Abstract
Collapsing shells form horizons, and when the curvature is small classical general relativity is believed to describe this process arbitrarily well. On the other hand, quantum information theory based (fuzzball/firewall) arguments suggest the existence of some structure at the black hole horizon. This structure can only form if classical general relativity stops being the correct description of the collapsing shell before it reaches the horizon size. We present strong evidence that classical general relativity can indeed break down prematurely, by explicitly computing the quantum tunneling amplitude of a collapsing shell of branes into smooth horizonless microstate geometries. We show that the amplitude for tunneling into microstate geometries with a large number of topologically non-trivial cycles is parametrically larger than e −SBH , which indicates that the shell can tunnel into a horizonless configuration long before the horizon has any chance to form. We also use this technology to investigate the tunneling of M2 branes into LLM bubbling geometries.
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References
S.D. Mathur, The information paradox: a pedagogical introduction, Class. Quant. Grav. 26 (2009) 224001 [arXiv:0909.1038] [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, S. Pirandola and K. Życzkowski, Better late than never: information retrieval from black holes, Phys. Rev. Lett. 110 (2013) 101301 [arXiv:0907.1190] [INSPIRE].
J.R. Oppenheimer and H. Snyder, On continued gravitational contraction, Phys. Rev. 56 (1939) 455 [INSPIRE].
S.D. Mathur, The fuzzball proposal for black holes: an elementary review, Fortsch. Phys. 53 (2005) 793 [hep-th/0502050] [INSPIRE].
I. Bena and N.P. Warner, Black holes, black rings and their microstates, Lect. Notes Phys. 755 (2008) 1 [hep-th/0701216] [INSPIRE].
V. Balasubramanian, J. de Boer, S. El-Showk and I. Messamah, Black holes as effective geometries, Class. Quant. Grav. 25 (2008) 214004 [arXiv:0811.0263] [INSPIRE].
K. Skenderis and M. Taylor, The fuzzball proposal for black holes, Phys. Rept. 467 (2008) 117 [arXiv:0804.0552] [INSPIRE].
S.D. Mathur, Fuzzballs and the information paradox: a summary and conjectures, arXiv:0810.4525 [INSPIRE].
B.D. Chowdhury and A. Virmani, Modave lectures on fuzzballs and emission from the D1-D5 system, in 5th Modave Summer School in Mathematical Physics, August 17-21, Modave, Belgium (2010), arXiv:1001.1444 [INSPIRE].
I. Bena and N.P. Warner, Resolving the structure of black holes: philosophizing with a hammer, arXiv:1311.4538 [INSPIRE].
I. Bena and N.P. Warner, Bubbling supertubes and foaming black holes, Phys. Rev. D 74 (2006) 066001 [hep-th/0505166] [INSPIRE].
P. Berglund, E.G. Gimon and T.S. Levi, Supergravity microstates for BPS black holes and black rings, JHEP 06 (2006) 007 [hep-th/0505167] [INSPIRE].
I. Bena, C.-W. Wang and N.P. Warner, Mergers and typical black hole microstates, JHEP 11 (2006) 042 [hep-th/0608217] [INSPIRE].
I. Bena, N. Bobev, S. Giusto, C. Ruef and N.P. Warner, An Infinite-Dimensional Family of Black-Hole Microstate Geometries, JHEP 03 (2011) 022 [Erratum ibid. 1104 (2011) 059] [arXiv:1006.3497] [INSPIRE].
I. Bena et al., Habemus superstratum! A constructive proof of the existence of superstrata, arXiv:1503.01463.
I. Bena, M. Shigemori and N.P. Warner, Black-Hole Entropy from Supergravity Superstrata States, JHEP 10 (2014) 140 [arXiv:1406.4506] [INSPIRE].
R. Serini, Euclideitá dello spazio completamente vuoto nella relativitá general di Einstein, Atti Acad. Lincei Ser. 5 Rend. 27 (1918) 235.
A. Einstein, Demonstration of the non-existence of gravitational fields with a non-vanishing total mass free of singularities, Univ. Nac. Tucumn. Rev. A 2 (1941) 5.
A. Einstein and W. Pauli, On the non-existence of regular stationary solutions of relativistic field equations, Ann. Math. 44 (1943) 131.
P. Breitenlohner, D. Maison and G.W. Gibbons, Four-dimensional black holes from Kaluza-Klein theories, Commun. Math. Phys. 120 (1988) 295.
B. Carter, Tensor and vector multiplets in six-dimensional supergravity, in Gravitation in Astrophysics: Cargese 1986, B. Carter and J. Hartle eds., Nato ASI series B volume 156, Plenum Press (1986).
G.W. Gibbons and N.P. Warner, Global structure of five-dimensional fuzzballs, Class. Quant. Grav. 31 (2014) 025016 [arXiv:1305.0957] [INSPIRE].
H.K. Kunduri and J. Lucietti, The first law of soliton and black hole mechanics in five dimensions, Class. Quant. Grav. 31 (2014) 032001 [arXiv:1310.4810] [INSPIRE].
