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Journal articles on the topic 'Black holes (Astronomy) – Mathematics'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Unruh, W. G. "Dumb holes: analogues for black holes." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 366, no. 1877 (June 5, 2008): 2905–13. http://dx.doi.org/10.1098/rsta.2008.0062.

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The use of sonic analogues to black and white holes, called dumb or deaf holes, to understand the particle production by black holes is reviewed. The results suggest that the black hole particle production is a low-frequency and low-wavenumber process.

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2

Vaughan, Simon. "Random time series in astronomy." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 371, no. 1984 (February 13, 2013): 20110549. http://dx.doi.org/10.1098/rsta.2011.0549.

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Progress in astronomy comes from interpreting the signals encoded in the light received from distant objects: the distribution of light over the sky (images), over photon wavelength (spectrum), over polarization angle and over time (usually called light curves by astronomers). In the time domain, we see transient events such as supernovae, gamma-ray bursts and other powerful explosions; we see periodic phenomena such as the orbits of planets around nearby stars, radio pulsars and pulsations of stars in nearby galaxies; and we see persistent aperiodic variations (‘noise’) from powerful systems such as accreting black holes. I review just a few of the recent and future challenges in the burgeoning area of time domain astrophysics, with particular attention to persistently variable sources, the recovery of reliable noise power spectra from sparsely sampled time series, higher order properties of accreting black holes, and time delays and correlations in multi-variate time series.

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3

Du, Yun-Zhi, Hui-Hua Zhao, and Li-Chun Zhang. "Phase Transition of the Horava-Lifshitz AdS Black Holes." International Journal of Theoretical Physics 60, no. 5 (April 28, 2021): 1963–71. http://dx.doi.org/10.1007/s10773-021-04814-z.

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AbstractSome ones have showed the first-order phase transition of the Horava-Lifshitz (HL) AdS black holes has unique characters from other AdS black holes. While the coexistence zone of the first-order phase transition was not exhibited. As well known the coexistence curve of a black hole carries a lot of information about black hole, which provides a powerful diagnostic of the thermodynamic properties on black hole. We study the first-order phase transition coexistence curves of the HL AdS black holes by the Maxwell’s equal-area law, and give the boundary of two-phase coexistence zone. It is very interesting that the first-order phase transition point is determined by the pressure F on the surface of the HL AdS black hole’s horizon, instead of only the pressure P (or the temperature T). This unique property distinguishes the HL AdS black hole from the other AdS black hole systems. Furthermore, this black hole system have the critical curves, and on which every point stands for a critical point.

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4

Chandrasekhar, S., and Kip S. Thorne. "The Mathematical Theory of Black Holes." American Journal of Physics 53, no. 10 (October 1985): 1013–15. http://dx.doi.org/10.1119/1.13992.

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5

Jamil, Mubasher. "Black Holes in Accelerated Universe." International Journal of Theoretical Physics 49, no. 8 (May 14, 2010): 1706–11. http://dx.doi.org/10.1007/s10773-010-0350-1.

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6

Rosen, Gerald. "Black holes associated with galaxies." International Journal of Theoretical Physics 30, no. 11 (November 1991): 1517–20. http://dx.doi.org/10.1007/bf00675615.

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7

Booth, Ivan. "Black-hole boundaries." Canadian Journal of Physics 83, no. 11 (November 1, 2005): 1073–99. http://dx.doi.org/10.1139/p05-063.

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Classical black holes and event horizons are highly nonlocal objects, defined in relation to the causal past of future null infinity. Alternative, quasilocal characterizations of black holes are often used in mathematical, quantum, and numerical relativity. These include apparent, Killing, trapping, isolated, dynamical, and slowly evolving horizons. All of these are closely associated with two-surfaces of zero outward null expansion. This paper reviews the traditional definition of black holes and provides an overview of some of the more recent work on alternative horizons.PACS Nos.: 04.20.Cv, 04.70.s, 04.70.Bw

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AHN, EUN-JOO, and MARCO CAVAGLIÀ. "COSMIC BLACK HOLES." International Journal of Modern Physics D 12, no. 09 (October 2003): 1699–704. http://dx.doi.org/10.1142/s0218271803004006.

