1049:âa realm devoid of all structure. Moreover, precisely at the singularityâthe heart of a classic black holeâspacetime itself is thought to break down catastrophically since infinite density demands infinite escape velocity; such conditions are problematic with known physics. Under the fuzzball premise, however, the strings comprising matter and photons are believed to fall onto and absorb into the fuzzball's surface, which is located at the event horizonâthe threshold at which the escape velocity has achieved the speed of light.
1350:
holds, in part, that the quantum information of the strings that fall onto a fuzzball is preserved as those strings dissolve into and contribute to the fuzzball's quantum makeup. The theory further holds that a fuzzball's quantum information is not only expressed at its surface but tunnels up through the tunneling fuzziness of the event horizon where it can be imprinted on
Hawking radiation, which very slowly carries that information into regular spacetime in the form of delicate correlations in the outgoing quanta.
25:
1544:
2365:
942:
1472:. All bosons (e.g., photons) and the boson-like sfermions will readily overlap each other when crowded, whereas fermions and the fermion-like gauginos possessing mass (such as electrons, protons, and quarks) will not; this is one reason why superpartnersâif they existâhave properties that are exceedingly different from their Standard Model counterparts. Take the example of the photon, which is a massless boson with an integer spin of 1 and is the carrier of
93:
3195:
1083:, or join. In doing so, all the quantum information of the in‑falling strings becomes part of larger, more complex strings. Due to fractional tension, string tension exponentially decreases as they become more complex with more vibration modes, relaxing to considerable lengths. The string theory formulas of Mathur and Lunin produce fuzzball surface radii that precisely equal Schwarzschild radii, which
1699:) by virtue of the nontrivial unique attributes of fuzzballs, which are extended objects with a physical structure. The team's simulations predicted slower-than-expected decay rates for certain vibration modes that would also be dominated by "echoes" from earlier ring oscillations. Moreover, a separate Italian team a year earlier posited that future gravitational-wave detectors, such as the proposed
1113:. This is an average, or mean, bulk density; as with neutron stars, the Sun, and its planets, a fuzzball's density varies from the surface where it is less dense, to its center where it is most dense. A bit of such a non-spinning fuzzball the size of a drop of water would, on average, have a mass of twenty million metric tons, which is equivalent to that of a granite ball 243 meters in diameter.
1358:âa quantum description of gravityâthat is in harmony with general relativity. However, all five variations of superstring theory, including the Type IIB variant upon which fuzzball theory is based, have quantum gravity incorporated into them. Moreover, all five versions have been hypothesized as actually constituting five different limits, or subsets, that are unified under
3205:
1379:
while they are actively being searched for, have yet to be detected. Moreover, fuzzball theory cannot be substantiated by observing its predicted subtle effects on
Hawking radiation because the radiation itself is for all practical purposes undetectable. However, fuzzball theory may be testable through
1539:
that have been employed since 1986. This difficulty in detecting supersymmetric particles is not surprising to particle physicists since the lightest ones are believed to be stable, electrically neutral, and interact weakly with the particles of the
Standard Model. Though many searches using particle
962:
published eight scientific papers between 2001 and 2012, assisted by postdoctoral researcher Oleg Lunin, who contributed to the first two papers. The papers propose that black holes are sphere-like extended objects with a definite volume and are composed of strings. This differs from the classic view
912:
that exists within the event horizon of a black hole. General relativity predicts that at the singularity, the curvature of spacetime becomes infinite, and it cannot determine the fate of matter and energy that falls into it. Physicists generally believe that the singularity is not a real phenomenon,
1349:
In a purely theoretical sense, the fuzzball theory advanced by Mathur and Lunin goes beyond
Hawking's formula relating the blackbody temperature of Hawking radiation and the mass of the black hole emitting it. Fuzzball theory satisfies the requirement that quantum information be conserved because it
1276:
from spacetime. This paradox can be viewed as a contradiction between two very different theories: general relativity, which describes the largest gravity-based phenomena in the
Universe, and quantum mechanics, which describes the smallest phenomena. Fuzzball theory purports to resolve this tension
945:
Shown over the
Hawaiian island of Oahu is a cross-section of an unremarkable 6.8-solar-mass, 40-kilometer-diameter (25 miles) classic black hole (albeit non-spinning and perfectly spherical for simplicity). It comprises a singularity, an event horizon, and a void between them, which is cut off from
1579:
just above a fuzzball's surface is subtly encoded with that information. As a practical matter, however, Hawking radiation is virtually impossible to detect because black holes emit it at astronomically low power levels and the individual photons constituting
Hawking radiation have extraordinarily
1378:
and one day be widely accepted as trueâas are
Einstein's theories of special and general relativityâtheories regarding the natural world must make predictions that are consistently affirmed through observations of nature. Superstring theory predicts the existence of highly elusive particles that,
1056:
a black hole; spacetime, photons, and all else not exquisitely close to the surface of a fuzzball are thought to be affected in precisely the same fashion as with the classical model of black holes featuring a singularity at its center. The two theories diverge only at the quantum level; that is,
1694:
of stellar-mass black holes, gravitational-wave signals have so far matched the predictions of general relativity for classical black holes with singularities at their centers. However, an
Italian team of scientists that ran computer simulations suggested in 2021 that existing gravitational-wave
1608:
Hawking showed that the energy of photons released by
Hawking radiation is inversely proportional to the mass of a black hole and, consequently, the smallest black holes emit the most energetic photons that are the least difficult to detect. However, the radiation emitted by even a minimum-size,
1296:
Yet, general relativity's implications for classic black holes are inescapable: Other than the fact that the two black holes would become increasingly massive due to the infalling matter and light, no difference in their quantum compositions would exist because if singularities have zero volume,
1284:
A black hole that fed primarily on the stellar atmosphere (protons, neutrons, and electrons) of a nearby companion star should, if it obeyed the known laws of quantum mechanics, grow to have a quantum composition different from another black hole that fed only on light (photons) from neighboring
1225:
can no longer resist the force of gravity and it will rapidly collapse until some new physical process takes over. In classical general relativity, the collapsing neutron star reaches a critical density and forms an event horizon; to the outside universe it becomes a black hole, and the collapse
1665:
black hole is emitting at most only ten photons per second.< Even if such a black hole was only 100 lightyears away, the odds of just one of its Hawking radiation photons landing anywhere on Earthâlet alone being captured by an antennaâwhile a human is watching are astronomically improbable.
