Abstract
At the heart of the black hole information loss paradox and the firewall controversy lies the conflict between quantum mechanics and general relativity. Much has been said about quantum corrections to general relativity, but much less in the opposite direction. It is therefore crucial to examine possible corrections to quantum mechanics due to gravity. Indeed, the Heisenberg Uncertainty Principle is one profound feature of quantum mechanics, which nevertheless may receive correction when gravitational effects become important. Such generalized uncertainty principle [GUP] has been motivated from not only quite general considerations of quantum mechanics and gravity, but also string theoretic arguments. We examine the role of GUP in the context of black hole complementarity. We find that while complementarity can be violated by large N rescaling if one assumes only the Heisenberg’s Uncertainty Principle, the application of GUP may save complementarity, but only if certain N -dependence is also assumed. This raises two important questions beyond the scope of this work, i.e., whether GUP really has the proposed form of N -dependence, and whether black hole complementarity is indeed correct.
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References
S.W. Hawking, Black hole explosions, Nature 248 (1974) 30 [INSPIRE].
S.W. Hawking, Particle Creation by Black Holes, Commun. Math. Phys. 43 (1975) 199 [Erratum ibid. 46 (1976) 206-206] [INSPIRE].
R.C. Myers, Pure states don’t wear black, Gen. Rel. Grav. 29 (1997) 1217 [gr-qc/9705065] [INSPIRE].
M. Arzano, Purity is not eternal at the Planck scale, Phys. Rev. D 90 (2014) 024016 [arXiv:1403.6457] [INSPIRE].
W.A. Hiscock and L.D. Weems, Evolution of Charged Evaporating Black Holes, Phys. Rev. D 41 (1990) 1142 [INSPIRE].
R.M. Wald, The thermodynamics of black holes, Living Rev. Rel. 4 (2001) 6 [gr-qc/9912119] [INSPIRE].
D.N. Page, Average entropy of a subsystem, Phys. Rev. Lett. 71 (1993) 1291 [gr-qc/9305007] [INSPIRE].
D.N. Page, Time Dependence of Hawking Radiation Entropy, JCAP 09 (2013) 028 [arXiv:1301.4995] [INSPIRE].
L. Susskind, L. Thorlacius and J. Uglum, The Stretched horizon and black hole complementarity, Phys. Rev. D 48 (1993) 3743 [hep-th/9306069] [INSPIRE].
D.-h. Yeom and H. Zoe, Constructing a Counterexample to the Black Hole Complementarity, Phys. Rev. D 78 (2008) 104008 [arXiv:0802.1625] [INSPIRE].
S.E. Hong, D.-i. Hwang, E.D. Stewart and D.-h. Yeom, The Causal structure of dynamical charged black holes, Class. Quant. Grav. 27 (2010) 045014 [arXiv:0808.1709] [INSPIRE].
D.-h. Yeom and H. Zoe, Semi-classical black holes with large-N re-scaling and information loss problem, Int. J. Mod. Phys. A 26 (2011) 3287 [arXiv:0907.0677] [INSPIRE].
A. Almheiri, D. Marolf, J. Polchinski and J. Sully, Black Holes: Complementarity or Firewalls?, JHEP 02 (2013) 062 [arXiv:1207.3123] [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.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].
S.D.H. Hsu and D. Reeb, Black holes, information and decoherence, Phys. Rev. D 79 (2009) 124037 [arXiv:0903.2258] [INSPIRE].
S.D.H. Hsu, The Black hole information paradox and macroscopic superpositions, J. Phys. Conf. Ser. 222 (2010) 012037 [arXiv:1003.5382] [INSPIRE].
S.D.H. Hsu, Macroscopic superpositions and black hole unitarity, arXiv:1302.0451 [INSPIRE].
S.D.H. Hsu, Factorization of unitarity and black hole firewalls, arXiv:1308.5686 [INSPIRE].
T.J. Hollowood, Schrödinger’s Cat and the Firewall, arXiv:1403.5947 [INSPIRE].
M. Sasaki and D.-h. Yeom, Thin-shell bubbles and information loss problem in anti de Sitter background, arXiv:1404.1565 [INSPIRE].
E. Okon and D. Sudarsky, The Black Hole Information Paradox and the Collapse of the Wave Function, arXiv:1406.2011 [INSPIRE].
S.B. Giddings, Nonviolent nonlocality, Phys. Rev. D 88 (2013) 064023 [arXiv:1211.7070] [INSPIRE].
R.J. Adler and D.I. Santiago, On gravity and the uncertainty principle, Mod. Phys. Lett. A 14 (1999) 1371 [gr-qc/9904026] [INSPIRE].
N. Itzhaki, Black hole information versus locality, Phys. Rev. D 54 (1996) 1557 [hep-th/9510212] [INSPIRE].
D. Harlow and P. Hayden, Quantum Computation vs. Firewalls, JHEP 06 (2013) 085 [arXiv:1301.4504] [INSPIRE].
L. Susskind, Black Hole Complementarity and the Harlow-Hayden Conjecture, arXiv:1301.4505 [INSPIRE].
J. Oppenheim and W.G. Unruh, Firewalls and flat mirrors: An alternative to the AMPS experiment which evades the Harlow-Hayden obstacle, JHEP 03 (2014) 120 [arXiv:1401.1523] [INSPIRE].