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Production of high-energy gravitational objects is a common feature of gravitational theories. The primordial universe is a natural setting for the creation of black holes and other nonperturbative gravitational entities. Cosmic black holes can be used to probe physical properties of the very early universe which would usually require the knowledge of the theory of quantum gravity. They may be the only tool to explore thermalization of the early universe. Whereas the creation of cosmic black holes was active in the past, it seems to be negligible at the present epoch.

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9

Lavenda, B. H., and J. Dunning-Davies. "Stefan-Boltzmann law for black bodies and black holes." International Journal of Theoretical Physics 29, no. 5 (May 1990): 501–14. http://dx.doi.org/10.1007/bf00673939.

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10

Vafa, Cumrun. "Black holes and Calabi–Yau threefolds." Advances in Theoretical and Mathematical Physics 2, no. 1 (1998): 207–18. http://dx.doi.org/10.4310/atmp.1998.v2.n1.a8.

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11

Pourdarvish, A., and B. Pourhassan. "Statistics of Myerse-Perry Black Holes." International Journal of Theoretical Physics 53, no. 1 (September 11, 2013): 136–45. http://dx.doi.org/10.1007/s10773-013-1791-0.

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12

De Paolis, Francesco, Mubasher Jamil, and Asghar Qadir. "Black Holes in Bulk Viscous Cosmology." International Journal of Theoretical Physics 49, no. 3 (December 31, 2009): 621–32. http://dx.doi.org/10.1007/s10773-009-0242-4.

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13

MARRANGHELLO, G. F. "DETECTING QUASI-NORMAL MODES FROM NEUTRON STARS AND BLACK HOLES." International Journal of Modern Physics D 16, no. 02n03 (February 2007): 319–23. http://dx.doi.org/10.1142/s0218271807010079.

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The properties of relativistic perturbations of neutron stars and black holes are discussed. They are of great relevance in the study of gravitational wave astronomy. In this work, we review the properties of quasi-normal modes of neutron stars and Schwarzschild black holes and the main features of their detection by actual gravitational wave interferometers.

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14

MAROLF, DONALD. "THE DANGERS OF EXTREMES." International Journal of Modern Physics D 19, no. 14 (December 2010): 2417–22. http://dx.doi.org/10.1142/s0218271810018542.

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While extreme black hole space–times with smooth horizons are known at the level of mathematics, we argue that the horizons of physical extreme black holes are effectively singular. Test particles encounter a singularity the moment they cross the horizon, and only objects with significant back-reaction can fall across a smooth (now non-extreme) horizon. As a result, classical interior solutions for extreme black holes are theoretical fictions that need not be reproduced by any quantum mechanical model. This observation suggests that significant quantum effects might be visible outside extreme or nearly extreme black holes. It also suggests that the microphysics of such black holes may be very different from that of their Schwarzschild cousins.

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15

Leonhardt, Ulf, and Thomas G. Philbin. "The case for artificial black holes." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 366, no. 1877 (June 5, 2008): 2851–57. http://dx.doi.org/10.1098/rsta.2008.0072.

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The event horizon is predicted to generate particles from the quantum vacuum, an effect that bridges three areas of physics—general relativity, quantum mechanics and thermodynamics. The quantum radiation of real black holes is too feeble to be detectable, but black-hole analogues may probe several aspects of quantum black holes. In this paper, we explain in simple terms some of the motivations behind the study of artificial black holes.

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16

ODA, ICHIRO. "STRINGS FROM BLACK HOLES." International Journal of Modern Physics D 01, no. 02 (January 1992): 355–61. http://dx.doi.org/10.1142/s0218271892000173.

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It is shown that surface fluctuation of the event horizon of black holes in four dimensions which have been previously studied by ’t Hooft can be understood in terms of the topological two-dimensional string. This interpretation is valid at the lowest order, with respect to the magnitude of the radial momentum per magnitude of the transverse momentum, when particles near the event horizon fall into the black hole and from which particles then emit to future null infinity, owing to the Hawking radiation. This implies that in such a kinematical regime only the zero mode, that is, the center-of-mass momentum of the Euclidean string, propagates on the surface of the event horizon.

