early universe"
2136:is the near-horizon position, near
7175:Brief Answers to the Big Questions
7056:GibbonsâHawkingâYork boundary term
5754:(1974). "Black hole explosions?".
4175:"Particle creation by black holes"
3919:In the same year, he proposed his
3038:
3035:
3017:
2852:
2849:
2695:
2650:
2385:
2374:
2353:
2319:
2292:
2278:
2159:
2079:
1586:
1562:
1538:
1493:
1469:
1445:
1387:
1277:
1273:
1238:
1175:
1116:
912:A black hole can form when enough
68:
25:
6964:Template:Quantum mechanics topics
6516:Hawking radiation calculator tool
2619:. Combining the formulas for the
7461:
7449:
7167:The Dreams That Stuff Is Made Of
7036:Chronology protection conjecture
6959:
6958:
6680:Topological quantum field theory
5725:Matson, John (October 1, 2010).
4433:See in particular equation (27).
831:
724:
723:
710:
40:
7226:George and the Unbreakable Code
6665:Jackiw–Teitelboim gravity
6417:10.1016/j.nuclphysb.2007.01.009
6330:"Quantum gravity faces reality"
5302:"The Case for Mini Black Holes"
5137:10.1016/j.nuclphysb.2007.11.038
5082:10.1016/j.nuclphysb.2007.01.009
4144:. University of Chicago Press.
1027:than it emits. A black hole of
842:needs additional citations for
7424:Black hole information paradox
6870:Causal dynamical triangulation
6738:Black hole information paradox
6490:10.1088/1367-2630/14/10/105032
6441:. Wiley-Interscience. p.
6079:10.1016/j.physletb.2004.01.019
5668:10.1103/PhysRevLett.105.203901
4646:Reports on Progress in Physics
4504:Lopresto, Michael (May 2003).
4071:The little book of Black Holes
3645:Black hole information paradox
3264:black hole information paradox
2408:
2389:
2162:
2156:
2082:
2076:
1854:
1843:
1601:
1582:
1570:
1558:
1546:
1534:
1508:
1489:
1477:
1465:
1453:
1441:
1395:
1383:
1281:
1269:
1246:
1234:
1183:
1171:
1124:
1112:
944:Alternatively, using a set of
799:Hawking radiation reduces the
1:
7210:George's Cosmic Treasure Hunt
6836:Wheeler–DeWitt equation
6521:The case for mini black holes
5271:10.1103/PhysRevLett.87.161602
4880:10.1103/PhysRevLett.88.221602
4546:Planck Collaboration (2016).
3871:L. Susskind and J. Lindesay,
3616:is analogous to gravity (see
1077:Bekenstein-Hawking radiation.
7119:The Nature of Space and Time
6758:Cosmic censorship hypothesis
6577:BatalinâVilkovisky formalism
5933:Astronomy & Astrophysics
5884:Astronomy & Astrophysics
4725:10.1016/0550-3213(85)90418-3
4366:10.1126/science.217.4560.593
2540:goes down in a complicated,
18:Bekenstein-Hawking radiation
7429:ThorneâHawkingâPreskill bet
6309:10.1088/0305-4470/36/27/317
4586:10.1051/0004-6361/201525830
4254:10.1103/PhysRevLett.71.3743
3675:ThorneâHawkingâPreskill bet
3588:theories are correct, then
772:is the theoretical thermal
221:Gravitational time dilation
7525:
7333:Stephen Hawking's Universe
7135:On the Shoulders of Giants
7127:The Universe in a Nutshell
6854:Hartle–Hawking state
6753:Bousso's holographic bound
6733:Black hole complementarity
6269:10.1103/PhysRevD.73.124022
6220:10.1103/PhysRevD.71.124039
6179:10.1103/PhysRevD.67.064025
5964:10.1051/0004-6361:20021588
5915:10.1051/0004-6361:20020313
5573:10.1038/s41567-020-01076-0
5216:10.1103/PhysRevD.65.056010
5027:10.1103/PhysRevLett.80.904
4677:10.1088/0034-4885/66/6/202
4317:10.1103/PhysRevD.78.064043
3580:Heavy-ion collider physics
3201:, the evaporation time is
3197:. But for a black hole of
341:MathissonâPapapetrouâDixon
182:Pseudo-Riemannian manifold
7373:Genius by Stephen Hawking
7143:A Briefer History of Time
7026:Black hole thermodynamics
6950:
6846:Euclidean quantum gravity
6823:Canonical quantum gravity
6773:Gravitational singularity
6743:Black-hole thermodynamics
6627:RyuâTakayanagi conjecture
6129:10.1142/S0217751X04018324
5982:The Astrophysical Journal
5500:10.1038/s41586-019-1241-0
5405:Steinhauer, Jeff (2016).
5384:10.1142/s0217751x0301615x
3999:10.1142/S0218271812420230
3817:Black hole survival guide
3650:Black hole thermodynamics
3628:BoseâEinstein condensates
3524:originally discovered by
3292:becomes shorter than the
3237:black hole thermodynamics
2588:will evaporate in around
2494:onto a bounding surface.
954:gravitational singularity
786:electromagnetic radiation
7306:The Theory of Everything
7234:George and the Blue Moon
7186:(2023, posthume message)
7151:God Created the Integers
6900:Superfluid vacuum theory
6655:2+1D topological gravity
4942:Ashtekar, Abhay (2020).
4817:10.1103/PhysRevD.52.4559
4762:10.1103/PhysRevD.44.1731
3887:Lettere al Nuovo Cimento
3660:BlandfordâZnajek process
3619:Analog models of gravity
3555:Experimental observation
2613:Schwarzschild black hole
2538:absorption cross section
2530:Schwarzschild black hole
1100:Schwarzschild black hole
899:gravitational attraction
346:HamiltonâJacobiâEinstein
326:Einstein field equations
149:Mathematical formulation
7499:Astronomical hypotheses
7282:A Brief History of Time
7218:George and the Big Bang
7103:A Brief History of Time
6890:Noncommutative geometry
6637:WeinbergâWitten theorem
6632:Trans-Planckian problem
6468:New Journal of Physics
5956:2003A&A...398..403B
5907:2002A&A...388..676B
5872:10.1093/mnras/168.2.399
5821:10.1103/PhysRevD.13.198
5637:Physical Review Letters
5240:Physical Review Letters
4996:Physical Review Letters
4979:10.3390/universe6020021
4849:Physical Review Letters
4578:2016A&A...594A..13P
4562:. A13, p. 31, Table 4.
4429:10.1103/PhysRevD.13.198
4224:Physical Review Letters
4173:Hawking, S. W. (1975).
4124:10.1103/PhysRevD.13.198
3939:A Brief History of Time
3508:In loop quantum gravity
3282:trans-Planckian problem
3276:Trans-Planckian problem
3271:Problems and extensions
2804:reduced Planck constant
2623:of the black hole, the
1035:(about the mass of the
940:: Andrew Hamilton, JILA
7504:Hypothetical processes
7241:Unlocking the Universe
7046:GibbonsâHawking effect
7041:GibbonsâHawking ansatz
6572:AdS/CFT correspondence
6366:on September 10, 2008.
3670:GibbonsâHawking effect
3574:primordial black holes
3549:primordial black holes
3532:, unless the value of
3478:
3376:large extra dimensions
3358:Large extra dimensions
3332:Schwarzschild solution
3211:primordial black holes
3121:
2820:gravitational constant
2785:
2708:
2498:Black hole evaporation
2480:
2418:
2333:
2250:
2193:
2123:
2050:
1813:
1617:
1364:
1297:
985:AdS/CFT correspondence
941:
817:primordial black holes
216:Gravitational redshift
109:
7183:On the Origin of Time
7051:GibbonsâHawking space
6798:Bosonic string theory
6710:Semiclassical gravity
6607:Holographic principle
6597:Gravitational anomaly
6288:Journal of Physics A
5608:MIT Technology Review
4001:– via CrossRef.