1580:
little energy. This underlies why theoretically perfectly quiescent black holes (ones in a universe containing no matter or other types of electromagnetic radiation to absorb) evaporate so slowly as they lose energy (and equivalent amounts of mass) via Hawking radiation; even a modest 4.9
963:
of black holes in which there is a singularity at their centers, which are thought to be a zero-dimensional, zero-volume point in which the entire mass of a black hole is concentrated at infinite density, surrounded many kilometers away by an event horizon below which light cannot escape.
1116:
Though such densities are almost unimaginably extreme, they are, mathematically speaking, infinitely far from infinite density. Although the densities of typical stellar-mass fuzzballs are extremeâabout the same as neutron starsâtheir densities are many orders of magnitude less than the
1301:
quantum composition. Moreover, even if quantum information was not extinguished at singularities, it could not climb against infinite gravitational intensity and reach up to and beyond the event horizon where it could reveal itself in normal spacetime. This is called the
1657:
Critically though, when signals are this weak, the challenge is no longer one of classic radio astronomy technological issues like gain and signal-to-noise ratio; Hawking radiation comprises individual photon quanta, so such a weak signal means a
1670:
which is an unremarkable supermassive black hole, emits Hawking radiation at a near-nonexistent radiant power of at most 13 photons per century and does so with a wavelength so great that a receiving antenna possessing even a modest degree of
1200:, will suddenly and nonviolently (relatively speaking) collapse into a black hole or fuzzball. Such a collapse can serve as a helpful case study when examining the differences between the physical properties of neutron stars and fuzzballs.
1986:
If the collapsing body was rotating or electrically charged, the resulting black hole would settle down to a stationary state which was described, not by the Schwarzchild solution, but by a charged Kerr solution characterised by the mass
1097:
for a non-rotating black hole), fuzzballs have a variable density that decreases as the inverse square of their mass (twice the mass is twice the diameter, which is eight times the volume, resulting in one-quarter the density). A typical
1703:(LISA), which is intended to have the ability to observe high-mass binary mergers at frequencies far below the limits of current observatories, would improve the ability to confirm aspects of fuzzball theory by orders of magnitude.
928:
As no direct experimental evidence supports either string theory in general or fuzzballs in particular, both are products purely of calculations and theoretical research. However, the existence of fuzzballs may be testable through
1574:
Fuzzball theory resolves a long-standing conflict between general relativity and quantum mechanics by holding that quantum information is preserved in fuzzballs and that Hawking radiation originating within the Planck-scale
1666:
Importantly, the above values are for the smallest possible stellar-mass black holes; far more difficult yet to detect is the Hawking radiation emitted by supermassive black holes at the center of galaxies. For instance,
982:), are actually strings of energy that take on their identities and respective masses by vibrating in different modes and frequencies. The fuzzball concept is rooted in a particular variant of superstring theory called
1353:
Fuzzball theory's proposed solution to the black hole information paradox resolves a significant incompatibility between quantum mechanics and general relativity. At present, there is no widely accepted theory of
1525:, suggesting hidden interactions); particle physicists have accordingly been searching for these superpartners. Based on cosmological effects, there is strong evidence for the existence of dark matter of
1234:) decompose into what could be regarded as the final stage of degenerate matter: a ball of strings, which the fuzzball model predicts is the true quantum description of not only black holes but theorized
1154:. The fuzzball model predicts that a non-spinning supermassive black hole with the same mass as Sagittarius A* has a mean density "only" 51 times that of gold. Moreover, at 3.9 billion
1034:âor fuzzballâis 20 kilometers when the effects of spin are excluded. He also determined that the event horizon of a fuzzball would, at a very tiny scale (likely on the order of a few
921:: the quantum information of matter falling into a black hole is trapped behind the event horizon, and seems to disappear from the universe entirely when the black hole evaporates due to
1139:
are actually less dense than neutron stars possessing the minimum possible density. Due to the mass-density inverse-square rule, fuzzballs need not even have unimaginable densities.