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LEONHARDT, ULF, and THOMAS G. PHILBIN. "ON ARTIFICIAL BLACK HOLES." International Journal of Modern Physics D 16, no. 12b (December 2007): 2541–50. http://dx.doi.org/10.1142/s0218271807011516.

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We explain some of the main motivations for creating laboratory analogs of horizons (artificial black holes). We present a concise derivation of the Hawking effect, the quantum radiation of black holes, using a simple analog model.

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NIELSEN, ALEX B. "BLACK HOLES WITHOUT BOUNDARIES." International Journal of Modern Physics D 17, no. 13n14 (December 2008): 2359–66. http://dx.doi.org/10.1142/s0218271808014205.

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We discuss some of the drawbacks of using event horizons to define black holes and suggest ways in which black holes can be described without event horizons, using trapping horizons. We show that these trapping horizons give rise to thermodynamic behavior and possibly Hawking radiation too. This raises the issue of whether the event horizon or the trapping horizon should be seen as the true boundary of a black hole. This difference is important if we believe that quantum gravity will resolve the central singularity of the black hole and clarifies several of the issues associated with black hole thermodynamics and information loss.

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19

Hervik, Sigbjørn. "Ricci nilsoliton black holes." Journal of Geometry and Physics 58, no. 9 (September 2008): 1253–64. http://dx.doi.org/10.1016/j.geomphys.2008.05.001.

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20

NIETO, J. A., E. A. LEÓN, and V. M. VILLANUEVA. "HIGHER-DIMENSIONAL CHARGED BLACK HOLES AS CONSTRAINED SYSTEMS." International Journal of Modern Physics D 22, no. 07 (June 2013): 1350047. http://dx.doi.org/10.1142/s0218271813500478.

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We construct a Lagrangian and Hamiltonian formulation for charged black holes in a d-dimensional maximally symmetric spherical space. By considering first new variables that give raise to an interesting dimensional reduction of the problem, we show that the introduction of a charge term is compatible with classical solutions to Einstein equations. In fact, we derive the well-known solutions for charged black holes, specially in the case of d = 4, where the Reissner–Nordström solution holds, without reference to Einstein field equations. We argue that our procedure may be of help for clarifying symmetries, dynamics and some quantum aspects of black holes.

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21

Kallosh, Renata. "M-theory, black holes and cosmology." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 477, no. 2245 (January 2021): 20200786. http://dx.doi.org/10.1098/rspa.2020.0786.

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This paper is dedicated to Michael J. Duff on the occasion of his 70th birthday. I discuss some issues of M-theory/string theory/supergravity closely related to Mike’s interests. I describe a relation between STU black hole entropy, the Cayley hyperdeterminant, the Bhargava cube and a three-qubit Alice–Bob–Charlie triality symmetry. I shortly describe my recent work with Gunaydin, Linde and Yamada on M-theory cosmology (Gunaydin et al. 2020 M-theory cosmology, octonions, error-correcting codes ( http://arxiv.org/abs/2008.01494 )), inspired by the work of Duff with Ferrara and Borsten, Levay, Marrani et al. Here, we have seven-qubits, a party including Alice, Bob, Charlie, Daisy, Emma, Fred and George. Octonions and Hamming error-correcting codes are at the base of these models. They lead to seven benchmark targets of future cosmic microwave background missions looking for primordial gravitational waves from inflation. I also show puzzling relations between the fermion mass eigenvalues in these cosmological models, the exceptional Jordan eigenvalue problem and black hole entropy. The symmetry of our cosmological models is illustrated by beautiful pictures of a Coxeter projection of the root system of E7.

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22

Giddings, Steven B. "Black holes in the quantum universe." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 377, no. 2161 (November 11, 2019): 20190029. http://dx.doi.org/10.1098/rsta.2019.0029.

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A succinct summary is given of the problem of reconciling observation of black hole-like objects with quantum mechanics. If quantum black holes behave like subsystems, and also decay, their information must be transferred to their environments. Interactions that accomplish this with ‘minimal’ departure from a standard description are parametrized. Possible sensitivity of gravitational wave or very long baseline interferometric observations to these interactions is briefly outlined. This article is part of a discussion meeting issue ‘Topological avatars of new physics’.