P.A. Haas, Smarr’s formula in eleven-dimensional supergravity, arXiv:1405.3708 [INSPIRE].
P. de Lange, D.R. Mayerson and B. Vercnocke, Structure of six-dimensional microstate geometries, JHEP 09 (2015) 075 [arXiv:1504.00798].
S.D. Mathur, Tunneling into fuzzball states, Gen. Rel. Grav. 42 (2010) 113 [arXiv:0805.3716] [INSPIRE].
S.D. Mathur, How fast can a black hole release its information?, Int. J. Mod. Phys. D 18 (2009) 2215 [arXiv:0905.4483] [INSPIRE].
P. Kraus and S.D. Mathur, Nature abhors a horizon, arXiv:1505.05078.
S. Kachru, J. Pearson and H.L. Verlinde, Brane/flux annihilation and the string dual of a nonsupersymmetric field theory, JHEP 06 (2002) 021 [hep-th/0112197] [INSPIRE].
I.R. Klebanov and M.J. Strassler, Supergravity and a confining gauge theory: Duality cascades and χ SB resolution of naked singularities, JHEP 08 (2000) 052 [hep-th/0007191] [INSPIRE].
I.R. Klebanov and S.S. Pufu, M-branes and metastable states, JHEP 08 (2011) 035 [arXiv:1006.3587] [INSPIRE].
M. Cvetič, G.W. Gibbons, H. Lü and C.N. Pope, Ricci flat metrics, harmonic forms and brane resolutions, Commun. Math. Phys. 232 (2003) 457 [hep-th/0012011] [INSPIRE].
S.R. Coleman, The fate of the false vacuum. 1. Semiclassical theory, Phys. Rev. D 15 (1977) 2929 [Erratum ibid. D 16 (1977) 1248] [INSPIRE].
I. Bena, A. Puhm and B. Vercnocke, Metastable supertubes and non-extremal black hole microstates, JHEP 04 (2012) 100 [arXiv:1109.5180] [INSPIRE].
I. Bena, A. Puhm and B. Vercnocke, Non-extremal black hole microstates: fuzzballs of fire or fuzzballs of fuzz?, JHEP 12 (2012) 014 [arXiv:1208.3468] [INSPIRE].
S. Massai, G. Pasini and A. Puhm, Metastability in bubbling AdS space, JHEP 02 (2015) 138 [arXiv:1407.6007] [INSPIRE].
H. Lin, O. Lunin and J.M. Maldacena, Bubbling AdS space and 1/2 BPS geometries, JHEP 10 (2004) 025 [hep-th/0409174] [INSPIRE].
I. Bena, The M-theory dual of a three-dimensional theory with reduced supersymmetry, Phys. Rev. D 62 (2000) 126006 [hep-th/0004142] [INSPIRE].
J. Gomis, D. Rodriguez-Gomez, M. Van Raamsdonk and H. Verlinde, A massive study of M 2-brane proposals, JHEP 09 (2008) 113 [arXiv:0807.1074] [INSPIRE].
S. Cheon, H.-C. Kim and S. Kim, Holography of mass-deformed M 2-branes, arXiv:1101.1101 [INSPIRE].
I. Bena, J. de Boer, M. Shigemori and N.P. Warner, Double, double supertube bubble, JHEP 10 (2011) 116 [arXiv:1107.2650] [INSPIRE].
F. Denef and G.W. Moore, Split states, entropy enigmas, holes and halos, JHEP 11 (2011) 129 [hep-th/0702146] [INSPIRE].
I. Bena, M. Berkooz, J. de Boer, S. El-Showk and D. Van den Bleeken, Scaling BPS solutions and pure-Higgs states, JHEP 11 (2012) 171 [arXiv:1205.5023] [INSPIRE].
I. Bena, C.-W. Wang and N.P. Warner, Plumbing the abyss: black ring microstates, JHEP 07 (2008) 019 [arXiv:0706.3786] [INSPIRE].
E.J. Martinec and B.E. Niehoff, Hair-brane ideas on the horizon, JHEP 11 (2015) 195 [arXiv:1509.00044].
J.D. Brown and C. Teitelboim, Neutralization of the cosmological constant by membrane creation, Nucl. Phys. B 297 (1988) 787 [INSPIRE].
T. Banks, C.M. Bender and T.T. Wu, Coupled anharmonic oscillators. 1. Equal mass case, Phys. Rev. D 8 (1973) 3346 [INSPIRE].
S.R. Coleman, V. Glaser and A. Martin, Action minima among solutions to a class of euclidean scalar field equations, Commun. Math. Phys. 58 (1978) 211 [INSPIRE].
J.B. Gutowski and H.S. Reall, General supersymmetric AdS 5 black holes, JHEP 04 (2004) 048 [hep-th/0401129] [INSPIRE].
B. Bates and F. Denef, Exact solutions for supersymmetric stationary black hole composites, JHEP 11 (2011) 127 [hep-th/0304094] [INSPIRE].
