7452:
701:
31:
918:
6949:
3255:. 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.
3114:
714:
822:
3323:, 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.
2828:
7440:
1610:
2043:
3109:{\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},}
1290:
3367:(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).
1368:
3334:
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
3318:
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
3326:
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
909:
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
2478:
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
1083:
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
3338:
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
964:
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
984:. 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
2541:
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
3622:
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.
2569:
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
1298:
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
1825:
1806:
1818:
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:
2510:, 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.
1097:
965:
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
3471:
2592:
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.
1680:
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
1084:
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.
2533:-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
5622:
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".
1605:{\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},}
3335:
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.
3231:
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
2701:
2326:
2411:
792:
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.
2525:. 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
102:
2706:
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:
3351:
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
1063:
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
2778:
2116:
2038:{\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)}}}}.}
1687:
3849:
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.
3593:
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
3209:, 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
4375:
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
2243:
804:
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
2186:
1357:
1285:{\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}.}
2473:
3307:
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
3373:
781:, 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
3327:
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.
1051:'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
937:
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
3489:
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" ~
925:. 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.
808:, 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.
3330:
The trans-Planckian problem is nowadays mostly considered a mathematical artifact of horizon calculations. The same effect occurs for regular matter falling onto a
472:
3285:
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
7407:
7131:
4432:
745:
6418:â studies the deviation of a loop quantized black hole from Hawking radiation. A novel observable quantum effect of black hole quantization is introduced.
3532:
Based on the fluctuations of the horizon area, a quantum black hole exhibits deviations from the Hawking radiation spectrum that would be observable were
941:
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
5828:
2629:
2262:
5147:
Fermi-LAT collaboration (January 31, 2018). "Search for Gamma-Ray Emission from Local Primordial Black Holes with the Fermi Large Area Telescope".
2337:
124:
3540:
to be observed. The quantum effects are centered at a set of discrete and unblended frequencies highly pronounced on top of the Hawking spectrum.
7099:
6318:
4898:
Carr, Bernard J. (2005). "Primordial Black Holes â Recent Developments". In Pisin Chen; Elliott Bloom; Greg Madejski; Vahe Patrosian (eds.).
37:
6224:
Ida, Daisuke; Oda, Kin'ya; Park, Seong-chan (2006). "Rotating Black Holes at Future Colliders. III. Determination of Black Hole Evolution".
945:, a place of infinite curvature and zero size, leaving behind a warped spacetime devoid of any matter; a classical black hole is pure empty
6034:
Barrau, AurĂ©lien; Grain, Julien; Alexeyev, Stanislav O. (2004). "GaussâBonnet black holes at the LHC: beyond the dimensionality of space".
4002:
329:
7083:
5968:
Barrau, Aurélien; Féron, Chloé; Grain, Julien (2005). "Astrophysical Production of Microscopic Black Holes in a Low-Planck-Scale World".
952:
Our current understanding of quantum physics can be used to investigate what may happen in the region around the event horizon. In 1974,
3769:
2491:
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
7044:
6175:
Ida, Daisuke; Oda, Kin'ya; Park, Seong-chan (2005). "Rotating black holes at future colliders. II. Anisotropic scalar field emission".
682:
5339:
BarcelĂł, Carlos; Liberati, Stefano; Visser, Matt (2003). "Towards the observation of Hawking radiation in BoseâEinstein condensates".
6986:
6537:
6086:
5341:
492:
334:
4772:
Brout, Robert; Massar, Serge; Parentani, Renaud; Spindel, Philippe (1995). "Hawking radiation without trans-Planckian frequencies".
7054:
6678:
6134:
Ida, Daisuke; Oda, Kin'ya; Park, Seong-chan (2003). "Rotating black holes at future colliders: Greybody factors for brane fields".
961:
886:
began to mount half a century later, and these objects are of current interest primarily because of their compact size and immense
738:
447:
2713:
7329:
2058:
1801:{\displaystyle T={\frac {\alpha }{2\pi }}={\frac {1}{2\pi \rho }}={\frac {1}{4\pi {\sqrt {2Mr\left(1-{\frac {2M}{r}}\right)}}}},}
4382:... the timescale for black holes to radiate away all their energy ranges from to 10 years for black holes of one solar mass ...
7345:
7190:
6643:
5592:
4168:
3864:, World Scientific (2005). The tunneling process is described on pp.26â28, and described as Black Hole Evaporation on pp.48â49.
360:
194:
2600:
emitted by a black hole in the form of Hawking radiation can be estimated for the simplest case of a nonrotating, non-charged
934:
922:
7313:
6439:
3206:
1013:
399:
7353:
7293:
4982:
Ashtekar, Abhay; Baez, John Carlos; Corichi, Alejandro; Krasnov, Kirill (1998). "Quantum Geometry and Black Hole Entropy".
4900:
Proceedings of the 22nd Texas Symposium on Relativistic Astrophysics at Stanford, Stanford California, December 13â17, 2004
3585:
may be able to create micro black holes and observe their evaporation. No such micro black hole has been observed at CERN.
2551:
4394:
Page, Don N. (1976). "Particle emission rates from a black hole: Massless particles from an uncharged, nonrotating hole".
2815:
is the mass of the black hole. It is worth mentioning that the above formula has not yet been derived in the framework of
2616:
of blackbody radiation, the above formula for the temperature of the radiation, and the formula for the surface area of a
7417:
3663:
731:
3690:
7402:
7163:
4924:
4067:
2197:
839:
111:
2517:
refined this estimate by calculating the power produced, and the time to evaporation, for a non-rotating, non-charged
1646:. The metric describes a frame that is accelerating to keep from falling into the black hole. The local acceleration,
7123:
6952:
6274:
Nicolaevici, Nistor (2003). "Blackbody spectrum from accelerated mirrors with asymptotically inertial trajectories".
4138:
4041:
3936:
3813:
2138:
861:
137:
1047:
developed a theory and reported that the black holes should have an entropy. Bekenstein's theory and report came to
7487:
7198:
7155:
7024:
6668:
6565:
4022:
For an alternative derivation and more detailed discussion of Hawking radiation as a form of Unruh radiation, see:
1305:
7451:
700:
417:
30:
7492:
7214:
3558:
2426:
324:
3525:
is set to cancel out various constants such that the BekensteinâHawking entropy formula is reproduced. However,
7412:
7269:
6858:
6726:
6504:
4634:
3633:
3360:). This is normally seen as an indication that the Planck mass is the lower limit on the mass of a black hole.
3252:
843:
2191:
Thus a field theory defined on a black-hole background is in a thermal state whose temperature at infinity is
7477:
7321:
6979:
6741:
6653:
6615:
6530:
5786:(1976). "Particle emission rates from a black hole: Massless particles from an uncharged, nonrotating hole".
4536:
4089:(1976). "Particle emission rates from a black hole: Massless particles from an uncharged, nonrotating hole".
914:; an observer outside it cannot observe, become aware of, or be affected by events within the event horizon.
411:
119:
5171:; Thomas, Scott (2002). "High energy colliders as black hole factories: The end of short distance physics".
4470:
4024:
de Witt, Bryce (1980). "Quantum gravity: the new synthesis". In Hawking, Stephen W.; Israel, Werner (eds.).
457:
7107:
6746:
5687:
3648:
3616:
3466:{\displaystyle \tau \sim {\frac {1}{M_{*}}}\left({\frac {M_{\text{BH}}}{M_{*}}}\right)^{\frac {n+3}{n+1}},}
477:
5528:"Observation of stationary spontaneous Hawking radiation and the time evolution of an analogue black hole"
796:
For all except the smallest black holes, this happens extremely slowly. The radiation temperature, called
7497:
6824:
6625:
5921:
5872:
4544:
718:
209:
129:
7430:
7115:
7034:
7029:
6721:
4272:
MacGibbon, Jane H.; Carr, B. J.; Page, Don N. (2008). "Do Evaporating Black Holes Form Photospheres?".
3658:
622:
170:
5311:
7361:
7039:
7014:
6834:
6811:
6761:
6731:
5970:
5715:
4494:
3638:
3225:
942:
774:
422:
234:
6349:
3953:
949:, and the simplest (nonrotating and uncharged) is characterized just by its mass and event horizon.
7482:
7222:
7139:
7049:
6972:
6888:
6842:
6523:
6431:
3784:
3607:
2613:
2601:
2526:
2518:
1088:
887:
657:
647:
497:
314:
2543:
7206:
7147:
7091:
6878:
6688:
6620:
6580:
5625:
5526:
Kolobov, Victor I.; Golubkov, Katrine; Muñoz de Nova, Juan Ramón; Steinhauer, Jeff (March 2021).
5228:
4984:
4837:
3926:
3270:
2792:
832:
642:
376:
4329:
See page 596: table 1 and the "black hole decay" section and previous sentence on that page in
3529:
corrections to the entropy and radiation of black holes have been computed based on the theory.
6560:
6456:
5453:
Muñoz de Nova, Juan Ramón; Golubkov, Katrine; Kolobov, Victor I.; Steinhauer, Jeff (May 2019).
4033:
3537:
3364:
3199:
2808:
973:
895:
805:
612:
597:
442:
204:
2585:. Some monster black holes in the universe are predicted to continue to grow up to perhaps 10
7171:
6786:
6698:
6595:
6585:
3582:
3574:
3562:
2816:
2480:
1080:
587:
155:
6423:
5944:
5919:
Barrau, Aurélien; et al. (2003). "Antideuterons as a probe of primordial black holes".
5895:
4566:
4025:
7472:
6819:
6465:
6393:
6358:
6333:
6285:
6276:
6245:
6196:
6155:
6105:
6055:
6018:
Barrau, Aurélien; Boudoul, Gaëlle (2002). "Some aspects of primordial black hole physics".
5989:
5940:
5891:
5847:
5797:
5783:
5754:
5644:
5549:
5476:
5419:
5360:
5290:
5247:
5192:
5113:
5058:
5003:
4954:
4913:
4856:
4793:
4738:
4701:
4653:
4562:
4509:
4405:
4342:
4293:
4230:
4177:
4100:
4086:
3975:
3724:
3506:
3320:
2609:
2514:
2507:
2248:
From the black-hole temperature, it is straightforward to calculate the black-hole entropy
977:
762:
407:
6084:
Kanti, Panagiota (2004). "Black Holes in Theories with Large Extra Dimensions: a Review".