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23

Tremaine, Scott. "The legacy and large–scale distribution of active galaxies." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 363, no. 1828 (January 12, 2005): 613–19. http://dx.doi.org/10.1098/rsta.2004.1523.

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If accretion onto massive black holes is the power source for active galaxies, then nearby galaxies should contain ‘dead quasars’: black holes that do not shine, either because they are starved for fuel or because they accrete with low radiative efficiency. This article briefly reviews the evidence that most inactive galaxies contain black holes at their centres, and how the local distribution of black holes is related to the population of active galaxies.

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24

Krasnov, Kirill, and Sergey N. Solodukhin. "Effective Stringy Description of Schwarzschild Black Holes." Advances in Theoretical and Mathematical Physics 8, no. 3 (2004): 421–60. http://dx.doi.org/10.4310/atmp.2004.v8.n3.a2.

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25

Harmark, Troels, José Natário, and Ricardo Schiappa. "Greybody Factors for d-Dimensional Black Holes." Advances in Theoretical and Mathematical Physics 14, no. 3 (2010): 727–94. http://dx.doi.org/10.4310/atmp.2010.v14.n3.a1.

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26

Saadat, H., and A. Pourdarvish. "Myerse-Perry Black Holes with Logarithmic Correction." International Journal of Theoretical Physics 53, no. 9 (April 24, 2014): 3014–25. http://dx.doi.org/10.1007/s10773-014-2097-6.

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27

Zhang, Ming, and Wen-Biao Liu. "f(R) Black Holes as Heat Engines." International Journal of Theoretical Physics 55, no. 12 (August 22, 2016): 5136–45. http://dx.doi.org/10.1007/s10773-016-3134-4.

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28

Ökcü, Özgür, and Ekrem Aydiner. "GUP-Corrected van der Waals Black Holes." International Journal of Theoretical Physics 59, no. 9 (July 14, 2020): 2839–51. http://dx.doi.org/10.1007/s10773-020-04544-8.

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29

Chen, Sen, and Yili Pei. "Holographic Complexity in AdS Accelerating Black Holes." International Journal of Theoretical Physics 60, no. 3 (February 2, 2021): 917–23. http://dx.doi.org/10.1007/s10773-021-04714-2.

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30

Schutz, B. F. "Gravitational-wave astronomy: delivering on the promises." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 376, no. 2120 (April 16, 2018): 20170279. http://dx.doi.org/10.1098/rsta.2017.0279.

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Now that LIGO and Virgo have begun to detect gravitational-wave events with regularity, the field of gravitational-wave astronomy is beginning to realize its promise. Binary black holes and, very recently, binary neutron stars have been observed, and we are already learning much from them. The future, with improved sensitivity, more detectors and detectors like LISA in different frequency bands, has even more promise to open a completely hidden side of the Universe to our exploration. This article is part of a discussion meeting issue ‘The promises of gravitational-wave astronomy’.

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31

Blázquez-Salcedo, Jose Luis, Sarah Kahlen, and Jutta Kunz. "Critical Solutions of Scalarized Black Holes." Symmetry 12, no. 12 (December 11, 2020): 2057. http://dx.doi.org/10.3390/sym12122057.

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We consider charged black holes with scalar hair obtained in a class of Einstein–Maxwell– scalar models, where the scalar field is coupled to the Maxwell invariant with a quartic coupling function. Besides the Reissner–Nordström black holes, these models allow for black holes with scalar hair. Scrutinizing the domain of existence of these hairy black holes, we observe a critical behavior. A limiting configuration is encountered at a critical value of the charge, where space time splits into two parts: an inner space time with a finite scalar field and an outer extremal Reissner–Nordström space time. Such a pattern was first observed in the context of gravitating non-Abelian magnetic monopoles and their hairy black holes.

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32

Lousto, C. O. "Some Thermodynamic Aspects of Black Holes and Singularities." International Journal of Modern Physics D 06, no. 05 (October 1997): 575–90. http://dx.doi.org/10.1142/s0218271897000352.