1978:
However there is a classical phenomenon called superradiance in which waves incident in certain modes on a rotating or charged black hole are scattered with increased amplitude .
1507:
The experimental detection of superpartners would not only bolster superstring theory but would also help fill gaps in current particle physics, such as the likely composition of
1370:
As no direct experimental evidence supports either string theory or fuzzball theory, both are products purely of calculations and theoretical research. However, theories must be
1755:
946:
spacetime. The fuzzball hypothesis posits that black holes are balls of the ultimate form of degenerate matter with a physical surface located precisely at the event horizon.
1132:
Since the mean densities of fuzzballs (and the effective densities of classic black holes) decrease as the inverse square of their mass, fuzzballs greater than 7
1041:
With classical-model black holes, objects passing through the event horizon on their way to the singularity are thought to enter a realm of curved spacetime where the
2044:
1682:(LIGO) have proven to be a revolutionary advancement in astronomy and are enabling astronomers and theoretical physicists to develop ever-more detailed insights into
2223:
305:
2827:
1695:
observatories are capable of discerning fuzzball-theory-supporting evidence in the signals from merging binary black holes (and the resultant effects on
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1340:, cannot circumvent the no-hair theorem as it can reveal only a black hole's mass. For all practical purposes, Hawking radiation is undetectable (see §
1204:
2591:
2765:
1687:
1460:
supersymmetry in the opposite direction, superstring theory predicts that fermions from the Standard Model have boson-like superpartners known as
865:
2167:
896:
The fuzzball hypothesis dispenses with the singularity at the heart of a black hole by positing that the entire region within the black hole's
2268:
1015:. Mathur calculated that the physical surfaces of fuzzballs have radii equal to that of the event horizon of classic black holes; thus, the
46:
1982:
In §3, 'Angular Momentum and Charge,' which is 2œ pages starting on page 213, Hawking began the formula-rich section with the following:
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1700:
239:
1272:, which conflicts with general relativity's requirement that if black holes have singularities at their centers, quantum information
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2219:
68:
1743:
2776:
2891:
1825:
The primary paper was a 2002 publication (#3, below) titled "A proposal to resolve the black hole information paradox". The list:
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900:
is actually an extended object: a ball of strings, which are advanced as the ultimate building blocks of matter and light. Under
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2608:
2188:
2034:
1725:
1536:
244:
2354:
2194:
2035:"Where is Physics Headed (and How Soon Do We Get There)? - Two leading scientists discuss the future of their field - Comment"
1570:, M87* emits invisible Hawking radiation with a peak-emission wavelength 43 times larger than the orbital diameter of Neptune.
3034:
2715:
1251:
992: ), which holds that strings are both "open" (double-ended entities) and "closed" (looped entities) and that there are
918:
611:
2155:
1686:
such as neutron stars and black holes. Ever since the first direct detection of gravitational waves, a 2015 event known as
1169:
of the Solar System's heliosphereâand a mean density equal to that of the Earth's atmosphere at sea level (1.2 kg/m).
2802:
2677:
2623:
1859:"Statistical interpretation of Bekenstein entropy for systems with a stretched horizon", Oleg Lunin and Samir D. Mathur,
1678:
However, fuzzball theory may be testable through gravitational-wave astronomy. Gravitational wave observatories like the
1177:
Black holes (or fuzzballs) are produced in various ways, most of which are exceedingly violent mass-shedding events like
3244:
2720:
2411:
1380:
930:
636:
904:, strings are bundles of energy vibrating in complex ways in both the three familiar dimensions of space as well as in
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3024:
2989:
2979:
1972:
1286:
858:
39:
33:
1940:
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2645:
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1535:), but if it is composed of subatomic particles, those particles have proven to be notoriously elusive despite the
1079:. When matter or energy (strings) fall onto a fuzzball, more strings are not simply added to the fuzzball; strings
3165:
2667:
2581:
2329:
2261:
1654:
of a drop of water (about one-quarter the volume of a typical grain of table salt) is to all the Earth's oceans.
909:
839:
471:
431:
50:
2119:
1422:(massless particles in the Standard Model with integer spins like 0, 1, and 2), there is a supersymmetric-spin
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834:
656:
576:
391:
3090:
2182:
536:
313:
925:. This would violate a fundamental law of quantum mechanics requiring that quantum information be conserved.
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2555:
2518:
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2416:
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1960:
1672:
1140:
801:
606:
223:
155:
3208:
2781:
3229:
3049:
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2922:
2474:
2364:
2288:
1843:
1835:
1616:
black hole (or fuzzball) comprises extremely low-energy photons that are equivalent to those emitted by a
1543:
851:
561:
280:
197:
711:
2927:
2740:
2484:
2339:
2107:
1333:
983:
959:
941:
908:. Fuzzballs provide resolutions to two major open problems in black hole physics. First, they avoid the
416:
356:
323:
300:
151:
138:
2657:
1193:
neutron star (one slowly siphoning off mass from a companion star) that exceeds a critical mass limit,
1067:, below). Fuzzballs are thought by their proponents to be the true quantum description of black holes.
