Abstract
The near-horizon geometry of evaporation black holes is determined according to the semi-classical Einstein equation. We consider spherically symmetric configurations in which the collapsing star has already collapsed below the Schwarzschild radius. The back-reaction of the vacuum energy-momentum, including Hawking radiation, is taken into account. The vacuum energy-momentum plays a crucial role in a small neighborhood of the apparent horizon, as it appears at the leading order in the semi-classical Einstein equation. Our study is focused on the time-dependent geometry in this region.
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References
H.A. Buchdahl, General Relativistic Fluid Spheres, Phys. Rev. 116 (1959) 1027 [INSPIRE].
P.-M. Ho and Y. Matsuo, Static Black Holes With Back Reaction From Vacuum Energy, Class. Quant. Grav. 35 (2018) 065012 [arXiv:1703.08662] [INSPIRE].
P.-M. Ho and Y. Matsuo, Static Black Hole and Vacuum Energy: Thin Shell and Incompressible Fluid, JHEP 03 (2018) 096 [arXiv:1710.10390] [INSPIRE].
A. Fabbri, S. Farese, J. Navarro-Salas, G.J. Olmo and H. Sanchis-Alepuz, Semiclassical zero-temperature corrections to Schwarzschild spacetime and holography, Phys. Rev. D 73 (2006) 104023 [hep-th/0512167] [INSPIRE].
A. Fabbri, S. Farese, J. Navarro-Salas, G.J. Olmo and H. Sanchis-Alepuz, Static quantum corrections to the Schwarzschild spacetime, J. Phys. Conf. Ser. 33 (2006) 457 [hep-th/0512179] [INSPIRE].
C. Berthiere, D. Sarkar and S.N. Solodukhin, The quantum fate of black hole horizons, arXiv:1712.09914 [INSPIRE].
O. Lunin and S.D. Mathur, AdS/CFT duality and the black hole information paradox, Nucl. Phys. B 623 (2002) 342 [hep-th/0109154] [INSPIRE].
O. Lunin and S.D. Mathur, Statistical interpretation of Bekenstein entropy for systems with a stretched horizon, Phys. Rev. Lett. 88 (2002) 211303 [hep-th/0202072] [INSPIRE].
S.N. Solodukhin, Can black hole relax unitarily?, hep-th/0406130 [INSPIRE].
S.N. Solodukhin, Restoring unitarity in BTZ black hole, Phys. Rev. D 71 (2005) 064006 [hep-th/0501053] [INSPIRE].
T. Damour and S.N. Solodukhin, Wormholes as black hole foils, Phys. Rev. D 76 (2007) 024016 [arXiv:0704.2667] [INSPIRE].
P.C.W. Davies and S.A. Fulling, Radiation from a moving mirror in two-dimensional space-time conformal anomaly, Proc. Roy. Soc. Lond. A 348 (1976) 393 [INSPIRE].
P.C.W. Davies, S.A. Fulling and W.G. Unruh, Energy Momentum Tensor Near an Evaporating Black Hole, Phys. Rev. D 13 (1976) 2720 [INSPIRE].
H. Kawai, Y. Matsuo and Y. Yokokura, A Self-consistent Model of the Black Hole Evaporation, Int. J. Mod. Phys. A 28 (2013) 1350050 [arXiv:1302.4733] [INSPIRE].
H. Kawai and Y. Yokokura, Phenomenological Description of the Interior of the Schwarzschild Black Hole, Int. J. Mod. Phys. A 30 (2015) 1550091 [arXiv:1409.5784] [INSPIRE].
P.-M. Ho, Comment on Self-Consistent Model of Black Hole Formation and Evaporation, JHEP 08 (2015) 096 [arXiv:1505.02468] [INSPIRE].
H. Kawai and Y. Yokokura, Interior of Black Holes and Information Recovery, Phys. Rev. D 93 (2016) 044011 [arXiv:1509.08472] [INSPIRE].
P.-M. Ho, The Absence of Horizon in Black-Hole Formation, Nucl. Phys. B 909 (2016) 394 [arXiv:1510.07157] [INSPIRE].
S.W. Hawking, Particle Creation by Black Holes, Commun. Math. Phys. 43 (1975) 199 [Erratum ibid. 46 (1976) 206] [INSPIRE].
C. Barcelo, S. Liberati, S. Sonego and M. Visser, Fate of gravitational collapse in semiclassical gravity, Phys. Rev. D 77 (2008) 044032 [arXiv:0712.1130] [INSPIRE].
S.M. Christensen and S.A. Fulling, Trace Anomalies and the Hawking Effect, Phys. Rev. D 15 (1977) 2088 [INSPIRE].
R. Parentani and T. Piran, The Internal geometry of an evaporating black hole, Phys. Rev. Lett. 73 (1994) 2805 [hep-th/9405007] [INSPIRE].
R. Brout, S. Massar, R. Parentani and P. Spindel, A Primer for black hole quantum physics, Phys. Rept. 260 (1995) 329 [arXiv:0710.4345] [INSPIRE].
S. Ayal and T. Piran, Spherical collapse of a massless scalar field with semiclassical corrections, Phys. Rev. D 56 (1997) 4768 [gr-qc/9704027] [INSPIRE].
J.A. Wheeler, Geometrodynamics and the issue of final state, in Relativity, Groups and Topology, B. DeWitt and C. DeWitt eds., Gordon and Breach (1974), p. 408.
P.-M. Ho, Asymptotic Black Holes, Class. Quant. Grav. 34 (2017) 085006 [arXiv:1609.05775] [INSPIRE].
H. Kawai and Y. Yokokura, A Model of Black Hole Evaporation and 4D Weyl Anomaly, Universe 3 (2017) 51 [arXiv:1701.03455] [INSPIRE].
S.W. Hawking, Breakdown of Predictability in Gravitational Collapse, Phys. Rev. D 14 (1976) 2460 [INSPIRE].
S.D. Mathur, The Information paradox: A Pedagogical introduction, Class. Quant. Grav. 26 (2009) 224001 [arXiv:0909.1038] [INSPIRE].
D. Marolf, The Black Hole information problem: past, present and future, Rept. Prog. Phys. 80 (2017) 092001 [arXiv:1703.02143] [INSPIRE].
A. Almheiri, D. Marolf, J. Polchinski and J. Sully, Black Holes: Complementarity or Firewalls?, JHEP 02 (2013) 062 [arXiv:1207.3123] [INSPIRE].
S.L. Braunstein, Black hole entropy as entropy of entanglement, or it’s curtains for the equivalence principle, arXiv:0907.1190v1.
S.L. Braunstein, S. Pirandola and K. Życzkowski, Better Late than Never: Information Retrieval from Black Holes, Phys. Rev. Lett. 110 (2013) 101301 [arXiv:0907.1190] [INSPIRE].
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Ho, PM., Matsuo, Y. On the near-horizon geometry of an evaporating black hole. J. High Energ. Phys. 2018, 47 (2018). https://doi.org/10.1007/JHEP07(2018)047
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DOI: https://doi.org/10.1007/JHEP07(2018)047