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We review and correct the classical critical exponents characterizing the transition from negative to positive black hole's heat capacity at high charge-angular momentum. We discuss the stability properties of black holes as a thermodynamic system in equilibrium with a radiation bath (canonical ensemble) by using the Helmholtz free energy potential. Finally we analytically extend the analysis to any value of the variables in the Helmholtz potential and show that this leads to the consideration of negative mass holes. We then study their curious thermodynamical stability behavior.

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33

Haehnelt, Martin G. "The connection between the formation of galaxies and that of their central supermassive black holes." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 363, no. 1828 (January 12, 2005): 705–13. http://dx.doi.org/10.1098/rsta.2004.1522.

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Massive black holes appear to be an essential ingredient of massive galactic bulges but little is known yet to what extent massive black holes reside in dwarf galaxies and globular clusters. Massive black holes most likely grow by a mixture of merging and accretion of gas in their hierarchically merging host galaxies. While the hierarchical merging of dark matter structures extends to sub-galactic scales and very high redshift, it is uncertain if the same is true for the build–up of massive black holes. I discuss here some of the relevant problems and open questions.

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34

Binney, James. "Black holes, cuspy atmospheres and galaxy formation." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 363, no. 1828 (January 12, 2005): 739–49. http://dx.doi.org/10.1098/rsta.2004.1520.

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In cuspy atmospheres, jets driven by supermassive black holes (BHs) offset radiative cooling. The jets fire episodically, but often enough that the cuspy atmosphere does not move very far towards a cooling catastrophe in the intervals of jet inactivity. The ability of energy released on the sub–parsec scale of the BH to balance cooling on scales of several tens of kiloparsecs arises through a combination of the temperature sensitivity of the accretion rate and the way in which the radius of jet disruption varies with ambient density. Accretion of hot gas does not significantly increase BH masses, which are determined by periods of rapid BH growth and star formation when cold gas is briefly abundant at the galactic centre. Hot gas does not accumulate in shallow potential wells. As the Universe ages, deeper wells form, and eventually hot gas accumulates. This gas soon prevents the formation of further stars, since jets powered by the BH prevent it from cooling, and it mops up most cold infalling gas before many stars can form. Thus, BHs set the upper limit to the masses of galaxies. The formation of low–mass galaxies is inhibited by a combination of photoheating and supernova–driven galactic winds. Working in tandem, these mechanisms can probably explain the profound difference between the galaxy luminosity function and the mass function of dark haloes expected in the cold dark matter cosmology.

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Peacock, J. A. "Black holes, cooling flows and galaxy formation." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 363, no. 1828 (January 12, 2005): 751–59. http://dx.doi.org/10.1098/rsta.2004.1524.

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Central black holes in galaxies are now well established as a ubiquitous phenomenon, and this fact is important for theories of cosmological structure formation. Merging of galaxy haloes must preserve the proportionality between black hole mass and baryonic mass; the way in which this happens may help solve difficulties with existing models of galaxy formation, which suffer from excessive cooling and thus overproduce stars. Feedback from active nuclei may be the missing piece of the puzzle, regulating galaxy–scale cooling flows. Such a process now seems to be observed in cluster–scale cooling flows, where dissipation of sound waves generated by radio lobes can plausibly balance the energy lost in X–rays, at least in a time–averaged sense.

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36

Melia, F., and T. M. McClintock. "Supermassive black holes in the early Universe." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 471, no. 2184 (December 2015): 20150449. http://dx.doi.org/10.1098/rspa.2015.0449.