3833:
8:
7285:
7277:
6512:
A. Barrau & J. Grain explain how the Hawking radiation could be detected at colliders
6509:
6478:
6451:
6424:
5720:
5396:"Observation of quantum Hawking radiation and its entanglement in an analogue black hole"
3643:
3175:
1616:
1060:
917:
602:
572:
567:
319:
6469:
6452:"Focus on Classical and Quantum Analogs for Gravitational Phenomena and Related Effects"
6397:
6337:
6289:
6249:
6200:
6159:
6109:
6059:
5993:
5851:
5801:
5758:
5648:
5553:
5480:
5455:"Observation of thermal Hawking radiation and its temperature in an analogue black hole"
5423:
5364:
5251:
5196:
5117:
5062:
5007:
4958:
4917:
4860:
4797:
4742:
4705:
4657:
4513:
4409:
4346:
4297:
4234:
4181:
4104:
3979:
3728:
1035:
across) would be in equilibrium at 2.7 K, absorbing as much radiation as it emits.
976:), black holes in certain cases (and perhaps in general) are equivalent to solutions of
582:
552:
6873:
6801:
6756:
6409:
6383:
6369:
6362:
6361:
about gravity in small scales including the deviation from Hawking radiation effect by
6301:
6261:
6235:
6212:
6186:
6145:
6121:
6095:
6071:
6045:
6019:
6005:
5979:
5956:
5930:
5907:
5881:
5837:
5770:
5668:
5634:
5573:
5539:
5508:
5466:
5435:
5409:
5376:
5350:
5271:
5237:
5226:
Dimopoulos, Savas; Landsberg, Greg (2001). "Black Holes at the Large Hadron Collider".
5208:
5182:
5148:
5129:
5103:
5074:
5048:
5019:
4993:
4944:
4903:
4880:
4846:
4817:
4783:
4687:
4669:
4643:
4612:
4586:
4552:
4437:
4366:
4309:
4283:
4254:
4220:
4193:
3965:
3891:
3748:
3510:
2492:
1056:
891:
879:
652:
537:
462:
309:
214:
199:
160:
22:
6297:
5716:"Artificial event horizon emits laboratory analog to theoretical black hole radiation"
5092:
Ansari, Mohammad H. (2008). "Generic degeneracy and entropy in loop quantum gravity".
3601:
are analogous to light in a gravitational black hole and the flow of an approximately
7337:
6918:
6913:
6658:
6435:
6374:
6305:
6226:
6177:
6136:
6036:
5788:
5660:
5577:
5565:
5527:
5512:
5500:
5492:
5439:
5275:
5263:
5173:
5133:
5094:
5039:
4872:
4809:
4774:
4754:
4729:
4713:
4692:
4665:
4590:
4396:
4358:
4333:
4313:
4274:
4246:
4144:
4134:
4091:
4063:
4037:
4026:
3932:
3895:
3809:
3740:
3522:
3340:
482:
257:
6405:
6310:â consistent derivation of the Hawking radiation in the FullingâDavies mirror model.
6216:
6125:
6075:
5911:
5600:
5454:
5125:
5070:
5023:
4884:
4821:
4673:
4370:
4197:
532:
7444:
7247:
7019:
6736:
6483:
6473:
6413:
6401:
6341:
6293:
6265:
6253:
6204:
6163:
6113:
6067:
6063:
6014:â experimental searches for primordial black holes thanks to the emitted antimatter
6009:
5997:
5960:
5948:
5899:
5855:
5805:
5774:
5762:
5745:
5692:
5672:
5656:
5652:
5557:
5484:
5427:
5380:
5368:
5255:
5212:
5200:
5121:
5078:
5066:
5011:
4962:
4864:
4801:
4746:
4709:
4661:
4578:
4570:
4517:
4413:
4350:
4301:
4258:
4238:
4185:
4108:
3983:
3883:
3752:
3732:
3612:
3594:
3514:
3303:
and the Hawking effect both talk about field modes in the superficially stationary
1044:
801:
607:
562:
542:
487:
5259:
4868:
4574:
3561:, which is searching for the terminal gamma-ray flashes expected from evaporating
627:
6995:
6923:
6546:
5952:
5903:
5870:
Barrau, Aurélien; et al. (2002). "Antiprotons from primordial black holes".
5819:
5740:
5168:
4354:
4163:
3922:
3909:
3652:
3526:
3518:
3237:
2597:
1052:
1048:
957:
778:
662:
637:
522:
517:
381:
262:
224:
5395:
4242:
432:
7456:
7059:
6893:
6257:
6208:
6167:
5561:
5400:
5204:
5037:
Ansari, Mohammad H. (2007). "Spectroscopy of a canonically quantized horizon".
5015:
4305:
2800:
2696:{\displaystyle T_{\mathrm {H} }={\frac {\hbar c^{3}}{8\pi GMk_{\mathrm {B} }}}}
2547:
2530:
2321:{\displaystyle \mathrm {d} S={\frac {\mathrm {d} Q}{T}}=8\pi M\,\mathrm {d} Q.}
972:
However, according to the conjectured gauge-gravity duality (also known as the
953:
777:
is inside the event horizon, it cannot escape. It is named after the physicist
705:
672:
667:
355:
219:
6117:
5860:
5823:
5488:
5372:
4727:
Jacobson, Theodore (1991). "Black-hole evaporation and ultrashort distances".
3987:
16:
Thermal radiation believed to be emitted by black holes due to quantum effects
7466:
6868:
6778:
5569:
5496:
4805:
4750:
4611:
Kapusta, Joseph (1999). "The Last Eight Minutes of a Primordial Black Hole".
4148:
4056:
For an accessible discussion of the Unruh effect and Hawking radiation, see:
3744:
3698:
3602:
3502:
3308:
3282:
3245:
2406:{\displaystyle \mathrm {d} S=8\pi M\,\mathrm {d} M=\mathrm {d} (4\pi M^{2}).}
911:
770:
632:
547:
527:
452:
350:
229:
6426:
Black Holes, White Dwarfs, and Neutron Stars: The Physics of Compact Objects
5809:
4967:
4932:
4835:
Cheung, Kingman (2002). "Black Hole Production and Large Extra Dimensions".
4417:
4112:
3862:
An Introduction to Black Holes. Information and the String Theory Revolution
3785:"Black Hole Entropy and 2D Conformal Field Theory - Towards Quantum Gravity"
3228:
by showing how black holes interact thermally with the rest of the universe.
592:
7385:
7379:
6796:
6703:
6610:
6605:
6600:
6575:
5664:
5504:
5295:
5267:
4876:
4813:
4758:
4442:
4362:
4250:
3668:
3300:
2506:). Consequently, an evaporating black hole will have a finite lifespan. By
2417:
1812:
1076:
577:
557:
6863:
6024:
5984:
5935:
5886:
4908:
4617:
4126:
3241:
981:
966:
883:
467:
437:
6080:â searches for new physics (quantum gravity) with primordial black holes
5312:"Stephen Hawkings 50 bet on the world the universe and the God particle"
4582:
3770:"John Michell: Country Parson Described Black Holes in 1783 | AMNH"
3286:
2496:
6928:
6713:
6648:
6570:
6388:
6314:
6240:
6191:
6150:
6100:
6050:
5242:
5187:
5053:
4851:
4788:
4225:
4211:
Page, Don N. (6 December 1993). "Information in Black Hole Radiation".
4189:
4062:. Princeton, New Jersey: Princeton University Press. pp. 154â162.
3887:
3331:
3278:
3150:
1295:
The black hole is the background spacetime for a quantum field theory.
1031:
996:
992:
923:
infalling into a Schwarzschild black hole at the Newtonian escape speed
846: in this section. Unsourced material may be challenged and removed.
766:
677:
239:
165:
97:{\displaystyle G_{\mu \nu }+\Lambda g_{\mu \nu }={\kappa }T_{\mu \nu }}
6488:
6345:
5525:
5452:
5431:
5355:
5108:
4998:
4648:
4521:
4131:
Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics
2420:, so the entropy of a black hole is proportional to its surface area:
6883:
6751:
6663:
6635:
5766:
5316:
3736:
3304:
3289:
3233:
946:
782:
248:
3198:. This is why some astronomers are searching for signs of exploding
2620:(the black hole's event horizon), several equations can be derived.
821:
6791:
6590:
6001:
5544:
5471:
5414:
5153:
4949:
4557:
3293:
890:. Early research into black holes were done by individuals such as
875:
617:
427:
267:
6964:
6515:
5842:
5639:
5590:
4288:
3970:
2331:
The heat energy that enters serves to increase the total mass, so
4933:"Black Hole Evaporation: A Perspective from Loop Quantum Gravity"
3485:
is the low-energy scale, which could be as low as a few TeV, and
3274:
3236:. A complete description of this dissolution requires a model of
5621:
3954:"Effective Temperature, Hawking Radiation and Quasinormal Modes"
3240:, however, as it occurs when the black hole's mass approaches 1
4464:
4462:
4460:
3598:
3356:), they result in impossible lifetimes below the Planck time (~
3315:
2617:
1009:
906:
902:
4331:
Frautschi, Steven (1982). "Entropy in an Expanding Universe".
5866:â links between primordial black holes and the early universe
4600:– via The University of Manchester's Research Explorer.
4488:
4486:
4484:
4003:"Hawking-Bekenstein radiation and the shifting of a paradigm"
3533:
3220:
Black hole evaporation has several significant consequences:
3214:
1005:
4457:
3691:"A conversation with Dr. Stephen Hawking & Lucy Hawking"
2773:{\displaystyle P={\frac {\hbar c^{6}}{15360\pi G^{2}M^{2}}}}
6372:(2007). "Spectroscopy of a canonically quantized horizon".
4771:
4001:
Nature, Research Communities by Springer (March 14, 2018).
3578:
3554:
3131:
are the mass and (Schwarzschild) volume of the black hole,
2554:
figure for the age of the universe yielded a mass bound of
2111:{\displaystyle T(\infty )={\frac {1}{4\pi {\sqrt {2Mr}}}},}
1025:
789:
4981:
4481:
3273:
is the issue that Hawking's original calculation includes
3251:
The simplest models of black hole evaporation lead to the
3224:
Black hole evaporation produces a more consistent view of
6270:â determination of black hole's life and extra dimensions
5591:
Emerging Technology from the arXiv (September 27, 2010).
3874:
Bekenstein, A. (1972). "Black holes and the second law".
3501:
A detailed study of the quantum geometry of a black hole
800:, is inversely proportional to the black hole's mass, so
6450:
Leonhardt, Ulf; Maia, Clovis; Schuetzhold, Ralf (2010).
6449:
2479:
the physical description of a gravitating theory can be
6357:
consists of the recent developments and predictions of
5146:
3715:
Hawking, S. W. (1974-03-01). "Black hole explosions?".
3611:). Observations of Hawking radiation were reported, in
3296:
frequency, and therefore a trans-Planckian wavelength.
2546:. A 2008 calculation using the particle content of the
3509:. Loop-quantization does not reproduce the result for
7428:
5814:â first detailed studies of the evaporation mechanism
5688:"Ultrafast Laser Pulse Makes Desktop Black Hole Glow"
5338:
3376:
3149:
are Planck mass and Planck time. A black hole of one
2831:
2716:
2632:
2429:
2340:
2265:
2200:
2141:
2061:
1828:
1690:
1371:
1308:
1100:
40:
4690:(1985). "On the quantum structure of a black hole".