3815:Levin, Janna (2020).
3594:Large Hadron Collider
3586:large extra dimension
3570:Fermi space telescope
3538:quantum gravitational
3479:
3122:
2828:semiclassical gravity
2786:
2709:
2481:
2419:
2334:
2251:
2194:
2124:
2051:
1814:
1618:
1365:
1298:
1092:equivalence principle
946:infalling coordinates
931:
796:' detecting ability.
504:WeylâLewisâPapapetrou
459:KerrâNewmanâde Sitter
279:EinsteinâRosen bridge
211:Gravitational lensing
167:Equivalence principle
110:
7489:Quantum field theory
7061:HartleâHawking state
6831:Loop quantum gravity
6690:Quantum field theory
6370:loop quantum gravity
3518:loop quantum gravity
3516:has been made using
3385:
3288:particles where the
2840:
2725:
2641:
2625:StefanâBoltzmann law
2621:Schwarzschild radius
2519:dimensional analysis
2438:
2349:
2274:
2209:
2150:
2143:, so this is really
2070:
1837:
1699:
1380:
1317:
1109:
1072:rotating black holes
1002:A black hole of one
989:quantum field theory
851:improve this article
774:black-body radiation
434:EinsteinâRosen waves
160:Fundamental concepts
49:
6700:BunchâDavies vacuum
6692:in curved spacetime
6592:FaddeevâPopov ghost
6481:2012NJPh...14j5032L
6409:2007NuPhB.783..179A
6381:Ansari, Mohammad H.
6349:2006PhT....59k..44S
6301:2003JPhA...36.7667N
6261:2006PhRvD..73l4022I
6212:2005PhRvD..71l4039I
6171:2003PhRvD..67f4025I
6121:2004IJMPA..19.4899K
6071:2004PhLB..584..114B
6005:2005ApJ...630.1015B
5863:1974MNRAS.168..399C
5831:Hawking, Stephen W.
5813:1976PhRvD..13..198P
5770:1974Natur.248...30H
5752:Hawking, Stephen W.
5732:Scientific American
5660:2010PhRvL.105t3901B
5565:2021NatPh..17..362K
5492:2019Natur.569..688M
5435:2016NatPh..12..959S
5376:2003IJMPA..18.3735B
5263:2001PhRvL..87p1602D
5208:2002PhRvD..65e6010G
5180:Giddings, Steven B.
5129:2008NuPhB.795..635A
5074:2007NuPhB.783..179A
5019:1998PhRvL..80..904A
4970:2020Univ....6...21A
4929:2005tsra.conf...89C
4872:2002PhRvL..88v1602C
4809:1995PhRvD..52.4559B
4754:1991PhRvD..44.1731J
4717:1985NuPhB.256..727T
4669:2003RPPh...66..943H
4525:2003PhTea..41..299L
4513:The Physics Teacher
4421:1976PhRvD..13..198P
4358:1982Sci...217..593F
4309:2008PhRvD..78f4043M
4246:1993PhRvL..71.3743P
4193:1975CMaPh..43..199H
4116:1976PhRvD..13..198P
3991:2012IJMPD..2142023C
3794:Karozis, Nikolaos.
3740:1974Natur.248...30H
3655:Black hole starship
3610:sound perturbations
3560:Astronomical search
3187:age of the universe
2504:Einstein's equation
1070:convinced him that
809:Hawking temperature
776:released outside a
388:KaluzaâKlein theory
274:Minkowski spacetime
226:Gravitational waves
7509:1974 introductions
7414:In popular culture
7391:Jane Wilde Hawking
7344:(2008 documentary)
7336:(1997 documentary)
6885:Group field theory
6813:Superstring theory
6768:Firewall (physics)
5829:Carr, Bernard J.;
4556:Astron. Astrophys.
4449:Starts With a Bang
4201:10.1007/BF02345020
3899:10.1007/BF02757029
3843:Hamilton, Andrew.
3712:on March 29, 2013.
3522:black hole entropy
3474:
3181:) takes more than
3117:
2781:
2704:
2476:
2414:
2329:
2246:
2189:
2119:
2046:
1809:
1613:
1360:
1293:
1068:Alexei Starobinsky
942:
903:Karl Schwarzschild
891:general relativity
889:'s 1915 theory of
717:Physics portal
489:OppenheimerâSnyder
429:ReissnerâNordström
321:Linearized gravity
269:Spacetime diagrams
172:Special relativity
105:
34:General relativity
7437:
7436:
7349:Genius of Britain
7269:
7268:
7021:Hawking radiation
6973:
6972:
6930:Eternal inflation
6925:Quantum cosmology
6913:
6912:
6705:Hawking radiation
6670:Liouville gravity
6452:978-0-471-87316-7
6386:Nuclear Physics B
6357:10.1063/1.2435646
6328:(November 2006).
6295:(27): 7667â7677.
6238:Physical Review D
6189:Physical Review D
6148:Physical Review D
6105:(29): 4899â4951.
6048:Physics Letters B
5800:Physical Review D
5476:(7758): 688â691.
5443:10.1038/nphys3863
5360:(21): 3735â3745.
5185:Physical Review D
5106:Nuclear Physics B
5051:Nuclear Physics B
4786:Physical Review D
4741:Physical Review D
4704:Nuclear Physics B
4533:10.1119/1.1571268
4408:Physical Review D
4352:(4560): 593â599.
4286:Physical Review D
4230:(23): 3743â3746.
4103:Physical Review D
3849:jila.colorado.edu
3624:sonic black holes
3606:sonic black holes
3468:
3438:
3425:
3409:
3102:
3081:
3077:
3042:
3023:
2981:
2978:
2958:
2939:
2906:
2779:
2702:
2471:
2303:
2241:
2219:
2184:
2114:
2111:
2041:
2038:
2031:
1974:
1973:
1970:
1942:
1917:
1914:
1907:
1804:
1801:
1794:
1742:
1721:
1428:
1355:
1231:
1224:
1163:
932:Picture of space
883:
882:
875:
813:micro black holes
770:Hawking radiation
767:
766:
400:
399:
286:
285:
16:(Redirected from
7516:
7466:
7465:
7454:
7453:
7452:
7445:
7259:My Brief History
7159:The Grand Design
7084:
7031:Micro black hole
7000:
6993:
6986:
6977:
6962:
6961:
6786:
6748:Bekenstein bound
6565:Central concepts
6551:
6544:
6537:
6528:
6504:
6502:
6492:
6456:
6440:
6428:
6402:
6367:
6365:
6359:. Archived from
6334:
6320:
6280:
6254:
6231:
6205:
6182:
6164:
6140:
6114:
6090:
6064:
6055:(1â2): 114â122.
6040:
6038:
6036:astro-ph/0212225
6024:
5998:
5996:astro-ph/0505436
5989:(2): 1015â1019.