J.P. Gauntlett and J.B. Gutowski, General concentric black rings, Phys. Rev. D 71 (2005) 045002 [hep-th/0408122] [INSPIRE].
I. Bena, P. Kraus and N.P. Warner, Black rings in Taub-NUT, Phys. Rev. D 72 (2005) 084019 [hep-th/0504142] [INSPIRE].
F. Denef, Supergravity flows and D-brane stability, JHEP 08 (2000) 050 [hep-th/0005049] [INSPIRE].
M. Billó, S. Cacciatori, F. Denef, P. Fré, A. Van Proeyen and D. Zanon, The 0-brane action in a general D = 4 supergravity background, Class. Quant. Grav. 16 (1999) 2335 [hep-th/9902100] [INSPIRE].
I. Bena, N. Bobev, C. Ruef and N.P. Warner, Supertubes in bubbling backgrounds: Born-Infeld meets supergravity, JHEP 07 (2009) 106 [arXiv:0812.2942] [INSPIRE].
J. de Boer, S. El-Showk, I. Messamah and D. Van den Bleeken, Quantizing N = 2 multicenter solutions, JHEP 05 (2009) 002 [arXiv:0807.4556] [INSPIRE].
M.C.N. Cheng, More bubbling solutions, JHEP 03 (2007) 070 [hep-th/0611156] [INSPIRE].
B.D. Chowdhury and D.R. Mayerson, Multi-centered D1-D5 solutions at finite B-moduli, JHEP 02 (2014) 043 [arXiv:1305.0831] [INSPIRE].
S. Giusto and R. Russo, Perturbative superstrata, Nucl. Phys. B 869 (2013) 164 [arXiv:1211.1957] [INSPIRE].
D. Mateos and P.K. Townsend, Supertubes, Phys. Rev. Lett. 87 (2001) 011602 [hep-th/0103030] [INSPIRE].
D. Mateos, S. Ng and P.K. Townsend, Tachyons, supertubes and brane/anti-brane systems, JHEP 03 (2002) 016 [hep-th/0112054] [INSPIRE].
S.D. Mathur and D. Turton, Comments on black holes I: the possibility of complementarity, JHEP 01 (2014) 034 [arXiv:1208.2005] [INSPIRE].
A. Almheiri, D. Marolf, J. Polchinski, D. Stanford and J. Sully, An apologia for firewalls, JHEP 09 (2013) 018 [arXiv:1304.6483] [INSPIRE].
S.G. Avery, B.D. Chowdhury and A. Puhm, Unitarity and fuzzball complementarity: ‘Alice fuzzes but may not even know it!’, JHEP 09 (2013) 012 [arXiv:1210.6996] [INSPIRE].
E. Silverstein, Backdraft: string creation in an old Schwarzschild black hole, arXiv:1402.1486 [INSPIRE].
I. Bena and N.P. Warner, A harmonic family of dielectric flow solutions with maximal supersymmetry, JHEP 12 (2004) 021 [hep-th/0406145] [INSPIRE].
P. Pasti, D.P. Sorokin and M. Tonin, Covariant action for a D = 11 five-brane with the chiral field, Phys. Lett. B 398 (1997) 41 [hep-th/9701037] [INSPIRE].
K. Hanaki and H. Lin, M 2-M 5 systems in N = 6 Chern-Simons theory, JHEP 09 (2008) 067 [arXiv:0807.2074] [INSPIRE].
K.A. Intriligator, N. Seiberg and D. Shih, Dynamical SUSY breaking in meta-stable vacua, JHEP 04 (2006) 021 [hep-th/0602239] [INSPIRE].
O. Aharony, S.S. Razamat, N. Seiberg and B. Willett, 3D dualities from 4D dualities, JHEP 07 (2013) 149 [arXiv:1305.3924] [INSPIRE].
G. Lopes Cardoso, B. de Wit, J. Kappeli and T. Mohaupt, Stationary BPS solutions in N = 2 supergravity with R 2 interactions, JHEP 12(2000) 019 [hep-th/0009234] [INSPIRE].
I. Bena and N.P. Warner, One ring to rule them all. . . and in the darkness bind them?, Adv. Theor. Math. Phys. 9 (2005) 667 [hep-th/0408106] [INSPIRE].
H. Elvang, R. Emparan, D. Mateos and H.S. Reall, Supersymmetric black rings and three-charge supertubes, Phys. Rev. D 71 (2005) 024033 [hep-th/0408120] [INSPIRE].
V.S. Rychkov, D1-D5 black hole microstate counting from supergravity, JHEP 01 (2006) 063 [hep-th/0512053] [INSPIRE].
C. Krishnan and A. Raju, A note on D1-D5 entropy and geometric quantization, JHEP 06 (2015) 054 [arXiv:1504.04330] [INSPIRE].
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Bena, I., Mayerson, D.R., Puhm, A. et al. Tunneling into microstate geometries: quantum effects stop gravitational collapse. J. High Energ. Phys. 2016, 31 (2016). https://doi.org/10.1007/JHEP07(2016)031
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DOI: https://doi.org/10.1007/JHEP07(2016)031