4537:"Planck 2015 results: XIII. Cosmological parameters"
4534:
2822:
The time that the black hole takes to dissipate is:
1012:); in fact, such a black hole would absorb far more
1004:) has a temperature of only 60 nanokelvins (60
6446:â Hawking radiation evaporation formula derivation.
6033:
5225:
4632:Helfer, Adam D. (2003). "Do black holes radiate?".
4433:"Ask Ethan: How Do Black Holes Actually Evaporate?"
3808:. New York: Alfred A. Knopf, Penguin Random House.
5829:Monthly Notices of the Royal Astronomical Society
3465:
3292:, if traced back to the horizon, must have had an
3108:
2772:
2695:
2467:
2405:
2320:
2237:
2180:
2110:
2037:
1800:
1604:
1351:
1284:
96:
5289:Barrau, Aurélien; Grain, Julien (November 2004).
4271:
3565:. As of Jan 1st, 2023, none have been detected.
2238:{\displaystyle T_{\text{H}}={\frac {1}{8\pi M}}.}
773:. This is counterintuitive because once ordinary
7464:
6421:
5967:
4204:
4050:
4028:General Relativity: An Einstein Centenary Survey
2416:The radius of a black hole is twice its mass in
2252:. The change in entropy when a quantity of heat
898:who modeled black holes as having zero entropy.
882:. Evidence for the astrophysical objects termed
7100:Black Holes and Baby Universes and Other Essays
6422:Shapiro, Stuart L.; Teukolsky, Saul A. (1983).
4471:"Viktor T. Toth - Hawking radiation calculator"
4057:
2181:{\displaystyle T(\infty )={\frac {1}{8\pi M}}.}
6130:â evaporating black holes and extra-dimensions
5167:
3710:
3708:
6980:
6531:
6017:
3568:
2787:is the luminosity, i.e., the radiated power,
1352:{\displaystyle r=2M+{\frac {\rho ^{2}}{8M}}.}
969:(although it actually came from outside it).
739:
4686:
4325:
4323:
4058:Gubser, Steven S.; Pretorius, Frans (2017).
4018:
4016:
3799:
3797:
3339:temperature can be calculated from ordinary
985:
6273:
5817:
5288:
4528:
4081:
4079:
3705:
3543:
2468:{\displaystyle S=\pi R^{2}={\frac {A}{4}}.}
874:Modern black holes were first predicted by
6987:
6973:
6538:
6524:
6223:
6174:
6133:
5615:
5393:
3873:
3827:
3825:
3496:
3264:
3259:
3213:must be less than 0.8% of the mass of the
3174:to evaporateâmuch longer than the current
2544:3 flavors of neutrinos with nonzero masses
746:
732:
6487:
6477:
6387:
6239:
6190:
6149:
6099:
6087:International Journal of Modern Physics A
6049:
6023:
5983:
5934:
5885:
5859:
5841:
5638:
5543:
5470:
5413:
5354:
5342:International Journal of Modern Physics A
5309:
5241:
5186:
5152:
5140:
5107:
5052:
4997:
4966:
4948:
4907:
4850:
4787:
4647:
4616:
4556:
4330:
4320:
4287:
4224:
4013:
3969:
3958:International Journal of Modern Physics D
3794:
3346:
3205:However, since the universe contains the
3062:
3004:
2939:
2486:
2361:
2306:
1522:
1429:
1257:
1222:
1159:
862:Learn how and when to remove this message
5685:
5593:"First Observation of Hawking Radiation"
4930:
4726:
4492:
4119:
4076:
3655:, other extractions of black-hole energy
3343:field theory, and is not controversial.
962:quantum field theory in curved spacetime
916:
7330:Stephen Hawking: Master of the Universe
7084:The Large Scale Structure of SpaceâTime
6030:â cosmology with primordial black holes
5739:
5282:
4610:
4495:"Some Simple Black Hole Thermodynamics"
4161:
4023:
4007:Research Communities by Springer Nature
3921:
3822:
3714:
7465:
7346:Into the Universe with Stephen Hawking
6368:
6313:
5918:
5869:
5779:â Hawking's first article on the topic
5713:
5091:
5036:
4834:
4631:
4169:Communications in Mathematical Physics
4032:. Cambridge University Press. p.
4000:
3834:"A Black Hole is a Waterfall of Space"
3764:
3762:
3548:
3536:from Hawking radiation of evaporating
3217:â approximately the mass of the Moon.
2623:The Hawking radiation temperature is:
2048:The inverse temperature redshifted to
1075:Hawking radiation is dependent on the
7314:God, the Universe and Everything Else
6968:
6519:
6083:
5686:Grossman, Lisa (September 29, 2010).
5310:Henderson, Mark (September 9, 2008).
4902:. Vol. 041213. pp. 89â100.
3952:Corda, Christian (October 29, 2012).
3951:
3803:
3207:cosmic microwave background radiation
1014:cosmic microwave background radiation
7354:Brave New World with Stephen Hawking
7055:PenroseâHawking singularity theorems
5782:
4897:
4393:
4387:
4210:
4125:
4085:
3831:
3244:, its radius will also approach two
1362:The local metric to lowest order is
844:adding citations to reliable sources
815:
7191:George's Secret Key to the Universe
6994:
6545:
5824:"Black holes in the early universe"
3782:
3759:
2125:is the near-horizon position, near
1070:
13:
7164:Brief Answers to the Big Questions
7045:GibbonsâHawkingâYork boundary term
5743:(1974). "Black hole explosions?".
5732:
4164:"Particle creation by black holes"
3908:In the same year, he proposed his
3027:
3024:
3006:
2841:
2838:
2684:
2639:
2374:
2363:
2342:
2308:
2281:
2267:
2148:
2068:
1575:
1551:
1527:
1482:
1458:
1434:
1376:
1266:
1262:
1227:
1164:
1105:
901:A black hole can form when enough
57:
14:
7509:
6953:Template:Quantum mechanics topics
6505:Hawking radiation calculator tool
6498:
2608:. Combining the formulas for the
7450:
7438:
7156:The Dreams That Stuff Is Made Of
7025:Chronology protection conjecture
6948:
6947:
6669:Topological quantum field theory
5714:Matson, John (October 1, 2010).
4468:
4422:See in particular equation (27).
3688:
820:
713:
712:
699:
29:
7215:George and the Unbreakable Code
6654:Jackiw–Teitelboim gravity
6406:10.1016/j.nuclphysb.2007.01.009
6319:"Quantum gravity faces reality"
5707:
5679:
5584:
5519:
5446:
5387:
5332:
5303:
5291:"The Case for Mini Black Holes"
5219:
5161:
5126:10.1016/j.nuclphysb.2007.11.038
5085:
5071:10.1016/j.nuclphysb.2007.01.009
5030:
4975:
4891:
4828:
4765:
4720:
4680:
4625:
4604:
4425:
4265:
4155:
4133:. University of Chicago Press.
3994:
3945:
3915:
3588:
1016:than it emits. A black hole of
831:needs additional citations for
7413:Black hole information paradox
6859:Causal dynamical triangulation
6727:Black hole information paradox
6479:10.1088/1367-2630/14/10/105032
6430:. Wiley-Interscience. p.
6068:10.1016/j.physletb.2004.01.019
5657:10.1103/PhysRevLett.105.203901
4635:Reports on Progress in Physics
4493:Lopresto, Michael (May 2003).
4060:The little book of Black Holes
3902:
3867:
3854:
3776:
3682:
3634:Black hole information paradox
3253:black hole information paradox
2397:
2378:
2151:
2145:
2071:
2065:
1843:
1832:
1590:
1571:
1559:
1547:
1535:
1523:
1497:
1478:
1466:
1454:
1442:
1430:
1384:
1372:
1270:
1258:
1235:
1223:
1172:
1160:
1113:
1101:
1038:
933:Alternatively, using a set of
788:Hawking radiation reduces the
1:
7199:George's Cosmic Treasure Hunt
6825:Wheeler–DeWitt equation
6510:The case for mini black holes
5260:10.1103/PhysRevLett.87.161602
4869:10.1103/PhysRevLett.88.221602
4535:Planck Collaboration (2016).
3860:L. Susskind and J. Lindesay,
3675:
3605:is analogous to gravity (see
1066:Bekenstein-Hawking radiation.
7108:The Nature of Space and Time
6747:Cosmic censorship hypothesis
6566:BatalinâVilkovisky formalism
5922:Astronomy & Astrophysics
5873:Astronomy & Astrophysics
4714:10.1016/0550-3213(85)90418-3
4355:10.1126/science.217.4560.593
2529:goes down in a complicated,
7:
7418:ThorneâHawkingâPreskill bet
6298:10.1088/0305-4470/36/27/317
4575:10.1051/0004-6361/201525830
4243:10.1103/PhysRevLett.71.3743
3664:ThorneâHawkingâPreskill bet
3626:
3577:theories are correct, then
811:
761:is the theoretical thermal
210:Gravitational time dilation
10:
7514:
7322:Stephen Hawking's Universe
7124:On the Shoulders of Giants
7116:The Universe in a Nutshell
6843:Hartle–Hawking state
6742:Bousso's holographic bound
6722:Black hole complementarity
6258:10.1103/PhysRevD.73.124022
6209:10.1103/PhysRevD.71.124039
6168:10.1103/PhysRevD.67.064025
5953:10.1051/0004-6361:20021588
5904:10.1051/0004-6361:20020313
5562:10.1038/s41567-020-01076-0
5205:10.1103/PhysRevD.65.056010
5016:10.1103/PhysRevLett.80.904
4666:10.1088/0034-4885/66/6/202
4306:10.1103/PhysRevD.78.064043
3569:Heavy-ion collider physics
3190:, the evaporation time is
3186:. But for a black hole of
330:MathissonâPapapetrouâDixon
171:Pseudo-Riemannian manifold
7395:
7372:
7362:Genius by Stephen Hawking
7305:
7262:
7239:
7182:
7132:A Briefer History of Time
7075:
7068:
7015:Black hole thermodynamics
7002:
6939:
6906:
6851:
6835:Euclidean quantum gravity
6833:
6812:Canonical quantum gravity
6810:
6777:
6770:
6762:Gravitational singularity
6732:Black-hole thermodynamics
6712:
6677:
6634:
6616:RyuâTakayanagi conjecture
6553:
6118:10.1142/S0217751X04018324
5971:The Astrophysical Journal
5489:10.1038/s41586-019-1241-0
5394:Steinhauer, Jeff (2016).
5373:10.1142/s0217751x0301615x
3988:10.1142/S0218271812420230
3806:Black hole survival guide
3639:Black hole thermodynamics
3617:BoseâEinstein condensates
3513:originally discovered by
3281:becomes shorter than the
3226:black hole thermodynamics
2577:will evaporate in around
2483:onto a bounding surface.