5975:
5949:
5947:astro-ph/0207395
5926:
5900:
5898:astro-ph/0112486
5876:
5874:
5856:
5824:
5789:
5778:10.1038/248030a0
5737:
5736:
5722:
5716:
5715:
5713:
5711:
5694:
5688:
5687:
5653:
5630:
5624:
5623:
5621:
5619:
5614:on March 1, 2012
5610:. Archived from
5599:
5593:
5592:
5558:
5534:
5528:
5527:
5485:
5461:
5455:
5454:
5428:
5402:
5396:
5395:
5369:
5347:
5341:
5340:
5338:
5336:
5318:
5312:
5311:
5297:
5291:
5290:
5256:
5234:
5228:
5227:
5201:
5176:
5170:
5169:
5167:
5155:
5149:
5148:
5122:
5100:
5094:
5093:
5067:
5045:
5039:
5038:
5012:
4990:
4984:
4983:
4981:
4963:
4939:
4933:
4932:
4922:
4920:astro-ph/0504034
4906:
4900:
4899:
4865:
4843:
4837:
4836:
4802:
4793:(8): 4559â4568.
4780:
4774:
4773:
4748:(6): 1731â1739.
4735:
4729:
4728:
4699:'t Hooft, Gerard
4695:
4689:
4688:
4662:
4640:
4634:
4633:
4631:
4629:astro-ph/9911309
4619:
4613:
4612:
4610:
4608:
4571:
4552:
4543:
4537:
4536:
4510:
4501:
4490:
4489:
4480:Toth, Viktor T.
4477:
4466:
4465:
4463:
4461:
4440:
4434:
4432:
4402:
4396:
4395:
4338:
4329:
4328:
4302:
4280:
4274:
4273:
4239:
4219:
4213:
4212:
4170:
4164:
4163:
4134:
4128:
4127:
4094:
4085:
4084:
4065:
4059:
4058:
4042:
4031:
4022:
4021:
4009:
4003:
4002:
3984:
3960:
3954:
3953:
3942:. Bantam Books.
3934:Hawking, Stephen
3930:
3924:
3921:no-hair theorems
3917:
3911:
3910:
3882:
3876:
3869:
3863:
3862:
3857:
3855:
3840:
3831:
3830:
3812:
3803:
3802:
3800:
3791:
3785:
3784:
3777:
3768:
3767:
3748:10.1038/248030a0
3723:
3714:
3713:
3708:. Archived from
3697:
3534:a free parameter
3503:
3499:
3495:
3483:
3481:
3480:
3475:
3470:
3469:
3467:
3456:
3445:
3443:
3439:
3437:
3436:
3427:
3426:
3423:
3417:
3410:
3408:
3407:
3395:
3374:In a model with
3370:
3366:
3223:
3208:
3206:
3200:
3196:
3194:
3184:
3180:
3178:
3172:
3159:
3150:
3141:
3135:
3126:
3124:
3123:
3118:
3113:
3112:
3107:
3103:
3101:
3100:
3088:
3079:
3078:
3075:
3072:
3071:
3053:
3052:
3047:
3043:
3041:
3030:
3021:
3020:
3014:
3013:
2992:
2991:
2986:
2982:
2980:
2979:
2976:
2967:
2960:
2959:
2956:
2940:
2938:
2930:
2926:
2925:
2912:
2907:
2905:
2904:
2903:
2890:
2889:
2888:
2879:
2878:
2862:
2857:
2856:
2855:
2825:
2817:
2809:
2801:
2797:
2790:
2788:
2787:
2782:
2780:
2778:
2777:
2776:
2767:
2766:
2750:
2749:
2748:
2735:
2713:
2711:
2710:
2705:
2703:
2701:
2700:
2699:
2698:
2675:
2674:
2673:
2660:
2655:
2654:
2653:
2618:
2595:
2593:
2576:
2574:
2570:
2551:
2549:
2535:
2516:
2485:
2483:
2482:
2477:
2472:
2464:
2459:
2458:
2423:
2421:
2420:
2415:
2407:
2406:
2388:
2377:
2356:
2338:
2336:
2335:
2330:
2322:
2304:
2299:
2295:
2289:
2281:
2266:
2262:
2255:
2253:
2252:
2247:
2242:
2240:
2226:
2221:
2220:
2217:
2198:
2196:
2195:
2190:
2185:
2183:
2169:
2142:
2135:
2128:
2126:
2125:
2120:
2115:
2113:
2112:
2101:
2089:
2062:
2055:
2053:
2052:
2047:
2042:
2040:
2039:
2037:
2033:
2032:
2030:
2022:
2014:
1992:
1980:
1975:
1972:
1971:
1969:
1961:
1953:
1944:
1943:
1938:
1930:
1921:
1920:
1918:
1916:
1915:
1913:
1909:
1908:
1903:
1895:
1873:
1861:
1853:
1818:
1816:
1815:
1810:
1805:
1803:
1802:
1800:
1796:
1795:
1790:
1782:
1760:
1748:
1743:
1741:
1727:
1722:
1720:
1709:
1687:
1680:
1679:
1677:
1676:
1671:
1668:
1656:
1655:
1653:
1652:
1646:
1643:
1622:
1620:
1619:
1614:
1609:
1608:
1599:
1598:
1589:
1578:
1577:
1565:
1554:
1553:
1541:
1532:
1531:
1516:
1515:
1506:
1505:
1496:
1485:
1484:
1472:
1461:
1460:
1448:
1439:
1438:
1433:
1429:
1427:
1416:
1403:
1402:
1390:
1369:
1367:
1366:
1361:
1356:
1354:
1346:
1345:
1336:
1302:
1300:
1299:
1294:
1289:
1288:
1276:
1267:
1266:
1254:
1253:
1241:
1232:
1230:
1226:
1225:
1220:
1212:
1196:
1191:
1190:
1178:
1169:
1165:
1164:
1159:
1151:
1132:
1131:
1119:
1082:Emission process
1056:Jacob Bekenstein
1045:
1034:
1032:
878:
871:
867:
864:
858:
835:
827:
759:
752:
745:
732:
727:
726:
719:
715:
714:
499:van Stockum dust
484:RobertsonâWalker
310:
200:
114:
112:
111:
106:
104:
103:
91:
83:
82:
64:
63:
44:
30:
21:
7524:
7523:
7519:
7518:
7517:
7515:
7514:
7513:
7494:Stephen Hawking
7474:
7473:
7472:
7460:
7450:
7448:
7440:
7438:
7433:
7402:
7379:
7312:
7265:
7246:
7189:
7075:
7009:
7007:Stephen Hawking
7004:
6974:
6969:
6968:
6946:
6935:FRW/CFT duality
6909:
6858:
6840:
6817:
6777:
6719:
6691:
6684:
6641:
6560:
6558:Quantum gravity
6555:
6512:
6507:
6460:
6453:
6432:
6379:
6363:
6332:
6324:
6284:
6234:
6185:
6144:
6094:
6044:
6028:
5978:
5929:
5880:
5828:
5793:
5764:(5443): 30â31.
5750:
5746:
5744:Further reading
5741:
5740:
5724:
5723:
5719:
5709:
5707:
5696:
5695:
5691:
5632:
5631:
5627:
5617:
5615:
5601:
5600:
5596:
5536:
5535:
5531:
5463:
5462:
5458:
5419:(10): 959â965.
5404:
5403:
5399:
5349:
5348:
5344:
5334:
5332:
5320:
5319:
5315:
5299:
5298:
5294:
5236:
5235:
5231:
5178:
5177:
5173:
5157:
5156:
5152:
5102:
5101:
5097:
5047:
5046:
5042:
4992:
4991:
4987:
4941:
4940:
4936:
4908:
4907:
4903:
4845:
4844:
4840:
4782:
4781:
4777:
4737:
4736:
4732:
4697:
4696:
4692:
4653:(6): 943â1008.