999:
Unlike the view of a black hole as a singularity, a small fuzzball can be thought of as an extra-dense
586:
2120:"Muon g-2 doubles down with latest measurement, explores uncharted territory in search of new physics"
2012:
1601:
supermassive black hole would require ten million-trillion-trillion times longer still to evaporate:
1306:, which states that black holes can reveal nothing about themselves to outside observers except their
1129:), which is equivalent to the mass of the universe packed into the volume of a single atomic nucleus.
3234:
3198:
2906:
2878:
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2689:
2501:
2309:
2254:
1851:
1839:
1016:
806:
275:
213:
147:
2007:
in 1954, and in 1973 was experimentally observed in hydrogen fluoride atoms by N. Skribanowitz
1143:, which are found at the center of virtually all galaxies, can have modest densities. For instance,
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3004:
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2932:
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2523:
2389:
2384:
2314:
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249:
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if there is to be a possibility of ascertaining their validity. To be in full accordance with the
1277:
because the Type IIB superstring theory it is based on is a quantum description of gravity called
1260:; there is no such paradox under the fuzzball hypothesis. The paradox was first raised in 1972 by
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2735:
2640:
2446:
2431:
2399:
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2319:
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1268:. The information paradox is born of a requirement of quantum mechanics that quantum information
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967:
890:
882:
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681:
581:
541:
421:
386:
259:
143:
2451:
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billion-billionths of one milliwatt). Such an infinitesimal transmitted power is to one watt as
1057:
classic black holes and fuzzballs differ only in their internal composition and how they affect
917:, such as superstring theory, are expected to explain its true nature. Second, they resolve the
741:
2143:
2080:
1540:
colliders have ruled out certain mass ranges for supersymmetric particles, the hunt continues.
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2999:
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2635:
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2535:
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2207:
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The first challenge insofar as the testability of fuzzball theory is it is rooted in unproven
1375:
1337:
1222:
1162:
1090:
Since the volume of fuzzballs is a function of the Schwarzschild radius (2953 meters per
1012:
922:
726:
631:
466:
376:
346:
3170:
2066:
1161:(a rather large super-massive black hole), a non-spinning fuzzball would have a radius of 77
3160:
3120:
2868:
2817:
2672:
2586:
2379:
2349:
1473:
1311:
1261:
1058:
1004:
905:
736:
671:
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521:
461:
426:
371:
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341:
218:
107:
1293:, the state of a system at one point in time should determine its state at any other time.
3180:
3130:
3105:
2901:
2745:
2652:
2618:
2530:
2004:
1847:
1830:"AdS/CFT duality and the black hole information paradox", Oleg Lunin and Samir D. Mathur,
1751:
1355:
1325:
1315:
1303:
1265:
1042:
996:
spacetime dimensions wherein five of the six extra spatial dimensions are "compactified".
955:
914:
821:
776:
721:
706:
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591:
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381:
285:
661:
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1854:. The AdS/CFT correspondence is central to resolving the black hole information paradox.
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2847:
2786:
2630:
2304:
2030:
1398:
1318:, whereby the latter two could theoretically be revealed through a phenomenon known as
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2065:"Philosophy of science for scientists", Lars-Göran Johansson, SpringerâCham, (2016),
1895:"Fuzzballs and the information paradox: a summary and conjectures", Samir D. Mathur,
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1776:"The fuzzball paradigm for black holes: FAQ", Samir D. Mathur, (January 22, 2009) (
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1000:
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651:
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comprising them. Accordingly, fuzzballs are theorized to be the terminal phase of
3150:
1555:. This image was captured using 230 GHz (1.3 mm) microwaves. At around
1504:, which is a massless boson but is not considered to be a primary force carrier.
3100:
3054:
2957:
2832:
2771:
2496:
2404:
1877:"The fuzzball proposal for black holes: an elementary review", Samir D. Mathur,
1531:
1508:
1500:) is an example of a mass-carrying fermion where its superpartner is the spin-0
1371:
1207:; this limit is not precisely known, but it is believed to lie between 2.2
1087:
calculated using an entirely different mathematical technique 87 years earlier.