943:gravitational singularity
775:electromagnetic radiation
7295:The Theory of Everything
7223:George and the Blue Moon
7175:(2023, posthume message)
7140:God Created the Integers
6889:Superfluid vacuum theory
6644:2+1D topological gravity
4931:Ashtekar, Abhay (2020).
4806:10.1103/PhysRevD.52.4559
4751:10.1103/PhysRevD.44.1731
3876:Lettere al Nuovo Cimento
3649:BlandfordâZnajek process
3608:Analog models of gravity
3544:Experimental observation
2602:Schwarzschild black hole
2527:absorption cross section
2519:Schwarzschild black hole
1089:Schwarzschild black hole
888:gravitational attraction
335:HamiltonâJacobiâEinstein
315:Einstein field equations
138:Mathematical formulation
7488:Astronomical hypotheses
7271:A Brief History of Time
7207:George and the Big Bang
7092:A Brief History of Time
6879:Noncommutative geometry
6626:WeinbergâWitten theorem
6621:Trans-Planckian problem
6457:New Journal of Physics
5945:2003A&A...398..403B
5896:2002A&A...388..676B
5861:10.1093/mnras/168.2.399
5810:10.1103/PhysRevD.13.198
5626:Physical Review Letters
5229:Physical Review Letters
4985:Physical Review Letters
4968:10.3390/universe6020021
4838:Physical Review Letters
4567:2016A&A...594A..13P
4551:. A13, p. 31, Table 4.
4418:10.1103/PhysRevD.13.198
4213:Physical Review Letters
4162:Hawking, S. W. (1975).
4113:10.1103/PhysRevD.13.198
3928:A Brief History of Time
3497:In loop quantum gravity
3271:trans-Planckian problem
3265:Trans-Planckian problem
3260:Problems and extensions
2793:reduced Planck constant
2612:of the black hole, the
1024:(about the mass of the
929:: Andrew Hamilton, JILA
7493:Hypothetical processes
7230:Unlocking the Universe
7035:GibbonsâHawking effect
7030:GibbonsâHawking ansatz
6561:AdS/CFT correspondence
6355:on September 10, 2008.
3659:GibbonsâHawking effect
3563:primordial black holes
3538:primordial black holes
3521:, unless the value of
3467:
3365:large extra dimensions
3347:Large extra dimensions
3321:Schwarzschild solution
3200:primordial black holes
3110:
2809:gravitational constant
2774:
2697:
2487:Black hole evaporation
2469:
2407:
2322:
2239:
2182:
2112:
2039:
1802:
1606:
1353:
1286:
974:AdS/CFT correspondence
930:
806:primordial black holes
205:Gravitational redshift
98:
7172:On the Origin of Time
7040:GibbonsâHawking space
6787:Bosonic string theory
6699:Semiclassical gravity
6596:Holographic principle
6586:Gravitational anomaly
6277:Journal of Physics A
5597:MIT Technology Review
3990:– via CrossRef.
3804:Levin, Janna (2020).
3583:Large Hadron Collider
3575:large extra dimension
3559:Fermi space telescope
3527:quantum gravitational
3468:
3111:
2817:semiclassical gravity
2775:
2698:
2470:
2408:
2323:
2240:
2183:
2113:
2040:
1803:
1607:
1354:
1287:
1081:equivalence principle
935:infalling coordinates
920:
785:' detecting ability.
493:WeylâLewisâPapapetrou
448:KerrâNewmanâde Sitter
268:EinsteinâRosen bridge
200:Gravitational lensing
156:Equivalence principle
99:
7478:Quantum field theory
7050:HartleâHawking state
6820:Loop quantum gravity
6679:Quantum field theory
6359:loop quantum gravity
3507:loop quantum gravity
3505:has been made using
3374:
3277:particles where the
2829:
2714:
2630:
2614:StefanâBoltzmann law
2610:Schwarzschild radius
2508:dimensional analysis
2427:
2338:
2263:
2198:
2139:
2132:, so this is really
2059:
1826:
1688:
1369:
1306:
1098:
1061:rotating black holes
991:A black hole of one
978:quantum field theory
840:improve this article
763:black-body radiation
423:EinsteinâRosen waves
149:Fundamental concepts
38:
6689:BunchâDavies vacuum
6681:in curved spacetime
6581:FaddeevâPopov ghost
6470:2012NJPh...14j5032L
6398:2007NuPhB.783..179A
6370:Ansari, Mohammad H.
6338:2006PhT....59k..44S
6290:2003JPhA...36.7667N
6250:2006PhRvD..73l4022I
6201:2005PhRvD..71l4039I
6160:2003PhRvD..67f4025I
6110:2004IJMPA..19.4899K
6060:2004PhLB..584..114B
5994:2005ApJ...630.1015B
5852:1974MNRAS.168..399C
5820:Hawking, Stephen W.
5802:1976PhRvD..13..198P
5759:1974Natur.248...30H
5741:Hawking, Stephen W.
5721:Scientific American
5649:2010PhRvL.105t3901B
5554:2021NatPh..17..362K
5481:2019Natur.569..688M
5424:2016NatPh..12..959S
5365:2003IJMPA..18.3735B
5252:2001PhRvL..87p1602D
5197:2002PhRvD..65e6010G
5169:Giddings, Steven B.
5118:2008NuPhB.795..635A
5063:2007NuPhB.783..179A
5008:1998PhRvL..80..904A
4959:2020Univ....6...21A
4918:2005tsra.conf...89C
4861:2002PhRvL..88v1602C
4798:1995PhRvD..52.4559B
4743:1991PhRvD..44.1731J
4706:1985NuPhB.256..727T
4658:2003RPPh...66..943H
4514:2003PhTea..41..299L
4502:The Physics Teacher
4410:1976PhRvD..13..198P
4347:1982Sci...217..593F
4298:2008PhRvD..78f4043M
4235:1993PhRvL..71.3743P
4182:1975CMaPh..43..199H
4105:1976PhRvD..13..198P
3980:2012IJMPD..2142023C
3783:Karozis, Nikolaos.
3729:1974Natur.248...30H
3644:Black hole starship
3599:sound perturbations
3549:Astronomical search
3176:age of the universe
2493:Einstein's equation
1059:convinced him that
798:Hawking temperature
765:released outside a
377:KaluzaâKlein theory
263:Minkowski spacetime
215:Gravitational waves
7498:1974 introductions
7403:In popular culture
7380:Jane Wilde Hawking
7333:(2008 documentary)
7325:(1997 documentary)
6874:Group field theory
6802:Superstring theory
6757:Firewall (physics)
5818:Carr, Bernard J.;
4545:Astron. Astrophys.
4438:Starts With a Bang
4190:10.1007/BF02345020
3888:10.1007/BF02757029
3832:Hamilton, Andrew.
3701:on March 29, 2013.
3511:black hole entropy
3463:
3170:) takes more than
3106:
2770:
2693:
2465:
2403:
2318:
2235:
2178:
2108:
2035:
1798:
1602:
1349:
1282:
1057:Alexei Starobinsky
931:
892:Karl Schwarzschild
880:general relativity
878:'s 1915 theory of
706:Physics portal
478:OppenheimerâSnyder
418:ReissnerâNordström
310:Linearized gravity
258:Spacetime diagrams
161:Special relativity
94:
23:General relativity
7426:
7425:
7338:Genius of Britain
7258:
7257:
7010:Hawking radiation
6962:
6961:
6919:Eternal inflation
6914:Quantum cosmology
6902:
6901:
6694:Hawking radiation
6659:Liouville gravity
6441:978-0-471-87316-7
6375:Nuclear Physics B
6346:10.1063/1.2435646
6317:(November 2006).
6284:(27): 7667â7677.
6227:Physical Review D
6178:Physical Review D
6137:Physical Review D
6094:(29): 4899â4951.
6037:Physics Letters B
5789:Physical Review D
5465:(7758): 688â691.
5432:10.1038/nphys3863
5349:(21): 3735â3745.
5174:Physical Review D
5095:Nuclear Physics B
5040:Nuclear Physics B
4775:Physical Review D
4730:Physical Review D
4693:Nuclear Physics B
4522:10.1119/1.1571268
4397:Physical Review D
4341:(4560): 593â599.
4275:Physical Review D
4219:(23): 3743â3746.
4092:Physical Review D
3838:jila.colorado.edu
3613:sonic black holes
3595:sonic black holes
3457:
3427:
3414:
3398:
3091:
3070:
3066:
3031:
3012:
2970:
2967:
2947:
2928:
2895:
2768:
2691:
2460:
2292:
2230:
2208:
2173:
2103:
2100:
2030:
2027:
2020:
1963:
1962:
1959:
1931:
1906:
1903:
1896:
1793:
1790:
1783:
1731:
1710:
1417:
1344:
1220:
1213:
1152:
921:Picture of space
872:
871:
864:
802:micro black holes
759:Hawking radiation
756:
755:
389:
388:
275:
274:
7505:
7455:
7454:
7443:
7442:
7441:
7434:
7248:My Brief History
7148:The Grand Design
7073:
7072:
7020:Micro black hole
6989:
6982:
6975:
6966:
6965:
6951:
6950:
6775:
6774:
6737:Bekenstein bound
6554:Central concepts
6540:
6533:
6526:
6517:
6516:
6493:
6491:
6481:
6445:
6429:
6417:
6391:
6356:
6354:
6348:. Archived from
6323:
6309:
6269:
6243:
6220:
6194:
6171:
6153:
6129:
6103:
6079:
6053:
6044:(1â2): 114â122.
6029:
6027:
6025:astro-ph/0212225
6013:
5987:
5985:astro-ph/0505436
5978:(2): 1015â1019.
5964:
5938:
5936:astro-ph/0207395
5915:
5889:
5887:astro-ph/0112486
5865:
5863:
5845:
5813:
5778:
5767:10.1038/248030a0
5726:
5725:
5711:
5705:
5704:
5702:
5700:
5683:
5677:
5676:
5642:
5619:
5613:
5612:
5610:
5608:
5603:on March 1, 2012
5599:. Archived from
5588:
5582:
5581:
5547:
5523:
5517:
5516:
5474:
5450:
5444:
5443:
5417:
5391:
5385:
5384:
5358:
5336:
5330:
5329:
5327:
5325:
5307:
5301:
5300:
5286:
5280:
5279:
5245:
5223:
5217:
5216:
5190:
5165:
5159:
5158:
5156:
5144:
5138:
5137:
5111:
5089:
5083:
5082:
5056:
5034:
5028:
5027:
5001:
4979:
4973:
4972:
4970:
4952:
4928:
4922:
4921:
4911:
4909:astro-ph/0504034
4895:
4889:
4888:
4854:
4832:
4826:
4825:
4791:
4782:(8): 4559â4568.