4642:
4641:
4637:
4621:
4620:
4616:
4606:
4604:
4550:
4545:
4544:
4540:
4508:
4503:
4502:
4493:
4479:
4478:
4469:
4459:
4457:
4442:
4441:
4437:
4404:
4403:
4399:
4392:
4389:
4341:
4339:
4332:
4282:
4281:
4277:
4221:
4220:
4216:
4172:
4171:
4167:
4152:
4138:Wald, Robert M.
4136:
4135:
4131:
4096:
4095:
4088:
4081:
4068:
4066:
4062:
4055:
4034:
4032:
4025:
4011:
4010:
4006:
3975:(11): 1242023.
3962:
3961:
3957:
3950:
3932:
3931:
3927:
3918:
3914:
3884:
3883:
3879:
3870:
3866:
3853:
3851:
3842:
3841:
3834:
3827:
3814:
3813:
3806:
3798:
3793:
3792:
3788:
3779:
3778:
3771:
3734:(5443): 30â31.
3725:
3724:
3717:
3706:charlierose.com
3700:Rose, Charlie.
3699:
3698:
3694:
3689:
3684:
3664:Penrose process
3640:
3602:
3584:If speculative
3582:
3562:
3557:
3510:
3501:
3497:
3494:
3488:
3457:
3446:
3428:
3418:
3412:
3411:
3399:
3383:
3382:
3368:
3364:
3360:
3278:
3273:
3249:quantum gravity
3221:
3204:
3202:
3198:
3192:
3190:
3182:
3176:
3174:
3171:
3168:
3165:
3158:
3152:
3149:
3143:
3137:
3131:
3092:
3083:
3082:
3063:
3025:
3024:
3002:
2971:
2962:
2961:
2951:
2931:
2917:
2913:
2895:
2891:
2880:
2870:
2863:
2843:
2838:
2837:
2823:
2815:
2807:
2799:
2795:
2768:
2758:
2751:
2740:
2736:
2723:
2722:
2689:
2676:
2665:
2661:
2644:
2639:
2638:
2616:
2602:
2599:
2591:
2589:
2587:
2584:
2572:
2568:
2566:
2547:
2545:
2533:
2506:
2500:
2492:somehow encoded
2450:
2436:
2435:
2398:
2347:
2346:
2290:
2272:
2271:
2264:
2260:
2230:
2212:
2207:
2206:
2173:
2148:
2147:
2137:
2133:
2093:
2068:
2067:
2063:at infinity is
2060:
2023:
2015:
2006:
2002:
1984:
1962:
1954:
1945:
1931:
1922:
1896:
1887:
1883:
1865:
1846:
1835:
1834:
1783:
1774:
1770:
1752:
1731:
1713:
1697:
1696:
1682:
1672:
1669:
1666:
1665:
1663:
1658:
1647:
1644:
1639:
1638:
1636:
1631:
1600:
1590:
1569:
1545:
1523:
1507:
1497:
1476:
1452:
1420:
1411:
1410:
1394:
1378:
1377:
1347:
1337:
1315:
1314:
1280:
1258:
1245:
1213:
1204:
1200:
1182:
1152:
1143:
1139:
1123:
1107:
1106:
1084:
1064:Yakov Zeldovich
1060:Stephen Hawking
1052:
1040:
1030:
1028:
1013:
1010:
969:Stephen Hawking
879:
868:
862:
859:
848:
836:
825:
790:Stephen Hawking
763:
722:
709:
708:
701:
700:
524:
523:
514:
513:
469:LemaĂźtreâTolman
414:
413:
402:
401:
393:Quantum gravity
380:Advanced theory
307:
306:
305:
288:
287:
236:Geodetic effect
197:
196:
187:
186:
162:
161:
145:
115:
92:
71:
52:
47:
46:
28:
23:
22:
15:
12:
11:
5:
7522:
7520:
7512:
7511:
7506:
7501:
7496:
7491:
7486:
7476:
7475:
7471:
7470:
7458:
7435:
7434:
7432:
7431:
7426:
7421:
7416:
7410:
7408:
7404:
7403:
7401:
7400:
7394:
7387:
7385:
7381:
7380:
7378:
7377:
7369:
7361:
7353:
7345:
7337:
7329:
7320:
7318:
7314:
7313:
7311:
7310:
7302:
7294:
7286:
7277:
7275:
7271:
7270:
7267:
7266:
7264:
7263:
7254:
7252:
7248:
7247:
7245:
7244:
7238:
7230:
7222:
7214:
7206:
7197:
7195:
7191:
7190:
7188:
7187:
7179:
7171:
7163:
7155:
7147:
7139:
7131:
7123:
7115:
7107:
7099:
7090:
7088:
7081:
7077:
7076:
7074:
7073:
7071:Hawking energy
7068:
7063:
7058:
7053:
7048:
7043:
7038:
7033:
7028:
7023:
7017:
7015:
7011:
7010:
7005:
7003:
7002:
6995:
6988:
6980:
6971:
6970:
6967:
6966:
6952:
6951:
6948:
6947:
6945:
6944:
6943:
6942:
6937:
6932:
6921:
6919:
6915:
6914:
6911:
6910:
6908:
6907:
6905:Twistor theory
6902:
6897:
6892:
6887:
6882:
6877:
6872:
6866:
6864:
6860:
6859:
6857:
6856:
6850:
6848:
6842:
6841:
6839:
6838:
6833:
6827:
6825:
6819:
6818:
6816:
6815:
6810:
6805:
6800:
6794:
6792:
6783:
6779:
6778:
6776:
6775:
6770:
6765:
6760:
6755:
6750:
6745:
6740:
6735:
6729:
6727:
6721:
6720:
6718:
6717:
6712:
6707:
6702:
6696:
6694:
6686:
6685:
6683:
6682:
6677:
6672:
6667:
6662:
6657:
6651:
6649:
6643:
6642:
6640:
6639:
6634:
6629:
6624:
6619:
6614:
6609:
6604:
6599:
6594:
6589:
6584:
6579:
6574:
6568:
6566:
6562:
6561:
6556:
6554:
6553:
6546:
6539:
6531:
6525:
6524:
6518:
6511:
6510:External links
6508:
6506:
6505:
6475:(10): 105032.
6458:
6451:
6430:
6400:hep-th/0607081
6393:(3): 179â212.
6377:
6322:
6282:
6252:hep-th/0602188
6245:(12): 124022.
6232:
6203:hep-th/0503052
6196:(12): 124039.
6183:
6162:hep-th/0212108
6142:
6112:hep-ph/0402168
6092:
6062:hep-ph/0311238
6042:
6026:
6013:10.1086/432033
5976:
5940:(2): 403â410.
5927:
5891:(2): 676â687.
5878:
5847:(2): 399â415.
5826:
5807:(2): 198â206.
5791:
5747:
5745:
5742:
5739:
5738:
5717:
5689:
5644:(20): 203901.
5625:
5594:
5549:(3): 362â367.
5543:Nature Physics
5529:
5456:
5412:Nature Physics
5397:
5342:
5313:
5292:
5254:hep-ph/0106295
5247:(16): 161602.
5229:
5199:hep-ph/0106219
5171:
5150:
5113:(3): 635â644.
5095:
5065:hep-th/0607081
5058:(3): 179â212.
5040:
5003:(5): 904â907.
4985:
4934:
4901:
4863:hep-ph/0110163
4856:(22): 221602.
4838:
4800:hep-th/9506121
4775:
4730:
4690:
4635:
4614:
4538:
4519:(5): 299â301.
4491:
4486:www.vttoth.com
4467:
4435:
4415:(2): 198â206.