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781:
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571:
526:
491:
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inversely proportional to the mass of a black hole. This radiation, now called
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3014:
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2962:
2947:
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2441:
2277:
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1329:
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1235:
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691:
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318:
1926:"A proposal to resolve the black hole information paradox", Samir D. Mathur,
1868:"A proposal to resolve the black hole information paradox", Samir D. Mathur,
1591:
times the current age of the Universe to vanish. Moreover, a top-of-the-list
3175:
2822:
2725:
2513:
2508:
1813:
1186:
1178:
1147:, the black hole at the center of our Milky Way galaxy, is 4.3 million
666:
456:
396:
182:
177:
172:
1927:
1878:
1869:
1860:
1831:
1289:. This follows a core precept of both classical and quantum physics that,
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All variations of string theory hold that the fundamental constituents of
3085:
3044:
2942:
1628:. More challenging still, such a black hole has a radiated powerâfor the
1501:
1461:
1359:
1226:
proceeds towards a gravitational singularity. In the fuzzball model, the
1182:
192:
187:
1904:"The information paradox: A pedagogical introduction", Samir D. Mathur,
3125:
2241:
2237:
2233:
2229:
1477:
1476:
in the Standard Model; it is predicted to have a superpartner called a
1427:
1423:
122:
2230:"The black hole information problem and the fuzzball proposal", Part 1
2228:
Video lecture series at CERN (four parts approximately an hour each):
1914:
1905:
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1887:
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3135:
3115:
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2426:
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1227:
1008:
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2168:"Phenomenological Imprints of the String-Theory 'Fuzzball' Scenario"
2013:
Black hole 'superradiance' phenomenon may aid quest for dark matter"
2011:. However, superradiance is yet to be detected at black holes, per "
1814:"A Way to Experimentally Test String Theory's 'Fuzzball' Prediction"
2144:"ATLAS releases comprehensive review of supersymmetric dark matter"
1838:, which examines the relationships between two different theories:
1480:, which is a mass-carrying fermion with a half-odd-integer spin of
2201:
2158:, Jonathan O'Callaghan, Scientific American, (September 12, 2019)
1465:
1419:
1231:
979:
117:
2215:
1679:
1307:
1256:
Classical black holes create a problem for physics known as the
2250:
1328:
showed that quantum effects will make black holes appear to be
1038:), be very much like a mist: fuzzy, hence the name "fuzzball."
2246:
2195:
Information paradox solved? If so, Black Holes are "Fuzzballs"
1941:
Information Paradox Solved? If So, Black Holes Are "Fuzzballs"
1230:
in its core (neutrons and perhaps a smattering of protons and
18:
1886:"What Exactly is the Information Paradox?", Samir D. Mathur,
2208:
Astronomers take virtual plunge into black hole (84 MB)
1075:
Fuzzballs become less dense as their mass increases due to
2122:, Fermi National Accelerator Laboratory, (August 10, 2023)
1547:
This is a false-color view of the supermassive black hole
1744:"Black Hole Singularities Are as Inescapable as Expected"
1468:
from the Standard Model, sfermions don't strongly act as
1203:
Neutron stars have a maximum possible mass, known as the
885:, intended to provide a fully quantum description of the
2083:, Dr. Alastair Gunn, BBC Science Focus, (April 16, 2022)
1515:(it should be precisely equal to 2 and is instead about
1792:"Why String Theory?", Joseph Conlon, CRC Press, (2016)
1397:
predicts that for each known quanta (particle) in the
2170:, University of RomeâLa Sapienza, (November 24, 2020)
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Laser Interferometer Gravitational-Wave Observatory
2146:, CERN/Updates/Physics-Briefing, (August 22, 2023)
1971:In his paper, "Particle Creation by Black Holes" (
1834:, (September 20, 2001). This is a paper about the
1620:with a temperature of around 23 billionths of one
2156:"The Gravitational-Wave âRevolutionâ Is Underway"
1975:), Hawking wrote, in §2 on page 204, as follows:
1943:", The Ohio State University, (February 29, 2004)
1450:) and possesses a rest mass. Examining this spin-
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2089:
1984:
1976:
1342:
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1809:
1807:
1805:
1061:that form close to their event horizons (see
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8:
2003:Superradiance was proposed theoretically by
2202:Unwinding of strings thrown into a fuzzball
2110:, CERN/News/News/Physics, (October 9, 2023)
1913:"Black Holes and Beyond", Samir D. Mathur,
1726:"The Fuzzball Fix for a Black Hole Paradox"
1721:
1719:
1717:
1715:
2828:Magnetospheric eternally collapsing object
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2255:
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852:
91:
80:
2189:The Fuzzball Fix for a Black Hole Paradox
2108:"In search of supersymmetric dark matter"
69:Learn how and when to remove this message
1955:
1953:
1951:
1949:
1788:
1786:
1542:
1430:that has a half-odd-integer spin (e.g.,
1063:
940:
32:This article includes a list of general
2076:
2074:
1711:
1675:would be larger than the Solar System.
1221:. If a neutron star exceeds this mass,
1003:in which the neutrons have undergone a
231:
205:
164:
130:
99:
83:
1105:fuzzball would have a mean density of
2214:), a 40-second animation produced by
2047:from the original on January 25, 2023
1846:(CFT), wherein the former deals with
7:
3204:
2204:â Stefano Giusto and Samir D. Mathur
2132:"The Hunt for Dark Matter Particles"
1816:, APS Journals, (September 16, 2021)
1537:wide variety of detection techniques
309:= 4 supersymmetric YangâMills theory
1532:Dark matter: Observational evidence
1758:from the original on 14 April 2020
1701:Laser Interferometer Space Antenna
240:Geometric Langlands correspondence
38:it lacks sufficient corresponding
16:Quantum description of black holes
14:
2220:University of Colorado at Boulder
2191:, June 23, 2015 â Quanta Magazine
1490:. Conversely, the electron (spin
3203:
3194:
3193:
2492:TolmanâOppenheimerâVolkoff limit
2363:
1742:Nadis, Steve (2 December 2019).