4769:
4763:
4762:
4737:(6): 1731â1739.
4724:
4718:
4717:
4688:'t Hooft, Gerard
4684:
4678:
4677:
4651:
4629:
4623:
4622:
4620:
4618:astro-ph/9911309
4608:
4602:
4601:
4599:
4597:
4560:
4541:
4532:
4526:
4525:
4499:
4490:
4479:
4478:
4469:Toth, Viktor T.
4466:
4455:
4454:
4452:
4450:
4429:
4423:
4421:
4391:
4385:
4384:
4327:
4318:
4317:
4291:
4269:
4263:
4262:
4228:
4208:
4202:
4201:
4159:
4153:
4152:
4123:
4117:
4116:
4083:
4074:
4073:
4054:
4048:
4047:
4031:
4020:
4011:
4010:
3998:
3992:
3991:
3973:
3949:
3943:
3942:
3931:. Bantam Books.
3923:Hawking, Stephen
3919:
3913:
3910:no-hair theorems
3906:
3900:
3899:
3871:
3865:
3858:
3852:
3851:
3846:
3844:
3829:
3820:
3819:
3801:
3792:
3791:
3789:
3780:
3774:
3773:
3766:
3757:
3756:
3737:10.1038/248030a0
3712:
3703:
3702:
3697:. Archived from
3686:
3523:a free parameter
3492:
3488:
3484:
3472:
3470:
3469:
3464:
3459:
3458:
3456:
3445:
3434:
3432:
3428:
3426:
3425:
3416:
3415:
3412:
3406:
3399:
3397:
3396:
3384:
3363:In a model with
3359:
3355:
3212:
3197:
3195:
3189:
3185:
3183:
3173:
3169:
3167:
3161:
3148:
3139:
3130:
3124:
3115:
3113:
3112:
3107:
3102:
3101:
3096:
3092:
3090:
3089:
3077:
3068:
3067:
3064:
3061:
3060:
3042:
3041:
3036:
3032:
3030:
3019:
3010:
3009:
3003:
3002:
2981:
2980:
2975:
2971:
2969:
2968:
2965:
2956:
2949:
2948:
2945:
2929:
2927:
2919:
2915:
2914:
2901:
2896:
2894:
2893:
2892:
2879:
2878:
2877:
2868:
2867:
2851:
2846:
2845:
2844:
2814:
2806:
2798:
2790:
2786:
2779:
2777:
2776:
2771:
2769:
2767:
2766:
2765:
2756:
2755:
2739:
2738:
2737:
2724:
2702:
2700:
2699:
2694:
2692:
2690:
2689:
2688:
2687:
2664:
2663:
2662:
2649:
2644:
2643:
2642:
2607:
2584:
2582:
2565:
2563:
2559:
2540:
2538:
2524:
2505:
2474:
2472:
2471:
2466:
2461:
2453:
2448:
2447:
2412:
2410:
2409:
2404:
2396:
2395:
2377:
2366:
2345:
2327:
2325:
2324:
2319:
2311:
2293:
2288:
2284:
2278:
2270:
2255:
2251:
2244:
2242:
2241:
2236:
2231:
2229:
2215:
2210:
2209:
2206:
2187:
2185:
2184:
2179:
2174:
2172:
2158:
2131:
2124:
2117:
2115:
2114:
2109:
2104:
2102:
2101:
2090:
2078:
2051:
2044:
2042:
2041:
2036:
2031:
2029:
2028:
2026:
2022:
2021:
2019:
2011:
2003:
1981:
1969:
1964:
1961:
1960:
1958:
1950:
1942:
1933:
1932:
1927:
1919:
1910:
1909:
1907:
1905:
1904:
1902:
1898:
1897:
1892:
1884:
1862:
1850:
1842:
1807:
1805:
1804:
1799:
1794:
1792:
1791:
1789:
1785:
1784:
1779:
1771:
1749:
1737:
1732:
1730:
1716:
1711:
1709:
1698:
1676:
1669:
1668:
1666:
1665:
1660:
1657:
1645:
1644:
1642:
1641:
1635:
1632:
1611:
1609:
1608:
1603:
1598:
1597:
1588:
1587:
1578:
1567:
1566:
1554:
1543:
1542:
1530:
1521:
1520:
1505:
1504:
1495:
1494:
1485:
1474:
1473:
1461:
1450:
1449:
1437:
1428:
1427:
1422:
1418:
1416:
1405:
1392:
1391:
1379:
1358:
1356:
1355:
1350:
1345:
1343:
1335:
1334:
1325:
1291:
1289:
1288:
1283:
1278:
1277:
1265:
1256:
1255:
1243:
1242:
1230:
1221:
1219:
1215:
1214:
1209:
1201:
1185:
1180:
1179:
1167:
1158:
1154:
1153:
1148:
1140:
1121:
1120:
1108:
1071:Emission process
1045:Jacob Bekenstein
1034:
1023:
1021:
867:
860:
856:
853:
847:
824:
816:
748:
741:
734:
721:
716:
715:
708:
704:
703:
488:van Stockum dust
473:RobertsonâWalker
299:
298:
189:
188:
103:
101:
100:
95:
93:
92:
80:
72:
71:
53:
52:
33:
19:
18:
7513:
7512:
7508:
7507:
7506:
7504:
7503:
7502:
7483:Stephen Hawking
7463:
7462:
7461:
7449:
7439:
7437:
7429:
7427:
7422:
7391:
7368:
7301:
7254:
7235:
7178:
7064:
6998:
6996:Stephen Hawking
6993:
6963:
6958:
6957:
6935:
6924:FRW/CFT duality
6898:
6847:
6829:
6806:
6766:
6708:
6680:
6673:
6630:
6549:
6547:Quantum gravity
6544:
6501:
6496:
6442:
6352:
6321:
5753:(5443): 30â31.
5735:
5733:Further reading
5730:
5729:
5712:
5708:
5698:
5696:
5684:
5680:
5620:
5616:
5606:
5604:
5589:
5585:
5524:
5520:
5451:
5447:
5408:(10): 959â965.
5392:
5388:
5337:
5333:
5323:
5321:
5308:
5304:
5287:
5283:
5224:
5220:
5166:
5162:
5145:
5141:
5090:
5086:
5035:
5031:
4980:
4976:
4929:
4925:
4896:
4892:
4833:
4829:
4770:
4766:
4725:
4721:
4685:
4681:
4642:(6): 943â1008.
4630:
4626:
4609:
4605:
4595:
4593:
4539:
4533:
4529:
4497:
4491:
4482:
4467:
4458:
4448:
4446:
4431:
4430:
4426:
4392:
4388:
4381:
4378:
4328:
4321:
4270:
4266:
4209:
4205:
4160:
4156:
4141:
4127:Wald, Robert M.
4124:
4120:
4084:
4077:
4070:
4055:
4051:
4044:
4021:
4014:
3999:
3995:
3964:(11): 1242023.
3950:
3946:
3939:
3920:
3916:
3907:
3903:
3872:
3868:
3859:
3855:
3842:
3840:
3830:
3823:
3816:
3802:
3795:
3787:
3781:
3777:
3768:
3767:
3760:
3723:(5443): 30â31.
3713:
3706:
3695:charlierose.com
3689:Rose, Charlie.
3687:
3683:
3678:
3673:
3653:Penrose process
3629:
3591:
3573:If speculative
3571:
3551:
3546:
3499:
3490:
3486:
3483:
3477:
3446:
3435:
3433:
3421:
3417:
3411:
3407:
3405:
3401:
3400:
3392:
3388:
3383:
3375:
3372:
3371:
3357:
3353:
3349:
3267:
3262:
3238:quantum gravity
3210:
3193:
3191:
3187:
3181:
3179:
3171:
3165:
3163:
3160:
3157:
3154:
3147:
3141:
3138:
3132:
3126:
3120:
3097:
3085:
3081:
3076:
3072:
3071:
3063:
3056:
3052:
3037:
3023:
3018:
3014:
3013:
3005:
2995:
2991:
2976:
2964:
2960:
2955:
2951:
2950:
2944:
2940:
2920:
2910:
2906:
2902:
2900:
2888:
2884:
2880:
2873:
2869:
2863:
2859:
2852:
2850:
2837:
2836:
2832:
2830:
2827:
2826:
2812:
2804:
2796:
2788:
2784:
2761:
2757:
2751:
2747:
2740:
2733:
2729:
2725:
2723:
2715:
2712:
2711:
2683:
2682:
2678:
2665:
2658:
2654:
2650:
2648:
2638:
2637:
2633:
2631:
2628:
2627:
2605:
2591:
2588:
2580:
2578:
2576:
2573:
2561:
2557:
2555:
2536:
2534:
2522:
2495:
2489:
2481:somehow encoded
2452:
2443:
2439:
2428:
2425:
2424:
2391:
2387:
2373:
2362:
2341:
2339:
2336:
2335:
2307:
2280:
2279:
2277:
2266:
2264:
2261:
2260:
2253:
2249:
2219:
2214:
2205:
2201:
2199:
2196:
2195:
2162:
2157:
2140:
2137:
2136:
2126:
2122:
2089:
2082:
2077:
2060:
2057:
2056:
2052:at infinity is
2049:
2012:
2004:
2002:
1995:
1991:
1980:
1973:
1968:
1951:
1943:
1941:
1934:
1920:
1918:
1911:
1908:
1885:
1883:
1876:
1872:
1861:
1854:
1849:
1835:
1827:
1824:
1823:
1772:
1770:
1763:
1759:
1748:
1741:
1736:
1720:
1715:
1702:
1697:
1689:
1686:
1685:
1671:
1661:
1658:
1655:
1654:
1652:
1647:
1636:
1633:
1628:
1627:
1625:
1620:
1593:
1589:
1583:
1579:
1574:
1562:
1558:
1550:
1538:
1534:
1526:
1516:
1512:
1500:
1496:
1490:
1486:
1481:
1469:
1465:
1457:
1445:
1441:
1433:
1423:
1409:
1404:
1400:
1399:
1387:
1383:
1375:
1370:
1367:
1366:
1336:
1330:
1326:
1324:
1307:
1304:
1303:
1273:
1269:
1261:
1251:
1247:
1238:
1234:
1226:
1202:
1200:
1193:
1189:
1184:
1175:
1171:
1163:
1141:
1139:
1132:
1128:
1116:
1112:
1104:
1099:
1096:
1095:
1073:
1053:Yakov Zeldovich
1049:Stephen Hawking
1041:
1029:
1019:
1017:
1002:
999:
958:Stephen Hawking
868:
857:
851:
848:
837:
825:
814:
779:Stephen Hawking
752:
711:
698:
697:
690:
689:
513:
512:
503:
502:
458:LemaĂźtreâTolman
403:
402:
391:
390:
382:Quantum gravity
369:Advanced theory
296:
295:
294:
277:
276:
225:Geodetic effect
186:
185:
176:
175:
151:
150:
134:
104:
85:
81:
76:
64:
60:
45:
41:
39:
36:
35:
17:
12:
11:
5:
7511:
7501:
7500:
7495:
7490:
7485:
7480:
7475:
7460:
7459:
7447:
7424:
7423:
7421:
7420:
7415:
7410:
7405:
7399:
7397:
7393:
7392:
7390:
7389:
7383:
7376:
7374:
7370:
7369:
7367:
7366:
7358:
7350:
7342:
7334:
7326:
7318:
7309:
7307:
7303:
7302:
7300:
7299:
7291:
7283:
7275:
7266:
7264:
7260:
7259:
7256:
7255:
7253:
7252:
7243:
7241:
7237:
7236:
7234:
7233:
7227:
7219:
7211:
7203:
7195:
7186:
7184:
7180:
7179:
7177:
7176:
7168:
7160:
7152:
7144:
7136:
7128:
7120:
7112:
7104:
7096:
7088:
7079:
7077:
7070:
7066:
7065:
7063:
7062:
7060:Hawking energy
7057:
7052:
7047:
7042:
7037:
7032:
7027:
7022:
7017:
7012:
7006:
7004:
7000:
6999:
6992:
6991:
6984:
6977:
6969:
6960:
6959:
6956:
6955:
6941:
6940:
6937:
6936:
6934:
6933:
6932:
6931:
6926:
6921:
6910:
6908:
6904:
6903:
6900:
6899:
6897:
6896:
6894:Twistor theory
6891:
6886:
6881:
6876:
6871:
6866:
6861:
6855:
6853:
6849:
6848:
6846:
6845:
6839:
6837:
6831:
6830:
6828:
6827:
6822:
6816:
6814:
6808:
6807:
6805:
6804:
6799:
6794:
6789:
6783:
6781:
6772:
6768:
6767:
6765:
6764:
6759:
6754:
6749:
6744:
6739:
6734:
6729:
6724:
6718:
6716:
6710:
6709:
6707:
6706:
6701:
6696:
6691:
6685:
6683:
6675:
6674:
6672:
6671:
6666:
6661:
6656:
6651:
6646:
6640:
6638:
6632:
6631:
6629:
6628:
6623:
6618:
6613:
6608:
6603:
6598:
6593:
6588:
6583:
6578:
6573:
6568:
6563:
6557:
6555:
6551:
6550:
6543:
6542:
6535:
6528:
6520:
6514:
6513:
6507:
6500:
6499:External links
6497:
6495:
6494:
6464:(10): 105032.