4397:
4390:
4387:
4330:
4275:
4237:hep-th/9306083
4214:
4187:(3): 199â220.
4165:
4150:
4129:
4110:(2): 198â206.
4086:
4080:978-0691163727
4079:
4060:
4053:
4023:
4004:
3955:
3948:
3925:
3912:
3893:(15): 99â104.
3877:
3864:
3832:
3825:
3804:
3786:
3769:
3715:
3691:
3690:
3688:
3685:
3683:
3682:
3677:
3672:
3667:
3657:
3652:
3647:
3641:
3639:
3636:
3601:
3598:
3581:
3578:
3564:In June 2008,
3561:
3558:
3556:
3553:
3509:
3506:
3492:
3485:
3484:
3473:
3466:
3463:
3460:
3455:
3452:
3449:
3442:
3435:
3431:
3421:
3415:
3406:
3402:
3398:
3393:
3390:
3359:
3356:
3320:Doppler shifts
3277:
3274:
3272:
3269:
3268:
3267:
3260:
3257:Planck lengths
3240:
3169:
3166:
3156:
3147:
3128:
3127:
3116:
3111:
3106:
3099:
3095:
3091:
3086:
3070:
3066:
3062:
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3056:
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3028:
3019:
3012:
3009:
3005:
3001:
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2995:
2990:
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2910:
2902:
2898:
2894:
2887:
2883:
2877:
2873:
2869:
2866:
2860:
2854:
2851:
2846:
2812:speed of light
2792:
2791:
2775:
2771:
2765:
2761:
2757:
2754:
2747:
2743:
2739:
2733:
2730:
2715:
2714:
2697:
2692:
2688:
2685:
2682:
2679:
2672:
2668:
2664:
2658:
2652:
2647:
2600:
2597:
2585:
2582:
2559:Standard Model
2499:
2496:
2487:
2486:
2475:
2470:
2467:
2462:
2457:
2453:
2449:
2446:
2443:
2425:
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2413:
2410:
2405:
2401:
2397:
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2362:
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2328:
2325:
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2316:
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2307:
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2298:
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2287:
2284:
2280:
2257:
2256:
2245:
2239:
2236:
2233:
2229:
2224:
2215:
2200:
2199:
2188:
2182:
2179:
2176:
2172:
2167:
2164:
2161:
2158:
2155:
2130:
2129:
2118:
2110:
2107:
2104:
2099:
2096:
2092:
2087:
2084:
2081:
2078:
2075:
2057:
2056:
2045:
2036:
2029:
2026:
2021:
2018:
2012:
2009:
2005:
2001:
1998:
1995:
1990:
1987:
1983:
1978:
1968:
1965:
1960:
1957:
1951:
1948:
1941:
1937:
1934:
1928:
1925:
1912:
1906:
1902:
1899:
1893:
1890:
1886:
1882:
1879:
1876:
1871:
1868:
1864:
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1856:
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1842:
1820:
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1808:
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1793:
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1786:
1780:
1777:
1773:
1769:
1766:
1763:
1758:
1755:
1751:
1746:
1740:
1737:
1734:
1730:
1725:
1719:
1716:
1712:
1707:
1704:
1681:, diverges as
1624:
1623:
1612:
1607:
1603:
1597:
1593:
1588:
1584:
1581:
1576:
1572:
1568:
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1371:
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1359:
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1328:
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1322:
1304:
1303:
1292:
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1283:
1279:
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1265:
1261:
1257:
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1248:
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1240:
1236:
1229:
1223:
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1216:
1210:
1207:
1203:
1199:
1194:
1189:
1185:
1181:
1177:
1173:
1168:
1162:
1158:
1155:
1149:
1146:
1142:
1138:
1135:
1130:
1126:
1122:
1118:
1114:
1083:
1080:
1051:
1048:
1011:
1008:
991:at a non-zero
881:
880:
839:
837:
830:
824:
821:
765:
764:
762:
761:
754:
747:
739:
736:
735:
734:
733:
720:
703:
702:
699:
698:
691:
686:
681:
676:
671:
666:
661:
656:
651:
646:
641:
636:
631:
626:
621:
616:
611:
606:
601:
596:
591:
586:
581:
576:
571:
566:
561:
556:
551:
546:
541:
536:
531:
525:
521:
520:
519:
516:
515:
512:
511:
506:
501:
496:
491:
486:
481:
476:
471:
466:
461:
456:
451:
446:
441:
436:
431:
426:
415:
409:
408:
407:
404:
403:
398:
397:
396:
395:
390:
382:
381:
377:
376:
375:
374:
372:Post-Newtonian
369:
364:
356:
355:
351:
350:
349:
348:
343:
338:
333:
328:
323:
315:
314:
308:
304:
303:
300:
296:
295:
294:
293:
290:
289:
284:
283:
282:
281:
276:
271:
263:
262:
256:
255:
254:
253:
248:
243:
238:
233:
231:Frame-dragging
228:
223:
218:
213:
208:
206:Kepler problem
198:
194:
193:
192:
189:
188:
185:
184:
179:
174:
169:
163:
159:
158:
157:
154:
153:
152:
151:
146:
144:
143:
138:
133:
127:
125:
117:
116:
102:
99:
95:
90:
86:
81:
78:
74:
70:
67:
62:
59:
55:
45:
37:
36:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
7521:
7510:
7507:
7505:
7502:
7500:
7497:
7495:
7492:
7490:
7487:
7485:
7482:
7481:
7479:
7469:
7464:
7459:
7457:
7447:
7443:
7430:
7427:
7425:
7422:
7420:
7417:
7415:
7412:
7411:
7409:
7405:
7398:
7395:
7392:
7389:
7388:
7386:
7382:
7376:(2016 series)
7375:
7374:
7370:
7368:(2011 series)
7367:
7366:
7362:
7360:(2010 series)
7359:
7358:
7354:
7352:(2010 series)
7351:
7350:
7346:
7343:
7342:
7338:
7335:
7334:
7330:
7327:
7326:
7322:
7321:
7319:
7315:
7308:
7307:
7303:
7300:
7299:
7295:
7292:
7291:
7287:
7284:
7283:
7279:
7278:
7276:
7272:
7261:
7260:
7256:
7255:
7253:
7249:
7242:
7239:
7236:
7235:
7231:
7228:
7227:
7223:
7220:
7219:
7215:
7212:
7211:
7207:
7204:
7203:
7199:
7198:
7196:
7192:
7185:
7184:
7180:
7177:
7176:
7172:
7169:
7168:
7164:
7161:
7160:
7156:
7153:
7152:
7148:
7145:
7144:
7140:
7137:
7136:
7132:
7129:
7128:
7124:
7121:
7120:
7116:
7113:
7112:
7108:
7105:
7104:
7100:
7097:
7096:
7092:
7091:
7089:
7085:
7082:
7078:
7072:
7069:
7067:
7064:
7062:
7059:
7057:
7054:
7052:
7049:
7047:
7044:
7042:
7039:
7037:
7034:
7032:
7029:
7027:
7024:
7022:
7019:
7018:
7016:
7012:
7008:
7001:
6996:
6994:
6989:
6987:
6982:
6981:
6978:
6965:
6957:
6954:
6953:
6949:
6941:
6938:
6936:
6933:
6931:
6928:
6927:
6926:
6923:
6922:
6920:
6916:
6906:
6903:
6901:
6898:
6896:
6893:
6891:
6888:
6886:
6883:
6881:
6880:Dual graviton
6878:
6876:
6873:
6871:
6868:
6867:
6865:
6861:
6855:
6852:
6851:
6849:
6847:
6843:
6837:
6834:
6832:
6829:
6828:
6826:
6824:
6820:
6814:
6811:
6809:
6806:
6804:
6801:
6799:
6796:
6795:
6793:
6791:
6790:String theory
6787:
6784:
6780:
6774:
6771:
6769:
6766:
6764:
6761:
6759:
6756:
6754:
6751:
6749:
6746:
6744:
6741:
6739:
6736:
6734:
6731:
6730:
6728:
6726:
6722:
6716:
6713:
6711:
6708:
6706:
6703:
6701:
6698:
6697:
6695:
6693:
6687:
6681:
6678:
6676:
6673:
6671:
6668:
6666:
6663:
6661:
6658:
6656:
6653:
6652:
6650:
6648:
6644:
6638:
6635:
6633:
6630:
6628:
6625:
6623:
6620:
6618:
6615:
6613:
6610:
6608:
6605:
6603:
6600:
6598:
6595:
6593:
6590:
6588:
6585:
6583:
6580:
6578:
6575:
6573:
6570:
6569:
6567:
6563:
6559:
6552:
6547:
6545:
6540:
6538:
6533:
6532:
6529:
6522:
6519:
6517:
6514:
6513:
6509:
6501:
6496:
6491:
6486:
6482:
6478:
6474:
6470:
6469:
6464:
6459:
6454:
6448:
6444:
6439:
6438:
6431:
6426:
6422:
6418:
6414:
6410:
6406:
6401:
6396:
6392:
6388:
6387:
6382:
6378:
6375:
6371:
6362:
6358:
6354:
6350:
6346:
6343:(11): 44â48.