1513:muon's anomalous magnetic moment
1405:particle exists that differs by
1205:TolmanâOppenheimerâVolkoff limit
23:
2609:Innermost stable circular orbit
1690:, which was a merger between a
1605:times the age of the Universe.
1007:and decomposed, liberating the
3035:Timeline of black hole physics
1258:black hole information paradox
1252:Black hole information paradox
919:black hole information paradox
1:
2803:Nonsingular black hole models
2067:doi:10.1007/978-3-319-26551-3
1392:supersymmetric string theory.
1032:stellar-mass-class black hole
951:String theory and composition
2081:"What is Hawking radiation?"
1961:Hawking radiation calculator
1551:at the center of the galaxy
1464:, except that unlike actual
1418:. This means that for every
1381:gravitational-wave astronomy
1165:âabout the same size as the
931:gravitational-wave astronomy
881:are hypothetical objects in
3025:Rossi X-ray Timing Explorer
2990:Hypercompact stellar system
2980:Gamma-ray burst progenitors
2197:â The Ohio State University
1287:cosmic microwave background
1223:neutron degeneracy pressure
3261:
2711:Black hole complementarity
2678:Bousso's holographic bound
2663:Quasi-periodic oscillation
2361:
2355:MalamentâHogarth spacetime
2183:Are Black Holes Fuzzballs?
1850:and the latter deals with
1426:-like particle known as a
1249:
1064:§ Information paradox
3189:
2582:Gravitational singularity
2284:
2218:â a joint venture of the
1587:black hole would require
1366:Testability of the theory
1343:Testability of the theory
1264:and later popularized by
1019:of a ubiquitous 6.8
913:and proposed theories of
910:gravitational singularity
3166:PSO J030947.49+271757.31
3091:SDSS J150243.09+111557.3
2624:BlandfordâZnajek process
1141:Supermassive black holes
165:Non-perturbative results
2422:Active galactic nucleus
1991:, the angular momentum
1372:experimentally testable
53:more precise citations.
3050:Tidal disruption event
3020:Supermassive dark star
2938:Black holes in fiction
2923:Outline of black holes
2556:Supermassive dark star
2475:Gravitational collapse
2098:, CERN/Science/Physics
2001:
1980:
1844:Conformal field theory
1836:AdS/CFT correspondence
1728:, Jennifer Ouellette,
1571:
1334:effective temperatures
947:
281:Conformal field theory
198:AdS/CFT correspondence
2928:Black Hole Initiative
2741:Holographic principle
2019:, (August 16, 2022).
1863:, (February 12, 2002)
1673:absorption efficiency
1546:
1390:, which is short for
1173:Neutron star collapse
960:Ohio State University
944:
324:Holographic principle
301:Twistor string theory
2731:Final parsec problem
2690:Schwarzschild radius
2185:â Space Today Online
2033:(January 24, 2023).
1928:ArXiv:hep-th/0205192
1908:, (January 25, 2011)
1899:, (October 24, 2008)
1881:, (February 3, 2005)
1879:ArXiv:hep-th/0502050
1870:ArXiv:hep-th/0205192
1861:ArXiv:hep-th/0202072
1852:quantum field theory
1840:Anti-de Sitter space
1832:arXiv:hep-th/0109154
1274:must be extinguished
1017:Schwarzschild radius
276:Theory of everything
3245:Stellar black holes
3030:Superluminal motion
3005:Population III star
2975:Gravitational waves
2933:Black hole starship
2716:Information paradox
1330:blackbody radiators
1246:Information paradox
968:subatomic particles
937:Physical properties
314:KaluzaâKlein theory
250:Monstrous moonshine
131:Perturbative theory
100:Fundamental objects
3240:Hypothetical stars
2864:Optical black hole
2777:ReissnerâNordström
2736:Firewall (physics)
2641:Gravitational lens
2212:10 MB version
2040:The New York Times
1890:, (March 13, 2008)
1748:quantamagazine.org
1572:
1388:superstring theory
1163:astronomical units
1085:Karl Schwarzschild
1077:fractional tension
948:
891:general relativity
883:superstring theory
3217:
3216:
3010:Supermassive star
3000:Naked singularity
2995:Membrane paradigm
2721:Cosmic censorship
2695:Spaghettification
2683:Immirzi parameter
2636:Hawking radiation
2577:Astrophysical jet
2546:Supermassive star
2536:Binary black hole
2470:Stellar evolution
2412:Intermediate-mass
1995:, and the charge
1732:, (June 23, 2015)
1376:scientific method
1338:Hawking radiation
1270:must be conserved
1167:termination shock
1059:virtual particles
1013:degenerate matter
994:9 + 1
923:Hawking radiation
876:
875:
607:van Nieuwenhuizen
79:
78:
71:
3252:
3207:
3206:
3197:
3196:
2869:Sonic black hole
2818:Dark-energy star
2673:Bekenstein bound
2658:Mâsigma relation
2587:Ring singularity
2367:
2271:
2264:
2257:
2248:
2200:ArXiv.org link:
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1930:, (May 19, 2002)
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1917:, (May 14, 2012)
1872:, (May 19, 2002)
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1474:electromagnetism
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1417:
1416:
1412:
1312:angular momentum
1262:Jacob Bekenstein
1128:
1126:
1112:
1110:
1005:phase transition
995:
970:, including the
906:extra dimensions
868:
861:
854:
270:Related concepts
95:
81:
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67:
63:
60:
54:
49:this article by
40:inline citations
27:
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3161:ULAS J1342+0928
3121:SDSS J0849+1114
3106:Phoenix Cluster
3059:
2911:
2873:
2852:
2791:
2750:
2746:No-hair theorem
2699:
2653:Bondi accretion
2619:Penrose process
2565:
2531:Gamma-ray burst