6447:
6440:
6419:
6389:hep-th/0607081
6382:(3): 179â212.
6366:
6311:
6271:
6241:hep-th/0602188
6234:(12): 124022.
6221:
6192:hep-th/0503052
6185:(12): 124039.
6172:
6151:hep-th/0212108
6131:
6101:hep-ph/0402168
6081:
6051:hep-ph/0311238
6031:
6015:
6002:10.1086/432033
5965:
5929:(2): 403â410.
5916:
5880:(2): 676â687.
5867:
5836:(2): 399â415.
5815:
5796:(2): 198â206.
5780:
5736:
5734:
5731:
5728:
5727:
5706:
5678:
5633:(20): 203901.
5614:
5583:
5538:(3): 362â367.
5532:Nature Physics
5518:
5445:
5401:Nature Physics
5386:
5331:
5302:
5281:
5243:hep-ph/0106295
5236:(16): 161602.
5218:
5188:hep-ph/0106219
5160:
5139:
5102:(3): 635â644.
5084:
5054:hep-th/0607081
5047:(3): 179â212.
5029:
4992:(5): 904â907.
4974:
4923:
4890:
4852:hep-ph/0110163
4845:(22): 221602.
4827:
4789:hep-th/9506121
4764:
4719:
4679:
4624:
4603:
4527:
4508:(5): 299â301.
4480:
4475:www.vttoth.com
4456:
4424:
4404:(2): 198â206.
4386:
4379:
4376:
4319:
4264:
4226:hep-th/9306083
4203:
4176:(3): 199â220.
4154:
4139:
4118:
4099:(2): 198â206.
4075:
4069:978-0691163727
4068:
4049:
4042:
4012:
3993:
3944:
3937:
3914:
3901:
3882:(15): 99â104.
3866:
3853:
3821:
3814:
3793:
3775:
3758:
3704:
3680:
3679:
3677:
3674:
3672:
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3661:
3656:
3646:
3641:
3636:
3630:
3628:
3625:
3590:
3587:
3570:
3567:
3553:In June 2008,
3550:
3547:
3545:
3542:
3498:
3495:
3481:
3474:
3473:
3462:
3455:
3452:
3449:
3444:
3441:
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3431:
3424:
3420:
3410:
3404:
3395:
3391:
3387:
3382:
3379:
3348:
3345:
3309:Doppler shifts
3266:
3263:
3261:
3258:
3257:
3256:
3249:
3246:Planck lengths
3229:
3158:
3155:
3145:
3136:
3117:
3116:
3105:
3100:
3095:
3088:
3084:
3080:
3075:
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3017:
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2887:
2883:
2876:
2872:
2866:
2862:
2858:
2855:
2849:
2843:
2840:
2835:
2801:speed of light
2781:
2780:
2764:
2760:
2754:
2750:
2746:
2743:
2736:
2732:
2728:
2722:
2719:
2704:
2703:
2686:
2681:
2677:
2674:
2671:
2668:
2661:
2657:
2653:
2647:
2641:
2636:
2589:
2586:
2574:
2571:
2548:Standard Model
2488:
2485:
2476:
2475:
2464:
2459:
2456:
2451:
2446:
2442:
2438:
2435:
2432:
2414:
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2399:
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2218:
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2204:
2189:
2188:
2177:
2171:
2168:
2165:
2161:
2156:
2153:
2150:
2147:
2144:
2119:
2118:
2107:
2099:
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2093:
2088:
2085:
2081:
2076:
2073:
2070:
2067:
2064:
2046:
2045:
2034:
2025:
2018:
2015:
2010:
2007:
2001:
1998:
1994:
1990:
1987:
1984:
1979:
1976:
1972:
1967:
1957:
1954:
1949:
1946:
1940:
1937:
1930:
1926:
1923:
1917:
1914:
1901:
1895:
1891:
1888:
1882:
1879:
1875:
1871:
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1865:
1860:
1857:
1853:
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1758:
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1740:
1735:
1729:
1726:
1723:
1719:
1714:
1708:
1705:
1701:
1696:
1693:
1670:, diverges as
1613:
1612:
1601:
1596:
1592:
1586:
1582:
1577:
1573:
1570:
1565:
1561:
1557:
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1199:
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1157:
1151:
1147:
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1131:
1127:
1124:
1119:
1115:
1111:
1107:
1103:
1072:
1069:
1040:
1037:
1000:
997:
980:at a non-zero
870:
869:
828:
826:
819:
813:
810:
754:
753:
751:
750:
743:
736:
728:
725:
724:
723:
722:
709:
692:
691:
688:
687:
680:
675:
670:
665:
660:
655:
650:
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640:
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570:
565:
560:
555:
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545:
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535:
530:
525:
520:
514:
510:
509:
508:
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500:
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490:
485:
480:
475:
470:
465:
460:
455:
450:
445:
440:
435:
430:
425:
420:
415:
404:
398:
397:
396:
393:
392:
387:
386:
385:
384:
379:
371:
370:
366:
365:
364:
363:
361:Post-Newtonian
358:
353:
345:
344:
340:
339:
338:
337:
332:
327:
322:
317:
312:
304:
303:
297:
293:
292:
289:
285:
284:
283:
282:
279:
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273:
272:
271:
270:
265:
260:
252:
251:
245:
244:
243:
242:
237:
232:
227:
222:
220:Frame-dragging
217:
212:
207:
202:
197:
195:Kepler problem
187:
183:
182:
181:
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177:
174:
173:
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163:
158:
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148:
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146:
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106:
105:
91:
88:
84:
79:
75:
70:
67:
63:
59:
56:
51:
48:
44:
34:
26:
25:
15:
9:
6:
4:
3:
2:
7510:
7499:
7496:
7494:
7491:
7489:
7486:
7484:
7481:
7479:
7476:
7474:
7471:
7470:
7468:
7458:
7453:
7448:
7446:
7436:
7435:
7432:
7419:
7416:
7414:
7411:
7409:
7406:
7404:
7401:
7400:
7398:
7394:
7387:
7384:
7381:
7378:
7377:
7375:
7371:
7365:(2016 series)
7364:
7363:
7359:
7357:(2011 series)
7356:
7355:
7351:
7349:(2010 series)
7348:
7347:
7343:
7341:(2010 series)
7340:
7339:
7335:
7332:
7331:
7327:
7324:
7323:
7319:
7316:
7315:
7311:
7310:
7308:
7304:
7297:
7296:
7292:
7289:
7288:
7284:
7281:
7280:
7276:
7273:
7272:
7268:
7267:
7265:
7261:
7250:
7249:
7245:
7244:
7242:
7238:
7231:
7228:
7225:
7224:
7220:
7217:
7216:
7212:
7209:
7208:
7204:
7201:
7200:
7196:
7193:
7192:
7188:
7187:
7185:
7181:
7174:
7173:
7169:
7166:
7165:
7161:
7158:
7157:
7153:
7150:
7149:
7145:
7142:
7141:
7137:
7134:
7133:
7129:
7126:
7125:
7121:
7118:
7117:
7113:
7110:
7109:
7105:
7102:
7101:
7097:
7094:
7093:
7089:
7086:
7085:
7081:
7080:
7078:
7074:
7071:
7067:
7061:
7058:
7056:
7053:
7051:
7048:
7046:
7043:
7041:
7038:
7036:
7033:
7031:
7028:
7026:
7023:
7021:
7018:
7016:
7013:
7011:
7008:
7007:
7005:
7001:
6997:
6990:
6985:
6983:
6978:
6976:
6971:
6970:
6967:
6954:
6946:
6943:
6942:
6938:
6930:
6927:
6925:
6922:
6920:
6917:
6916:
6915:
6912:
6911:
6909:
6905:
6895:
6892:
6890:
6887:
6885:
6882:
6880:
6877:
6875:
6872:
6870:
6869:Dual graviton
6867:
6865:
6862:
6860:
6857:
6856:
6854:
6850:
6844:
6841:
6840:
6838:
6836:
6832:
6826:
6823:
6821:
6818:
6817:
6815:
6813:
6809:
6803:
6800:
6798:
6795:
6793:
6790:
6788:
6785:
6784:
6782:
6780:
6779:String theory
6776:
6773:
6769:
6763:
6760:
6758:
6755:
6753:
6750:
6748:
6745:
6743:
6740:
6738:
6735:
6733:
6730:
6728:
6725:
6723:
6720:
6719:
6717:
6715:
6711:
6705:
6702:
6700:
6697:
6695:
6692:
6690:
6687:
6686:
6684:
6682:
6676:
6670:
6667:
6665:
6662:
6660:
6657:
6655:
6652:
6650:
6647:
6645:
6642:
6641:
6639:
6637:
6633:
6627:
6624:
6622:
6619:
6617:
6614:
6612:
6609:
6607:
6604:
6602:
6599:
6597:
6594:
6592:
6589:
6587:
6584:
6582:
6579:
6577:
6574:
6572:
6569:
6567:
6564:
6562:
6559:
6558:
6556:
6552:
6548:
6541:
6536:
6534:
6529:
6527:
6522:
6521:
6518:
6511:
6508:
6506:
6503:
6502:
6490:
6485:
6480:
6475:
6471:
6467:
6463:
6459:
6458:
6453:
6448:
6443:
6437:
6433:
6428:
6427:
6420:
6415:
6411:
6407:
6403:
6399:
6395:
6390:
6385:
6381:
6377:
6376:
6371:
6367:
6364:
6360:
6351:
6347:
6343:
6339:
6335:
6332:(11): 44â48.