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The recent discovery of the ultraluminous quasar SDSS J010013.02+280225.8 at redshift 6.3 has exacerbated the time compression problem implied by the appearance of supermassive black holes only approximately 900 Myr after the big bang, and only approximately 500 Myr beyond the formation of Pop II and III stars. Aside from heralding the onset of cosmic re-ionization, these first and second generation stars could have reasonably produced the approximately 5–20 M ⊙ seeds that eventually grew into z approximately 6–7 quasars. But this process would have taken approximately 900 Myr, a timeline that appears to be at odds with the predictions of Λ CDM without an anomalously high accretion rate, or some exotic creation of approximately 10 5 M ⊙ seeds. There is no evidence of either of these happening in the local Universe. In this paper, we show that a much simpler, more elegant solution to the supermassive black hole anomaly is instead to view this process using the age–redshift relation predicted by the R h = ct Universe, an Friedmann–Robertson–Walker (FRW) cosmology with zero active mass. In this context, cosmic re-ionization lasted from t approximately 883 Myr to approximately 2 Gyr ( 6 ≲ z ≲ 15 ), so approximately 5–20 M ⊙ black hole seeds formed shortly after re-ionization had begun, would have evolved into approximately 10 10 M ⊙ quasars by z approximately 6–7 simply via the standard Eddington-limited accretion rate. The consistency of these observations with the age–redshift relationship predicted by R h = ct supports the existence of dark energy; but not in the form of a cosmological constant.

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Harvey, Jeffrey A. "Ramanujan's influence on string theory, black holes and moonshine." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 378, no. 2163 (December 9, 2019): 20180440. http://dx.doi.org/10.1098/rsta.2018.0440.

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Ramanujan influenced many areas of mathematics, but his work on q -series, on the growth of coefficients of modular forms and on mock modular forms stands out for its depth and breadth of applications. I will give a brief overview of how this part of Ramanujan's work has influenced physics with an emphasis on applications to string theory, counting of black hole states and moonshine. This paper contains the material from my presentation at the meeting celebrating the centenary of Ramanujan's election as FRS and adds some additional material on black hole entropy and the AdS/CFT correspondence. This article is part of a discussion meeting issue ‘Srinivasa Ramanujan: in celebration of the centenary of his election as FRS’.

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Katz, Sheldon, Albrecht Klemm, and Cumrun Vafa. "M-theory, topological strings and spinning black holes." Advances in Theoretical and Mathematical Physics 3, no. 5 (1999): 1445–537. http://dx.doi.org/10.4310/atmp.1999.v3.n5.a6.

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Chrúsciel, Piotr T., and Sebastian J. Szybka. "Stable causality of the Pomeransky–Senkov black holes." Advances in Theoretical and Mathematical Physics 15, no. 1 (2011): 175–78. http://dx.doi.org/10.4310/atmp.2011.v15.n1.a5.

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40

Bhadra, Jhumpa, and Ujjal Debnath. "Primordial Black Holes Evolution in f(T) Gravity." International Journal of Theoretical Physics 53, no. 2 (October 12, 2013): 645–51. http://dx.doi.org/10.1007/s10773-013-1852-4.

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41

Dhayal, Renu, Meghna Rathore, and K. K. Venkataratnam. "Single-Mode Squeezed Thermal States and Black Holes." International Journal of Theoretical Physics 58, no. 12 (November 7, 2019): 4311–22. http://dx.doi.org/10.1007/s10773-019-04303-4.

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42

Radinschi, I., F. Rahaman, and A. Banerjee. "On the Energy of Hořava–Lifshitz Black Holes." International Journal of Theoretical Physics 50, no. 9 (May 3, 2011): 2906–16. http://dx.doi.org/10.1007/s10773-011-0791-1.

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43

Saltı, Mustafa, and Oktay Aydogdu. "On the Møller Energy Associated with Black Holes." International Journal of Theoretical Physics 45, no. 12 (July 6, 2006): 2437–52. http://dx.doi.org/10.1007/s10773-006-9212-2.

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44

KOZAMEH, CARLOS, OSVALDO M. MORESCHI, and ALEJANDRO PÉREZ. "CHARACTERIZING SMOOTH ISOLATED BLACK HOLES." International Journal of Modern Physics D 20, no. 05 (May 20, 2011): 757–66. http://dx.doi.org/10.1142/s0218271811019098.

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45

Vaz, Cenalo. "Black holes as gravitational atoms." International Journal of Modern Physics D 23, no. 12 (October 2014): 1441002. http://dx.doi.org/10.1142/s0218271814410028.