2458:
2368:
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2345:Direct collapse
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2096:"Supersymmetry"
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2031:Overbye, Dennis
2029:
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2015:, Paul Sutter,
2005:Robert H. Dicke
2000:
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1915:ArXiv:1205.0776
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1888:ArXiv:0803.2030
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1848:quantum gravity
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1752:Quanta Magazine
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1326:Stephen Hawking
1316:electric charge
1304:no-hair theorem
1266:Stephen Hawking
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956:Samir D. Mathur
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915:quantum gravity
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286:Quantum gravity
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245:Mirror symmetry
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2668:Thermodynamics
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1470:force carriers
1399:Standard Model
1367:
1364:
1285:stars and the
1250:Main article:
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1189:. However, an
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1047:speed of light
1036:Planck lengths
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989:String duality
972:force carriers
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2310:Schwarzschild
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2134:, Caltech.edu
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1626:absolute zero
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1475:
1471:
1467:
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1400:
1396:
1395:Supersymmetry
1393:
1389:
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1377:
1373:
1365:
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1361:
1357:
1351:
1347:
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1321:
1320:superradiance
1317:
1313:
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1300:
1294:
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1280:
1275:
1271:
1267:
1263:
1259:
1253:
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1233:
1229:
1224:
1214:and 2.9
1206:
1201:
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1188:
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1172:
1170:
1168:
1164:
1146:
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1120:
1114:
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1033:
1022:
1018:
1014:
1010:
1006:
1002:
997:
991:
990:
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984:Type IIB
981:
977:
973:
969:
964:
961:
957:
950:
943:
936:
934:
932:
926:
924:
920:
916:
911:
907:
903:
902:string theory
899:
898:event horizon
894:
892:
889:predicted by
888:
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807:Zamolodchikov
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802:Zamolodchikov
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291:Supersymmetry
289:
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214:Phenomenology
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206:Phenomenology
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113:Cosmic string
111:
109:
106:
105:
104:
103:
98:
94:
90:
89:
86:
85:String theory
82:
73:
70:
62:
59:December 2023
52:
48:
42:
41:
35:
30:
21:
20:
3111:PKS 1302-102
2985:Gravity well
2953:Compact star
2907:Microquasars
2892:Most massive
2842:
2796:Alternatives
2561:X-ray binary
2480:Neutron star
2417:Supermassive
2394:Hawking star
2335:Supermassive
2163:
2151:
2139:
2127:
2115:
2103:
2061:
2049:. Retrieved
2038:
2025:
2016:
2008:
2002:
1996:
1992:
1988:
1981:
1967:
1959:Vttoth.com:
1935:
1922:
1910:
1901:
1892:
1883:
1874:
1865:
1856:
1827:
1821:
1772:
1760:. Retrieved
1747:
1737:
1729:
1677:
1656:
1638:10 watt
1629:
1607:
1593:106 billion
1577:quantum foam
1573:
1530:
1526:
1506:
1466:gauge bosons
1403:superpartner
1391:
1387:
1385:
1369:
1352:
1348:
1341:
1324:
1298:
1297:black holes
1295:
1291:in principle
1290:
1283:
1279:supergravity
1273:
1269:
1257:
1255:
1240:quark matter
1238:composed of
1202:
1194:
1176:
1131:
1127:10 kg/m
1115:
1111:10 kg/m
1089:
1080:
1076:
1074:
1062:
1053:
1051:
1045:exceeds the
1040:
1001:neutron star
998:
987:
965:
954:
927:
895:
878:
877:
347:Arkani-Hamed
306:
296:Supergravity
65:
56:
37:
3235:Black holes
3101:Centaurus A
3055:Planet Nine
2958:Exotic star
2887:Black holes
2833:Planck star
2782:KerrâNewman
2497:White dwarf
2447:Radio-Quiet
2405:Microquasar
2278:Black holes
2051:January 28,
1842:(AdS), and
1778:395 KB
1692:binary pair
1642:12 billion-
1509:dark matter
1236:quark stars
1052:A fuzzball
887:black holes
707:Silverstein
232:Mathematics
144:Superstring
51:introducing
3224:Categories
3151:Q0906+6930
3141:Hercules A
3071:Cygnus X-1
3040:White hole
3015:Quasi-star
2968:Preon star
2963:Quark star
2948:Big Bounce
2808:Black star
2766:Derivation
2614:Ergosphere
2570:Properties
2551:Quasi-star
2541:Quark star
2452:Radio-Loud
2340:Primordial
2330:Kugelblitz
1707:References
1618:black body
1553:Messier 87
1529:sort (see
1346:, below).