6342:
6338:
6337:Physics Today
6331:
6327:
6323:
6318:
6314:
6310:
6306:
6302:
6298:
6294:
6290:
6289:
6283:
6278:
6274:
6270:
6266:
6262:
6258:
6253:
6248:
6244:
6240:
6239:
6233:
6229:
6225:
6221:
6217:
6213:
6209:
6204:
6199:
6195:
6191:
6190:
6184:
6180:
6176:
6172:
6168:
6163:
6158:
6155:(6): 064025.
6154:
6150:
6149:
6143:
6138:
6134:
6130:
6126:
6122:
6118:
6113:
6108:
6104:
6100:
6099:
6093:
6088:
6084:
6080:
6076:
6072:
6068:
6063:
6058:
6054:
6050:
6049:
6043:
6037:
6032:
6027:
6022:
6018:
6014:
6010:
6006:
6002:
5997:
5992:
5988:
5984:
5983:
5977:
5973:
5969:
5965:
5961:
5957:
5953:
5948:
5943:
5939:
5935:
5934:
5928:
5924:
5920:
5916:
5912:
5908:
5904:
5899:
5894:
5890:
5886:
5885:
5879:
5873:
5868:
5864:
5860:
5855:
5850:
5846:
5842:
5841:
5836:
5832:
5827:
5822:
5818:
5814:
5810:
5806:
5802:
5801:
5796:
5792:
5787:
5783:
5779:
5775:
5771:
5767:
5763:
5759:
5758:
5753:
5749:
5748:
5743:
5734:
5733:
5728:
5721:
5718:
5706:
5705:
5700:
5693:
5690:
5685:
5681:
5677:
5673:
5669:
5665:
5661:
5657:
5652:
5647:
5643:
5639:
5638:
5629:
5626:
5618:September 27,
5613:
5609:
5605:
5598:
5595:
5590:
5586:
5582:
5578:
5574:
5570:
5566:
5562:
5557:
5552:
5548:
5544:
5540:
5533:
5530:
5525:
5521:
5517:
5513:
5509:
5505:
5501:
5497:
5493:
5489:
5484:
5479:
5475:
5471:
5467:
5460:
5457:
5452:
5448:
5444:
5440:
5436:
5432:
5427:
5422:
5418:
5414:
5413:
5408:
5401:
5398:
5393:
5389:
5385:
5381:
5377:
5373:
5368:
5367:gr-qc/0110036
5363:
5359:
5355:
5354:
5346:
5343:
5330:
5329:
5324:
5317:
5314:
5309:
5308:
5303:
5296:
5293:
5288:
5284:
5280:
5276:
5272:
5268:
5264:
5260:
5255:
5250:
5246:
5242:
5241:
5233:
5230:
5225:
5221:
5217:
5213:
5209:
5205:
5200:
5195:
5192:(5): 056010.
5191:
5187:
5186:
5181:
5175:
5172:
5166:
5161:
5154:
5151:
5146:
5142:
5138:
5134:
5130:
5126:
5121:
5120:gr-qc/0603121
5116:
5112:
5108:
5107:
5099:
5096:
5091:
5087:
5083:
5079:
5075:
5071:
5066:
5061:
5057:
5053:
5052:
5044:
5041:
5036:
5032:
5028:
5024:
5020:
5016:
5011:
5010:gr-qc/9710007
5006:
5002:
4998:
4997:
4989:
4986:
4980:
4975:
4971:
4967:
4962:
4957:
4953:
4949:
4945:
4938:
4935:
4930:
4926:
4921:
4916:
4912:
4905:
4902:
4897:
4893:
4889:
4885:
4881:
4877:
4873:
4869:
4864:
4859:
4855:
4851:
4850:
4842:
4839:
4834:
4830:
4826:
4822:
4818:
4814:
4810:
4806:
4801:
4796:
4792:
4788:
4787:
4779:
4776:
4771:
4767:
4763:
4759:
4755:
4751:
4747:
4743:
4742:
4734:
4731:
4726:
4722:
4718:
4714:
4710:
4706:
4705:
4700:
4694:
4691:
4686:
4682:
4678:
4674:
4670:
4666:
4661:
4660:gr-qc/0304042
4656:
4652:
4648:
4647:
4639:
4636:
4630:
4625:
4618:
4615:
4603:
4599:
4595:
4591:
4587:
4583:
4579:
4575:
4570:
4565:
4561:
4558:
4557:
4549:
4542:
4539:
4534:
4530:
4526:
4522:
4518:
4514:
4507:
4500:
4498:
4496:
4492:
4487:
4483:
4476:
4474:
4472:
4468:
4455:
4451:
4450:
4445:
4439:
4436:
4430:
4426:
4422:
4418:
4414:
4410:
4409:
4401:
4398:
4394:
4383:
4379:
4375:
4371:
4367:
4363:
4359:
4355:
4351:
4347:
4346:
4337:
4335:
4331:
4326:
4322:
4318:
4314:
4310:
4306:
4301:
4296:
4293:(6): 064043.