Y.C. Ong, B. McInnes and P. Chen, Why Hawking Radiation Cannot Be Decoded, arXiv:1403.4886 [INSPIRE].
Y.C. Ong and P. Chen, Charge Loss (or the Lack Thereof ) for AdS Black Holes, JHEP 06 (2014) 061 [arXiv:1404.5215] [INSPIRE].
L. Susskind and L. Thorlacius, Gedanken experiments involving black holes, Phys. Rev. D 49 (1994) 966 [hep-th/9308100] [INSPIRE].
P. Hayden and J. Preskill, Black holes as mirrors: Quantum information in random subsystems, JHEP 09 (2007) 120 [arXiv:0708.4025] [INSPIRE].
M. Maggiore, Black hole complementarity and the physical origin of the stretched horizon, Phys. Rev. D 49 (1994) 2918 [hep-th/9310157] [INSPIRE].
M. Maggiore, A Generalized uncertainty principle in quantum gravity, Phys. Lett. B 304 (1993) 65 [hep-th/9301067] [INSPIRE].
M. Maggiore, Quantum groups, gravity and the generalized uncertainty principle, Phys. Rev. D 49 (1994) 5182 [hep-th/9305163] [INSPIRE].
F. Scardigli, Generalized uncertainty principle in quantum gravity from micro-black hole Gedanken experiment, Phys. Lett. B 452 (1999) 39 [hep-th/9904025] [INSPIRE].
G. Veneziano, A Stringy Nature Needs Just Two Constants, Europhys. Lett. 2 (1986) 199 [INSPIRE].
D.J. Gross and P.F. Mende, String Theory Beyond the Planck Scale, Nucl. Phys. B 303 (1988) 407 [INSPIRE].
D. Amati, M. Ciafaloni and G. Veneziano, Can Space-Time Be Probed Below the String Size?, Phys. Lett. B 216 (1989) 41 [INSPIRE].
K. Konishi, G. Paffuti and P. Provero, Minimum Physical Length and the Generalized Uncertainty Principle in String Theory, Phys. Lett. B 234 (1990) 276 [INSPIRE].
E. Witten, Reflections on the Fate of Spacetime, Phys. Today 49N4 (1996) 24 [INSPIRE].
R.J. Adler, P. Chen and D.I. Santiago, The Generalized uncertainty principle and black hole remnants, Gen. Rel. Grav. 33 (2001) 2101 [gr-qc/0106080] [INSPIRE].
S. Hossenfelder, Minimal Length Scale Scenarios for Quantum Gravity, Living Rev. Rel. 16 (2013) 2 [arXiv:1203.6191] [INSPIRE].
G. Dvali, Black Holes and Large-N Species Solution to the Hierarchy Problem, Fortsch. Phys. 58 (2010) 528 [arXiv:0706.2050] [INSPIRE].
G. Dvali, M. Redi, S. Sibiryakov and A. Vainshtein, Gravity Cutoff in Theories with Large Discrete Symmetries, Phys. Rev. Lett. 101 (2008) 151603 [arXiv:0804.0769] [INSPIRE].
R. Brustein, G. Dvali and G. Veneziano, A Bound on the effective gravitational coupling from semiclassical black holes, JHEP 10 (2009) 085 [arXiv:0907.5516] [INSPIRE].
S. Das and E.C. Vagenas, Universality of Quantum Gravity Corrections, Phys. Rev. Lett. 101 (2008) 221301 [arXiv:0810.5333] [INSPIRE].
I. Fuentes-Schuller and R.B. Mann, Alice falls into a black hole: Entanglement in non-inertial frames, Phys. Rev. Lett. 95 (2005) 120404 [quant-ph/0410172] [INSPIRE].
Y. Sekino and L. Susskind, Fast Scramblers, JHEP 10 (2008) 065 [arXiv:0808.2096] [INSPIRE].
L. Susskind, Addendum to Fast Scramblers, arXiv:1101.6048 [INSPIRE].
R. Wald, General Relativity, The University of Chicago Press, Chicago and London (1984).
D.N. Page, Particle Emission Rates from a Black Hole: Massless Particles from an Uncharged, Nonrotating Hole, Phys. Rev. D 13 (1976) 198 [INSPIRE].
D.-h. Yeom, Reviews and perspectives on black hole complementarity, Int. J. Mod. Phys. Conf. Ser. 1 (2011) 311 [arXiv:0901.1929] [INSPIRE].
S. Hossenfelder, Gravity can be neither classical nor quantized, arXiv:1212.0454 [INSPIRE].
W. Kim, B.-H. Lee and D.-h. Yeom, Black hole complementarity and firewall in two dimensions, JHEP 05 (2013) 060 [arXiv:1301.5138] [INSPIRE].
M. Isi, J. Mureika and P. Nicolini, Self-Completeness and the Generalized Uncertainty Principle, JHEP 11 (2013) 139 [arXiv:1310.8153] [INSPIRE].
S. Hossenfelder and L. Smolin, Conservative solutions to the black hole information problem, Phys. Rev. D 81 (2010) 064009 [arXiv:0901.3156] [INSPIRE].
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Chen, P., Ong, Y.C. & Yeom, Dh. Generalized uncertainty principle: implications for black hole complementarity. J. High Energ. Phys. 2014, 21 (2014). https://doi.org/10.1007/JHEP12(2014)021
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DOI: https://doi.org/10.1007/JHEP12(2014)021