1187:hypernovas
1179:supernovas
1021:solar mass
986:(see also
727:Strominger
722:Steinhardt
717:Staudacher
632:Polchinski
582:Nanopoulos
542:Mandelstam
522:Kontsevich
362:Berenstein
319:Multiverse
34:references
3176:AT2018hyz
2823:Gravastar
2813:Dark star
2646:Microlens
2519:Hypernova
2514:Micronova
2509:Supernova
2463:Formation
2017:Space.com
1697:ringdowns
1658:2.7
1609:2.7
1502:selectron
1462:sfermions
1191:accreting
1183:kilonovas
1098:6.8
1071:Densities
879:Fuzzballs
767:Veneziano
642:Rajaraman
537:Maldacena
427:Gopakumar
377:Dijkgraaf
372:Curtright
336:Theorists
224:Landscape
219:Cosmology
183:U-duality
178:T-duality
173:S-duality
156:Heterotic
3199:Category
3086:A0620-00
3045:Wormhole
2943:Big Bang
2843:Fuzzball
2726:ER = EPR
2592:Theorems
2390:Electron
2385:Extremal
2315:Rotating
2222:and the
2045:Archived
1762:22 April
1756:Archived
1688:GW150914
1663:☉
1614:☉
1598:☉
1585:☉
1568:☉
1511:and the
1360:M-theory
1219:☉
1212:☉
1159:☉
1152:☉
1137:☉
1103:☉
1095:☉
1028:☉
840:Glossary
822:Zwiebach
777:Verlinde
772:Verlinde
747:Townsend
742:'t Hooft
737:Susskind
672:Sagnotti
637:Polyakov
592:Nekrasov
557:Minwalla
552:Martinec
517:Knizhnik
512:Klebanov
507:Kapustin
477:Horowitz
407:Fischler
342:AganagiÄ
260:K-theory
193:F-theory
188:M-theory
3209:Commons
3171:P172+18
3126:TON 618
3064:Notable
2916:Related
2902:Quasars
2897:Nearest
2857:Analogs
2787:Hayward
2755:Metrics
2400:Stellar
2325:Virtual
2320:Charged
2289:Outline
1495:⁄
1485:⁄
1478:photino
1455:⁄
1445:⁄
1435:⁄
1428:gaugino
1424:fermion
1413:⁄
1299:have no
1228:hadrons
976:photons
974:(e.g.,
835:History
752:Trivedi
732:Sundrum
697:Shenker
687:Seiberg
682:Schwarz
652:Randall
612:Novikov
602:Nielsen
587:NÄstase
497:Kallosh
482:Gibbons
422:Gliozzi
412:Friedan
402:Ferrara
387:Douglas
382:Distler
152:Type II
139:Bosonic
123:D-brane
47:improve
3146:3C 273
3136:NeVe 1
3116:OJ 287
2838:Q star
2704:Issues
2437:Blazar
2427:Quasar
2242:Part 4
2238:Part 3
2234:Part 2
1796:
1630:entire
1624:above
1622:kelvin
1563:
1314:, and
1232:mesons
1185:, and
1009:quarks
980:gluons
817:Zumino
812:Zaslow
797:Yoneya
787:Witten
702:Siegel
677:Scherk
647:Ramond
622:Ooguri
547:Marolf
502:Kaluza
487:Kachru
472:HoĆava
467:Harvey
462:Hanson
447:Gubser
437:Greene
367:Bousso
352:Atiyah
148:Type I
108:String
36:, but
2879:Lists
2380:Micro
2350:Rogue
2298:Types
2009:et al
1517:2.002
1420:boson
1332:with
1123:5.155
757:Turok
662:RoÄek
627:Ovrut
617:Olive
597:Neveu
577:Myers
572:Mukhi
562:Moore
532:Linde
527:Klein
452:Gukov
442:Gross
432:Green
417:Gates
397:Dvali
357:Banks
118:Brane
2848:Geon
2772:Kerr
2373:Size
2224:NIST
2216:JILA
2053:2023
1794:ISBN
1764:2020
1668:M87*
1648:3000
1549:M87*
1527:some
1440:and
1407:spin
1401:, a
1308:mass
1081:fuse
978:and
782:Wess
762:Vafa
667:Rohm
567:Motl
492:Kaku
457:Guth
392:Duff
2442:OVV
2432:LQG
1973:PDF
1634:1.2
1557:6.5
1519:331
1198:max
1107:4.0
958:of
792:Yau
712:SÆĄn
692:Sen
3226::
2240:,
2236:,
2232:,
2088:^
2073:^
2043:.
2037:.
1948:^
1911:8)
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1785:^
1754:.
1750:.
1746:.
1714:^
1651:th
1603:10
1589:10
1561:10
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1054:is
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1997:Q
1993:J
1989:M
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