4292:
4288:
4287:
4279:
4276:
4271:
4267:
4263:
4259:
4255:
4251:
4247:
4243:
4238:
4233:
4229:
4225:
4218:
4215:
4210:
4206:
4202:
4198:
4194:
4190:
4186:
4182:
4181:
4176:
4169:
4166:
4161:
4157:
4153:
4151:9780226870250
4147:
4143:
4139:
4133:
4130:
4125:
4121:
4117:
4113:
4109:
4105:
4104:
4099:
4093:
4091:
4087:
4082:
4076:
4072:
4064:
4061:
4056:
4054:0-521-29928-4
4050:
4046:
4041:
4040:
4030:
4028:
4024:
4019:
4015:
4008:
4005:
4000:
3996:
3992:
3988:
3983:
3978:
3974:
3970:
3966:
3959:
3956:
3951:
3949:0-553-38016-8
3945:
3941:
3940:
3935:
3929:
3926:
3922:
3916:
3913:
3908:
3904:
3900:
3896:
3892:
3888:
3881:
3878:
3874:
3868:
3865:
3861:
3850:
3846:
3839:
3837:
3833:
3828:
3826:9780525658221
3822:
3818:
3811:
3809:
3805:
3797:
3790:
3787:
3782:
3776:
3774:
3770:
3765:
3761:
3757:
3753:
3749:
3745:
3741:
3737:
3733:
3729:
3722:
3720:
3716:
3711:
3707:
3703:
3696:
3693:
3686:
3681:
3678:
3676:
3673:
3671:
3668:
3665:
3661:
3658:
3656:
3653:
3651:
3648:
3646:
3643:
3642:
3637:
3635:
3631:
3629:
3625:
3621:
3620:
3615:
3614:perfect fluid
3611:
3607:
3599:
3597:
3595:
3591:
3587:
3579:
3577:
3575:
3571:
3568:launched the
3567:
3559:
3554:
3552:
3550:
3546:
3541:
3539:
3535:
3531:
3527:
3523:
3519:
3515:
3514:event horizon
3507:
3505:
3491:
3471:
3464:
3461:
3458:
3453:
3450:
3447:
3440:
3433:
3429:
3419:
3413:
3404:
3400:
3396:
3391:
3388:
3381:
3380:
3379:
3377:
3372:
3357:
3355:
3353:
3347:
3344:
3339:
3335:
3333:
3328:
3323:
3321:
3317:
3313:
3308:
3306:
3302:
3299:
3295:
3294:Planck length
3291:
3287:
3283:
3275:
3270:
3265:
3261:
3258:
3254:
3250:
3246:
3241:
3238:
3234:
3233:
3232:
3229:
3227:
3219:
3214:
3212:
3207:10 years
3195:10 years
3188:
3183:10 years
3163:
3155:
3146:
3140:
3134:
3114:
3109:
3104:
3097:
3093:
3089:
3084:
3068:
3064:
3060:
3057:
3054:
3049:
3044:
3031:
3026:
3010:
3007:
3003:
2999:
2996:
2993:
2988:
2983:
2972:
2968:
2963:
2952:
2947:
2944:
2941:
2935:
2927:
2922:
2918:
2914:
2908:
2900:
2896:
2885:
2881:
2875:
2871:
2867:
2864:
2858:
2844:
2836:
2835:
2834:
2831:
2829:
2821:
2813:
2805:
2773:
2769:
2763:
2759:
2755:
2752:
2745:
2741:
2731:
2728:
2721:
2720:
2719:
2690:
2686:
2683:
2680:
2677:
2670:
2666:
2656:
2645:
2637:
2636:
2635:
2632:
2630:
2626:
2622:
2614:
2610:
2605:
2594:10 years
2578:
2564:
2560:
2556:
2543:
2539:
2531:
2527:
2522:
2520:
2515:
2514:
2510:
2505:
2497:
2495:
2493:
2473:
2468:
2465:
2460:
2455:
2451:
2447:
2444:
2441:
2434:
2433:
2432:
2430:
2411:
2403:
2399:
2395:
2392:
2381:
2378:
2369:
2366:
2363:
2360:
2357:
2345:
2344:
2343:
2326:
2323:
2314:
2311:
2308:
2305:
2300:
2296:
2285:
2282:
2270:
2269:
2268:
2243:
2237:
2234:
2231:
2227:
2222:
2213:
2205:
2204:
2203:
2186:
2180:
2177:
2174:
2170:
2165:
2153:
2146:
2145:
2144:
2141:
2116:
2108:
2105:
2102:
2097:
2094:
2090:
2085:
2073:
2066:
2065:
2064:
2043:
2034:
2027:
2024:
2019:
2016:
2010:
2007:
2003:
1999:
1996:
1993:
1988:
1985:
1981:
1976:
1966:
1963:
1958:
1955:
1949:
1946:
1939:
1935:
1932:
1926:
1923:
1910:
1904:
1900:
1897:
1891:
1888:
1884:
1880:
1877:
1874:
1869:
1866:
1862:
1857:
1850:
1847:
1840:
1833:
1832:
1831:
1827:
1825:
1822:which is the
1806:
1797:
1791:
1787:
1784:
1778:
1775:
1771:
1767:
1764:
1761:
1756:
1753:
1749:
1744:
1738:
1735:
1732:
1728:
1723:
1717:
1714:
1710:
1705:
1702:
1695:
1694:
1693:
1689:
1685:
1675:
1661:
1651:
1642:
1634:
1629:
1610:
1605:
1595:
1591:
1579:
1574:
1566:
1555:
1550:
1542:
1528:
1524:
1520:
1517:
1512:
1502:
1498:
1486:
1481:
1473:
1462:
1457:
1449:
1435:
1430:
1424:
1421:
1417:
1412:
1407:
1404:
1399:
1391:
1376:
1375:
1374:
1357:
1351:
1348:
1342:
1338:
1332:
1329:
1326:
1323:
1320:
1313:
1312:
1311:
1307:
1290:
1285:
1263:
1259:
1255:
1250:
1242:
1227:
1221:
1217:
1214:
1208:
1205:
1201:
1197:
1192:
1187:
1179:
1166:
1160:
1156:
1153:
1147:
1144:
1140:
1136:
1133:
1128:
1120:
1105:
1104:
1103:
1102:has a metric
1101:
1096:
1093:
1089:
1081:
1079:
1078:
1073:
1069:
1065:
1061:
1057:
1049:
1047:
1044:
1038:
1026:
1022:
1018:
1014:
1005:
1000:
998:
994:
990:
986:
981:
979:
974:
970:
966:
961:
959:
955:
951:
947:
939:
935:
930:
926:
924:
923:event horizon
919:
915:
910:
908:
904:
900:
896:
892:
888:
877:
874:
866:
856:
852:
846:
845:
840:This section
838:
834:
829:
828:
822:
820:
818:
814:
810:
805:
802:
797:
795:
791:
787:
783:
782:event horizon
779:
775:
771:
760:
755:
753:
748:
746:
741:
740:
738:
737:
731:
721:
718:
713:
707:
706:
705:
704:
697:
696:
692:
690:
687:
685:
682:
680:
677:
675:
672:
670:
667:
665:
662:
660:
657:
655:
652:
650:
647:
645:
642:
640:
637:
635:
634:Chandrasekhar
632:
630:
627:
625:
622:
620:
617:
615:
612:
610:
607:
605:
602:
600:
597:
595:
592:
590:
587:
585:
582:
580:
577:
575:
572:
570:
567:
565:
562:
560:
557:
555:
552:
550:
549:Schwarzschild
547:
545:
542:
540:
537:
535:
532:
530:
527:
526:
518:
517:
510:
509:HartleâThorne
507:
505:
502:
500:
497:
495:
492:
490:
487:
485:
482:
480:
477:
475:
472:
470:
467:
465:
462:
460:
457:
455:
452:
450:
447:
445:
442:
440:
437:
435:
432:
430:
427:
424:
420:
419:Schwarzschild
417:
416:
412:
406:
405:
394:
391:
389:
386:
385:
384:
383:
378:
373:
370:
368:
365:
363:
360:
359:
358:
357:
352:
347:
344:
342:
339:
337:
334:
332:
329:
327:
324:
322:
319:
318:
317:
316:
311:
301:
298:
297:
292:
291:
280:
277:
275:
272:
270:
267:
266:
265:
264:
261:
257:
252:
249:
247:
244:
242:
241:Event horizon
239:
237:
234:
232:
229:
227:
224:
222:
219:
217:
214:
212:
209:
207:
204:
203:
202:
201:
191:
190:
183:
180:
178:
175:
173:
170:
168:
165:
164:
156:
155:
150:
147:
142:
139:
137:
134:
132:
129:
128:
126:
124:
121:
120:
119:
118:
100:
97:
93:
88:
84:
79:
76:
72:
65:
60:
57:
53:
43:
39:
38:
35:
31:
19:
7397:Lucy Hawking
7393:(first wife)
7371:
7363:
7355:
7347:
7339:
7331:
7323:
7305:
7297:
7289:
7281:
7257:
7240:
7232:
7224:
7216:
7208:
7200:
7181:
7173:
7165:
7157:
7149:
7141:
7133:
7125:
7117:
7109:
7101:
7093:
7020:
6955:
6918:Applications
6808:Supergravity
6715:Unruh effect
6704:
6622:Quantum foam
6617:Planck units
6612:IR/UV mixing
6587:Causal patch
6472:
6466:
6436:
6390:
6384:
6361:the original
6340:
6336:
6292:
6286:
6242:
6236:
6193:
6187:
6152:
6146:
6102:
6096:
6052:
6046:
5986:
5980:
5937:
5931:
5888:
5882:
5844:
5838:
5804:
5798:
5795:Page, Don N.