6331:
6327:
6326:Physics Today
6320:
6316:
6312:
6307:
6303:
6299:
6295:
6291:
6287:
6283:
6279:
6278:
6272:
6267:
6263:
6259:
6255:
6251:
6247:
6242:
6237:
6233:
6229:
6228:
6222:
6218:
6214:
6210:
6206:
6202:
6198:
6193:
6188:
6184:
6180:
6179:
6173:
6169:
6165:
6161:
6157:
6152:
6147:
6144:(6): 064025.
6143:
6139:
6138:
6132:
6127:
6123:
6119:
6115:
6111:
6107:
6102:
6097:
6093:
6089:
6088:
6082:
6077:
6073:
6069:
6065:
6061:
6057:
6052:
6047:
6043:
6039:
6038:
6032:
6026:
6021:
6016:
6011:
6007:
6003:
5999:
5995:
5991:
5986:
5981:
5977:
5973:
5972:
5966:
5962:
5958:
5954:
5950:
5946:
5942:
5937:
5932:
5928:
5924:
5923:
5917:
5913:
5909:
5905:
5901:
5897:
5893:
5888:
5883:
5879:
5875:
5874:
5868:
5862:
5857:
5853:
5849:
5844:
5839:
5835:
5831:
5830:
5825:
5821:
5816:
5811:
5807:
5803:
5799:
5795:
5791:
5790:
5785:
5781:
5776:
5772:
5768:
5764:
5760:
5756:
5752:
5748:
5747:
5742:
5738:
5737:
5723:
5722:
5717:
5710:
5695:
5694:
5689:
5682:
5674:
5670:
5666:
5662:
5658:
5654:
5650:
5646:
5641:
5636:
5632:
5628:
5627:
5618:
5607:September 27,
5602:
5598:
5594:
5587:
5579:
5575:
5571:
5567:
5563:
5559:
5555:
5551:
5546:
5541:
5537:
5533:
5529:
5522:
5514:
5510:
5506:
5502:
5498:
5494:
5490:
5486:
5482:
5478:
5473:
5468:
5464:
5460:
5456:
5449:
5441:
5437:
5433:
5429:
5425:
5421:
5416:
5411:
5407:
5403:
5402:
5397:
5390:
5382:
5378:
5374:
5370:
5366:
5362:
5357:
5356:gr-qc/0110036
5352:
5348:
5344:
5343:
5335:
5319:
5318:
5313:
5306:
5298:
5297:
5292:
5285:
5277:
5273:
5269:
5265:
5261:
5257:
5253:
5249:
5244:
5239:
5235:
5231:
5230:
5222:
5214:
5210:
5206:
5202:
5198:
5194:
5189:
5184:
5181:(5): 056010.
5180:
5176:
5175:
5170:
5164:
5155:
5150:
5143:
5135:
5131:
5127:
5123:
5119:
5115:
5110:
5109:gr-qc/0603121
5105:
5101:
5097:
5096:
5088:
5080:
5076:
5072:
5068:
5064:
5060:
5055:
5050:
5046:
5042:
5041:
5033:
5025:
5021:
5017:
5013:
5009:
5005:
5000:
4999:gr-qc/9710007
4995:
4991:
4987:
4986:
4978:
4969:
4964:
4960:
4956:
4951:
4946:
4942:
4938:
4934:
4927:
4919:
4915:
4910:
4905:
4901:
4894:
4886:
4882:
4878:
4874:
4870:
4866:
4862:
4858:
4853:
4848:
4844:
4840:
4839:
4831:
4823:
4819:
4815:
4811:
4807:
4803:
4799:
4795:
4790:
4785:
4781:
4777:
4776:
4768:
4760:
4756:
4752:
4748:
4744:
4740:
4736:
4732:
4731:
4723:
4715:
4711:
4707:
4703:
4699:
4695:
4694:
4689:
4683:
4675:
4671:
4667:
4663:
4659:
4655:
4650:
4649:gr-qc/0304042
4645:
4641:
4637:
4636:
4628:
4619:
4614:
4607:
4592:
4588:
4584:
4580:
4576:
4572:
4568:
4564:
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4554:
4550:
4547:
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4538:
4531:
4523:
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4511:
4507:
4503:
4496:
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4444:
4440:
4439:
4434:
4428:
4419:
4415:
4411:
4407:
4403:
4399:
4398:
4390:
4383:
4372:
4368:
4364:
4360:
4356:
4352:
4348:
4344:
4340:
4336:
4335:
4326:
4324:
4315:
4311:
4307:
4303:
4299:
4295:
4290:
4285:
4282:(6): 064043.
4281:
4277:
4276:
4268:
4260:
4256:
4252:
4248:
4244:
4240:
4236:
4232:
4227:
4222:
4218:
4214:
4207:
4199:
4195:
4191:
4187:
4183:
4179:
4175:
4171:
4170:
4165:
4158:
4150:
4146:
4142:
4140:9780226870250
4136:
4132:
4128:
4122:
4114:
4110:
4106:
4102:
4098:
4094:
4093:
4088:
4082:
4080:
4071:
4065:
4061:
4053:
4045:
4043:0-521-29928-4
4039:
4035:
4030:
4029:
4019:
4017:
4008:
4004:
3997:
3989:
3985:
3981:
3977:
3972:
3967:
3963:
3959:
3955:
3948:
3940:
3938:0-553-38016-8
3934:
3930:
3929:
3924:
3918:
3911:
3905:
3897:
3893:
3889:
3885:
3881:
3877:
3870:
3863:
3857:
3850:
3839:
3835:
3828:
3826:
3817:
3815:9780525658221
3811:
3807:
3800:
3798:
3786:
3779:
3771:
3765:
3763:
3754:
3750:
3746:
3742:
3738:
3734:
3730:
3726:
3722:
3718:
3711:
3709:
3700:
3696:
3692:
3685:
3681:
3670:
3667:
3665:
3662:
3660:
3657:
3654:
3650:
3647:
3645:
3642:
3640:
3637:
3635:
3632:
3631:
3624:
3620:
3618:
3614:
3610:
3609:
3604:
3603:perfect fluid
3600:
3596:
3586:
3584:
3580:
3576:
3566:
3564:
3560:
3557:launched the
3556:
3541:
3539:
3535:
3530:
3528:
3524:
3520:
3516:
3512:
3508:
3504:
3503:event horizon
3494:
3480:
3460:
3453:
3450:
3447:
3442:
3439:
3436:
3429:
3422:
3418:
3408:
3402:
3393:
3389:
3385:
3380:
3377:
3370:
3369:
3368:
3366:
3361:
3344:
3342:
3336:
3333:
3328:
3324:
3322:
3317:
3312:
3310:
3306:
3302:
3297:
3295:
3291:
3288:
3284:
3283:Planck length
3280:
3276:
3272:
3254:
3250:
3247:
3243:
3239:
3235:
3230:
3227:
3223:
3222:
3221:
3218:
3216:
3208:
3203:
3201:
3196:10 years
3184:10 years
3177:
3172:10 years
3152:
3144:
3135:
3129:
3123:
3103:
3098:
3093:
3086:
3082:
3078:
3073:
3057:
3053:
3049:
3046:
3043:
3038:
3033:
3020:
3015:
2999:
2996:
2992:
2988:
2985:
2982:
2977:
2972:
2961:
2957:
2952:
2941:
2936:
2933:
2930:
2924:
2921:
2916:
2911:
2907:
2903:
2897:
2889:
2885:
2881:
2874:
2870:
2864:
2860:
2856:
2853:
2847:
2833:
2825:
2824:
2823:
2820:
2818:
2810:
2802:
2794:
2762:
2758:
2752:
2748:
2744:
2741:
2734:
2730:
2726:
2720:
2717:
2710:
2709:
2708:
2679:
2675:
2672:
2669:
2666:
2659:
2655:
2651:
2645:
2634:
2626:
2625:
2624:
2621:
2619:
2615:
2611:
2603:
2599:
2594:
2583:10 years
2567:
2553:
2549:
2545:
2532:
2528:
2520:
2516:
2511:
2509:
2504:
2503:
2499:
2494:
2484:
2482:
2462:
2457:
2454:
2449:
2444:
2440:
2436:
2433:
2430:
2423:
2422:
2421:
2419:
2400:
2392:
2388:
2384:
2381:
2370:
2367:
2358:
2355:
2352:
2349:
2346:
2334:
2333:
2332:
2315:
2312:
2303:
2300:
2297:
2294:
2289:
2285:
2274:
2271:
2259:
2258:
2257:
2232:
2226:
2223:
2220:
2216:
2211:
2202:
2194:
2193:
2192:
2175:
2169:
2166:
2163:
2159:
2154:
2142:
2135:
2134:
2133:
2130:
2105:
2097:
2094:
2091:
2086:
2083:
2079:
2074:
2062:
2055:
2054:
2053:
2032:
2023:
2016:
2013:
2008:
2005:
1999:
1996:
1992:
1988:
1985:
1982:
1977:
1974:
1970:
1965:
1955:
1952:
1947:
1944:
1938:
1935:
1928:
1924:
1921:
1915:
1912:
1899:
1893:
1889:
1886:
1880:
1877:
1873:
1869:
1866:
1863:
1858:
1855:
1851:
1846:
1839:
1836:
1829:
1822:
1821:
1820:
1816:
1814:
1811:which is the
1795:
1786:
1780:
1776:
1773:
1767:
1764:
1760:
1756:
1753:
1750:
1745:
1742:
1738:
1733:
1727:
1724:
1721:
1717:
1712:
1706:
1703:
1699:
1694:
1691:
1684:
1683:
1682:
1678:
1674:
1664:
1650:
1640:
1631:
1623:
1618:
1599:
1594:
1584:
1580:
1568:
1563:
1555:
1544:
1539:
1531:
1517:
1513:
1509:
1506:
1501:
1491:
1487:
1475:
1470:
1462:
1451:
1446:
1438:
1424:
1419:
1413:
1410:
1406:
1401:
1396:
1393:
1388:
1380:
1365:
1364:
1363:
1346:
1340:
1337:
1331:
1327:
1321:
1318:
1315:
1312:
1309:
1302:
1301:
1300:
1296:
1279:
1274:
1252:
1248:
1244:
1239:
1231:
1216:
1210:
1206:
1203:
1197:
1194:
1190:
1186:
1181:
1176:
1168:
1155:
1149:
1145:
1142:
1136:
1133:
1129:
1125:
1122:
1117:
1109:
1094:
1093:
1092:
1091:has a metric
1090:
1085:
1082:
1078:
1068:
1067:
1062:
1058:
1054:
1050:
1046:
1036:
1033:
1027:
1015:
1011:
1007:
1003:
994:
989:
987:
983:
979:
975:
970:
968:
963:
959:
955:
950:
948:
944:
940:
936:
928:
924:
919:
915:
913:
912:event horizon
908:
904:
899:
897:
893:
889:
885:
881:
877:
866:
863:
855:
845:
841:
835:
834:
829:This section
827:
823:
818:
817:
809:
807:
803:
799:
794:
791:
786:
784:
780:
776:
772:
771:event horizon
768:
764:
760:
749:
744:
742:
737:
735:
730:
729:
727:
726:
720:
710:
707:
702:
696:
695:
694:
693:
686:
685:
681:
679:
676:
674:
671:
669:
666:
664:
661:
659:
656:
654:
651:
649:
646:
644:
641:
639:
636:
634:
631:
629:
626:
624:
623:Chandrasekhar
621:
619:
616:
614:
611:
609:
606:
604:
601:
599:
596:
594:
591:
589:
586:
584:
581:
579:
576:
574:
571:
569:
566:
564:
561:
559:
556:
554:
551:
549:
546:
544:
541:
539:
538:Schwarzschild
536:
534:
531:
529:
526:
524:
521:
519:
516:
515:
507:
506:
499:
498:HartleâThorne
496:
494:
491:
489:
486:
484:
481:
479:
476:
474:
471:
469:
466:
464:
461:
459:
456:
454:
451:
449:
446:
444:
441:
439:
436:
434:
431:
429:
426:
424:
421:
419:
416:
413:
409:
408:Schwarzschild
406:
405:
401:
395:
394:
383:
380:
378:
375:
374:
373:
372:
368:
367:
362:
359:
357:
354:
352:
349:
348:
347:
346:
342:
341:
336:
333:
331:
328:
326:
323:
321:
318:
316:
313:
311:
308:
307:
306:
305:
301:
300:
290:
287:
286:
281:
280:
269:
266:
264:
261:
259:
256:
255:
254:
253:
250:
247:
246:
241:
238:
236:
233:
231:
230:Event horizon
228:
226:
223:
221:
218:
216:
213:
211:
208:
206:
203:
201:
198:
196:
193:
192:
191:
190:
180:
179:
172:
169:
167:
164:
162:
159:
157:
154:
153:
145:
144:
139:
136:
131:
128:
126:
123:
121:
118:
117:
115:
113:
110:
109:
108:
107:
89:
86:
82:
77:
73:
68:
65:
61:
54:
49:
46:
42:
32:
28:
27:
24:
21:
20:
7386:Lucy Hawking
7382:(first wife)
7360:
7352:
7344:
7336:
7328:
7320:
7312:
7294:
7286:
7278:
7270:
7246:
7229:
7221:
7213:
7205:
7197:
7189:
7170:
7162:
7154:
7146:
7138:
7130:
7122:
7114:
7106:
7098:
7090:
7082:
7009:
6944:
6907:Applications
6797:Supergravity
6704:Unruh effect
6693:
6611:Quantum foam
6606:Planck units
6601:IR/UV mixing
6576:Causal patch
6461:
6455:
6425:
6379:
6373:
6350:the original
6329:
6325:
6281:
6275:
6231:
6225:
6182:
6176:
6141:
6135:
6091:
6085:
6041:
6035:
5975:
5969:
5926:
5920:
5877:
5871:
5833:
5827:
5793:
5787:
5784:Page, Don N.
5750:
5744:
5719:
5709:
5697:. Retrieved
5691:
5681:
5630:
5624:
5617:
5605:. Retrieved
5601:the original
5596:
5586:
5535:
5531:
5521:
5462:
5458:
5448:
5405:
5399:
5389:
5346:
5340:
5334:
5322:. Retrieved
5315:
5305:
5296:CERN Courier
5294:
5284:
5233:
5227:
5221:
5178:
5172:
5163:
5142:
5099:
5093:
5087:
5044:
5038:
5032:
4989:
4983:
4977:
4940:
4936:
4926:
4899:
4893:
4842:
4836:
4830:
4779:
4773:
4767:
4734:
4728:
4722:
4697:
4691:
4682:
4639:
4633:
4627:
4606:
4594:. Retrieved
4583:10261/140585
4548:
4543:
4530:
4505:
4501:
4474:
4447:. Retrieved
4443:Ethan Siegel
4436:
4427:
4401:
4395:
4389:
4374:
4338:
4332:
4279:
4273:
4267:
4216:
4212:
4206:
4173:
4167:
4157:
4130:
4121:
4096:
4090:
4087:Page, Don N.
4059:
4052:
4027:
4006:
3996:
3961:
3957:
3947:
3927:
3917:
3904:
3879:
3875:
3869:
3861:
3856:
3848:
3841:. Retrieved
3837:
3805:
3778:
3720:
3716:
3699:the original
3694:
3684:
3669:Unruh effect
3621:
3606:
3592:
3589:Experimental
3572:
3552:
3531:
3500:
3478:
3475:
3362:
3350:
3337:
3329:
3325:
3314:An outgoing
3313:
3301:Unruh effect
3298:
3268:
3219:
3204:
3142:
3133:
3127:
3121:
3118:
2821:
2782:
2705:
2622:
2595:
2568:
2512:
2501:
2497:
2490:
2477:
2418:Planck units
2415:
2330:
2256:is added is
2247:
2190:
2128:
2120:
2047:
1817:
1813:Unruh effect
1810:
1679:
1672:
1662:
1648:
1638:
1629:
1621:
1619:in terms of
1614:
1361:
1297:
1294:
1086:
1077:Unruh effect
1074:
1065:
1042:
990:
971:
951:
938:
932:
926:
900:
896:John Wheeler
873:
858:
849:
838:Please help
833:verification
830:
797:
795:
787:
758:
757:
683:
643:Raychaudhuri
112:Introduction
7473:Black holes
6864:Causal sets
6714:Black holes
6315:Smolin, Lee
4700:: 727â745.
3843:1 September
3597:, in which
3311:the modes.
3242:Planck mass
1039:Formulation
1028:, or about
982:temperature
967:evaporating
884:black holes
658:van Stockum
588:Oppenheimer
443:KerrâNewman
235:Singularity
7467:Categories
7388:(daughter)
7306:Television
6929:Multiverse
6771:Approaches
6649:CGHS model
6636:Toy models
6571:CA-duality
6489:10023/4760
5545:1910.09363
5472:1809.00913
5415:1510.00621
5154:1802.00100
4950:2001.08833
4596:27 October
4558:1502.01589
3676:References
3615:employing
3515:Bekenstein
3354:10 kg
3332:white hole
3279:wavelength
3234:gamma rays
3188:10 kg
3168:10 kg
3151:solar mass
2564:10 kg
2539:10 kg
1022:10 kg
1006:billionths
993:solar mass
956:physicist
783:telescopes
767:black hole
511:Scientists
343:Formalisms
291:Formalisms
240:Black hole
166:World line
7445:Astronomy
7408:Namesakes
6945:See also:
6884:Spin foam
6664:RST model
6306:121117052
5843:1209.2243
5699:April 30,
5640:1009.4634
5578:230508375
5570:1745-2481
5513:119327617
5497:1476-4687
5440:119197166
5317:The Times
5276:119375071
5134:119039723
4943:(2): 21.
4591:119262962
4314:119230843
4289:0709.2380
4149:832158297
3971:1205.5251
3896:120254309
3745:1476-4687
3491:10 s
3423:∗
3394:∗
3381:∼
3378:τ
3358:10 s
3341:Minkowski
3305:spacetime
3290:frequency
3087:⊙
3050:×
3044:≈
2997:−
2989:×
2983:≈
2937:π
2922:ℏ
2882:ℏ
2857:π
2745:π
2727:ℏ
2670:π
2652:ℏ
2570:billion)
2513:In 1976,
2437:π
2385:π
2356:π
2301:π
2224:π
2167:π
2149:∞
2087:π
2069:∞
2000:−
1978:π
1939:−
1916:−
1881:−
1859:π
1768:−
1746:π
1728:ρ
1725:π
1707:π
1700:α
1615:which is
1585:⊥
1556:ρ
1532:τ
1514:ρ
1510:−
1492:⊥
1463:ρ
1407:ρ
1397:−
1328:ρ
1267:Ω
1198:−
1137:−
1126:−
1043:In 1972,
1030:133
947:spacetime
603:Robertson
568:Friedmann
563:Eddington
553:Nordström
543:de Sitter
400:Solutions
325:Geodesics
320:Friedmann
302:Equations
288:Equations
249:Spacetime
184:Phenomena
90:ν
87:μ
78:κ
69:ν
66:μ
58:Λ
50:ν
47:μ
6792:M-theory
6752:ER = EPR
6591:Graviton
6217:28276606
6126:11863375
6076:14275281
5912:17033284
5822:(1974).
5665:21231233
5505:31142857
5320:. London
5268:11690198
5024:18980849
4937:Universe
4885:14228817
4877:12059412
4822:26432764
4814:10019680
4759:10014053
4674:16668175
4380:☉
4371:27717447
4363:17817517
4251:10055062
4198:55539246
4129:(1994).
3925:(1988).
3627:See also
3294:infinite
3159:☉
2604:of mass
2590:☉
2575:☉
2550:and the
2521:of mass
2515:Don Page
2017:′
1956:′
1840:′
1079:and the
1001:☉
876:Einstein
852:May 2023
812:Overview
719:Category
583:LemaĂźtre
548:Reissner
533:Poincaré
518:Einstein
463:TaubâNUT
428:Wormhole
412:interior
125:Timeline
7457:Physics
7431:Portals
7287:Hawking
7279:Hawking
7240:Memoirs
7183:Fiction
7076:Science
7003:Physics
6466:Bibcode
6414:9966483
6394:Bibcode
6334:Bibcode
6286:Bibcode
6266:6702415
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