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Recently, it was argued [A. Almheiri et al., arXiv: 1207.3123, A. Almheiri et al., arXiv: 1304.6483], via a delicate thought experiment, that it is not consistent to simultaneously require that (a) Hawking radiation is pure, (b) effective field theory is valid outside a stretched horizon and (c) infalling observers encounter nothing unusual as they cross the horizon. These are the three fundamental assumptions underlying Black Hole Complementarity and the authors proposed that the most conservative resolution of the paradox is that (c) is false and the infalling observer burns up at the horizon (the horizon acts as a "firewall"). However, the firewall violates the equivalence principle and breaks the CPT invariance of quantum gravity. This led Hawking to propose recently that gravitational collapse may not end up producing event horizons, although he did not give a mechanism for how this may happen. Here we will support Hawking's conclusion in a quantum gravitational model of dust collapse. We will show that continued collapse to a singularity can only be achieved by combining two independent and entire solutions of the Wheeler–DeWitt equation. We interpret the paradox as simply forbidding such a combination. This leads naturally to a picture in which matter condenses on the apparent horizon during quantum collapse.

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David Brown, J., and Viqar Husain. "Black Holes with Short Hair." International Journal of Modern Physics D 06, no. 05 (October 1997): 563–73. http://dx.doi.org/10.1142/s0218271897000340.

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We present spherically symmetric black hole solutions for Einstein gravity coupled to anisotropic matter. We show that these black holes have arbitrarily short hair, and argue for stability by showing that they can arise from dynamical collapse. We also show that a recent "no short hair" theorem does not apply to these solutions.

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HUBENY, VERONIKA E. "PRECURSORS SEE INSIDE BLACK HOLES." International Journal of Modern Physics D 12, no. 09 (October 2003): 1693–98. http://dx.doi.org/10.1142/s0218271803003992.

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We consider, within a string theoretic context, the accessibility of events inside a black hole horizon. We present a gedankenexperiment which uses the nonlocal nature of precursors in the AdS/CFT correspondence, as well as the global nature of event horizons, to argue that the dual field theory does contain information about physics inside black holes. This alleviates the causal obstacles to accessing behind-the-horizon physics, thereby rendering more tractable certain long-standing questions of quantum gravity, such as the information paradox and possibly even singularity resolution.

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HELFER, ADAM D. "QUANTUM NATURE OF BLACK HOLES." International Journal of Modern Physics D 13, no. 10 (December 2004): 2299–305. http://dx.doi.org/10.1142/s021827180400636x.

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I reconsider Hawking's analysis of the effects of gravitational collapse on quantum fields, taking into account interactions between the fields. The ultra-high energy vacuum fluctuations, which had been considered to be an awkward peripheral feature of the analysis, are shown to play a key role. By interactions, they can scatter particles to, or create pairs of particle at, ultra-high energies. The energies rapidly become so great that quantum gravity must play a dominant role. Thus the vicinities of black holes are essentially quantum-gravitational regimes.

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MAIA, M. D. "INFORMATION STORAGE IN BLACK HOLES." International Journal of Modern Physics D 14, no. 12 (December 2005): 2251–55. http://dx.doi.org/10.1142/s0218271805007838.

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The information loss paradox for Schwarzschild black holes is examined, using the ADS/CFT correspondence extended to the M6(4, 2) bulk. It is found that the only option compatible with the preservation of the quantum unitarity is when a regular remnant region of the black hole survives to the black hole evaporation process, where information can be stored and eventually retrieved.

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BALASUBRAMANIAN, VIJAY, DONALD MAROLF, and MOSHE ROZALI. "INFORMATION RECOVERY FROM BLACK HOLES." International Journal of Modern Physics D 15, no. 12 (December 2006): 2285–92. http://dx.doi.org/10.1142/s0218271806009765.

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We argue that if black hole entropy arises from a finite number of underlying quantum states, then any particular such state can be identified from infinity. The finite density of states implies a discrete energy spectrum, and, in general, such spectra are non-degenerate except as determined by symmetries. Therefore, knowledge of the precise energy, and of other commuting conserved charges, determines the quantum state. In a gravitating theory, all conserved charges including the energy are given by boundary terms that can be measured at infinity. Thus, within any theory of quantum gravity, no information can be lost in black holes with a finite number of states. However, identifying the state of a black hole from infinity requires measurements with Planck scale precision. Hence, observers with insufficient resolution will experience information loss.

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