5761:
5755:
5730:
5720:
5708:. Retrieved
5702:
5692:
5641:
5635:
5628:
5616:. Retrieved
5612:the original
5607:
5597:
5546:
5542:
5532:
5473:
5469:
5459:
5416:
5410:
5400:
5357:
5351:
5345:
5333:. Retrieved
5326:
5316:
5307:CERN Courier
5305:
5295:
5244:
5238:
5232:
5189:
5183:
5174:
5153:
5110:
5104:
5098:
5055:
5049:
5043:
5000:
4994:
4988:
4951:
4947:
4937:
4910:
4904:
4853:
4847:
4841:
4790:
4784:
4778:
4745:
4739:
4733:
4708:
4702:
4693:
4650:
4644:
4638:
4617:
4605:. Retrieved
4594:10261/140585
4559:
4554:
4541:
4516:
4512:
4485:
4458:. Retrieved
4454:Ethan Siegel
4447:
4438:
4412:
4406:
4400:
4385:
4349:
4343:
4290:
4284:
4278:
4227:
4223:
4217:
4184:
4178:
4168:
4141:
4132:
4107:
4101:
4098:Page, Don N.
4070:
4063:
4038:
4017:
4007:
3972:
3968:
3958:
3938:
3928:
3915:
3890:
3886:
3880:
3872:
3867:
3859:
3852:. Retrieved
3848:
3816:
3789:
3731:
3727:
3710:the original
3705:
3695:
3680:Unruh effect
3632:
3617:
3603:
3600:Experimental
3583:
3563:
3542:
3511:
3489:
3486:
3373:
3361:
3348:
3340:
3336:
3325:An outgoing
3324:
3312:Unruh effect
3309:
3279:
3230:
3215:
3153:
3144:
3138:
3132:
3129:
2832:
2793:
2716:
2633:
2606:
2579:
2523:
2512:
2508:
2501:
2488:
2429:Planck units
2426:
2341:
2267:is added is
2258:
2201:
2139:
2131:
2058:
1828:
1824:Unruh effect
1821:
1690:
1683:
1673:
1659:
1649:
1640:
1632:
1630:in terms of
1625:
1372:
1308:
1305:
1097:
1088:Unruh effect
1085:
1076:
1053:
1001:
982:
962:
949:
943:
937:
911:
907:John Wheeler
884:
869:
860:
849:Please help
844:verification
841:
808:
806:
798:
769:
768:
694:
654:Raychaudhuri
123:Introduction
7484:Black holes
6875:Causal sets
6725:Black holes
6326:Smolin, Lee
4711:: 727â745.
3854:1 September
3608:, in which
3322:the modes.
3253:Planck mass
1050:Formulation
1039:, or about
993:temperature
978:evaporating
895:black holes
669:van Stockum
599:Oppenheimer
454:KerrâNewman
246:Singularity
7478:Categories
7399:(daughter)
7317:Television
6940:Multiverse
6782:Approaches
6660:CGHS model
6647:Toy models
6582:CA-duality
6500:10023/4760
5556:1910.09363
5483:1809.00913
5426:1510.00621
5165:1802.00100
4961:2001.08833
4607:27 October
4569:1502.01589
3687:References
3626:employing
3526:Bekenstein
3365:10 kg
3343:white hole
3290:wavelength
3245:gamma rays
3199:10 kg
3179:10 kg
3162:solar mass
2575:10 kg
2550:10 kg
1033:10 kg
1017:billionths
1004:solar mass
967:physicist
794:telescopes
778:black hole
522:Scientists
354:Formalisms
302:Formalisms
251:Black hole
177:World line
7456:Astronomy
7419:Namesakes
6956:See also:
6895:Spin foam
6675:RST model
6317:121117052
5854:1209.2243
5710:April 30,
5651:1009.4634
5589:230508375
5581:1745-2481
5524:119327617
5508:1476-4687
5451:119197166
5328:The Times
5287:119375071
5145:119039723
4954:(2): 21.
4602:119262962
4325:119230843
4300:0709.2380
4160:832158297
3982:1205.5251
3907:120254309
3756:1476-4687
3502:10 s
3434:∗
3405:∗
3392:∼
3389:τ
3369:10 s
3352:Minkowski
3316:spacetime
3301:frequency
3098:⊙
3061:×
3055:≈
3008:−
3000:×
2994:≈
2948:π
2933:ℏ
2893:ℏ
2868:π
2756:π
2738:ℏ
2681:π
2663:ℏ
2581:billion)
2524:In 1976,
2448:π
2396:π
2367:π
2312:π
2235:π
2178:π
2160:∞
2098:π
2080:∞
2011:−
1989:π
1950:−
1927:−
1892:−
1870:π
1779:−
1757:π
1739:ρ
1736:π
1718:π
1711:α
1626:which is
1596:⊥
1567:ρ
1543:τ
1525:ρ
1521:−
1503:⊥
1474:ρ
1418:ρ
1408:−
1339:ρ
1278:Ω
1209:−
1148:−
1137:−
1054:In 1972,
1041:133
958:spacetime
614:Robertson
579:Friedmann
574:Eddington
564:Nordström
554:de Sitter
411:Solutions
336:Geodesics
331:Friedmann
313:Equations
299:Equations
260:Spacetime
195:Phenomena
101:ν
98:μ
89:κ
80:ν
77:μ
69:Λ
61:ν
58:μ
6803:M-theory
6763:ER = EPR
6602:Graviton
6228:28276606
6137:11863375
6087:14275281
5923:17033284
5833:(1974).
5676:21231233
5516:31142857
5331:. London
5279:11690198
5035:18980849
4948:Universe
4896:14228817
4888:12059412
4833:26432764
4825:10019680
4770:10014053
4685:16668175
4391:☉
4382:27717447
4374:17817517
4262:10055062
4209:55539246
4140:(1994).
3936:(1988).
3638:See also
3305:infinite
3170:☉
2615:of mass
2601:☉
2586:☉
2561:and the
2532:of mass
2526:Don Page
2028:′
1967:′
1851:′
1090:and the
1012:☉
887:Einstein
863:May 2023
823:Overview
730:Category
594:LemaĂźtre
559:Reissner
544:Poincaré
529:Einstein
474:TaubâNUT
439:Wormhole
423:interior
136:Timeline
7468:Physics
7442:Portals
7298:Hawking
7290:Hawking
7251:Memoirs
7194:Fiction
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