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Black holes: complementarity or firewalls?


We argue that the following three statements cannot all be true: (i) Hawking radiation is in a pure state, (ii) the information carried by the radiation is emitted from the region near the horizon, with low energy effective field theory valid beyond some microscopic distance from the horizon, and (iii) the infalling observer encounters nothing unusual at the horizon. Perhaps the most conservative resolution is that the infalling observer burns up at the horizon. Alternatives would seem to require novel dynamics that nevertheless cause notable violations of semiclassical physics at macroscopic distances from the horizon.

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  1. S. Hawking, Breakdown of predictability in gravitational collapse, Phys. Rev. D 14 (1976) 2460 [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  2. L. Susskind, L. Thorlacius and J. Uglum, The stretched horizon and black hole complementarity, Phys. Rev. D 48 (1993) 3743 [hep-th/9306069] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  3. C.R. Stephens, G. ’t Hooft and B.F. Whiting, Black hole evaporation without information loss, Class. Quant. Grav. 11 (1994) 621 [gr-qc/9310006] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  4. L. Susskind and L. Thorlacius, Gedanken experiments involving black holes, Phys. Rev. D 49 (1994) 966 [hep-th/9308100] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  5. J. Preskill, unpublished, quoted in ref. [2].

  6. 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].

    Article  MathSciNet  ADS  Google Scholar 

  7. P. Hayden and J. Preskill, Black holes as mirrors: quantum information in random subsystems, JHEP 09 (2007) 120 [arXiv:0708.4025] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  8. Y. Sekino and L. Susskind, Fast scramblers, JHEP 10 (2008) 065 [arXiv:0808.2096] [INSPIRE].

    Article  ADS  Google Scholar 

  9. J.L. Barbon and J.M. Magan, Chaotic fast scrambling at black holes, Phys. Rev. D 84 (2011) 106012 [arXiv:1105.2581] [INSPIRE].

    ADS  Google Scholar 

  10. N. Lashkari, D. Stanford, M. Hastings, T. Osborne and P. Hayden, Towards the fast scrambling conjecture, arXiv:1111.6580 [INSPIRE].

  11. S.B. Giddings, Models for unitary black hole disintegration, Phys. Rev. D 85 (2012) 044038 [arXiv:1108.2015] [INSPIRE].

    ADS  Google Scholar 

  12. S.B. Giddings, Black holes, quantum information and unitary evolution, Phys. Rev. D 85 (2012) 124063 [arXiv:1201.1037] [INSPIRE].

    ADS  Google Scholar 

  13. S.B. Giddings and Y. Shi, Quantum information transfer and models for black hole mechanics, arXiv:1205.4732 [INSPIRE].

  14. S.D. Mathur, The information paradox: a pedagogical introduction, Class. Quant. Grav. 26 (2009) 224001 [arXiv:0909.1038] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  15. S.D. Mathur, The information paradox and the infall problem, Class. Quant. Grav. 28 (2011) 125010 [arXiv:1012.2101] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  16. S.D. Mathur and C.J. Plumberg, Correlations in Hawking radiation and the infall problem, JHEP 09 (2011) 093 [arXiv:1101.4899] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  17. S.D. Mathur, What the information paradox is not, arXiv:1108.0302 [INSPIRE].

  18. B. Czech, K. Larjo and M. Rozali, Black holes as Rubiks cubes, JHEP 08 (2011) 143 [arXiv:1106.5229] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  19. S.G. Avery, Qubit models of black hole evaporation, arXiv:1109.2911 [INSPIRE].

  20. S.D. Mathur, Black holes and beyond, Annals Phys. 327 (2012) 2760 [arXiv:1205.0776] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  21. D.N. Page, Average entropy of a subsystem, Phys. Rev. Lett. 71 (1993) 1291 [gr-qc/9305007] [INSPIRE].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  22. D.N. Page, Black hole information, hep-th/9305040 [INSPIRE].

  23. Y. Nomura, J. Varela and S.J. Weinberg, Complementarity endures: no firewall for an infalling observer, arXiv:1207.6626 [INSPIRE].

  24. L. Susskind, Singularities, firewalls and complementarity, arXiv:1208.3445 [INSPIRE].

  25. S. Hawking and D.N. Page, Thermodynamics of black holes in anti-de Sitter space, Commun. Math. Phys. 87 (1983) 577 [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  26. J.M. Maldacena, Eternal black holes in anti-de Sitter, JHEP 04 (2003) 021 [hep-th/0106112] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  27. D. Marolf and A.C. Wall, Eternal black holes and superselection in AdS/CFT, Class. Quant. Grav. 30 (2013) 025001 [arXiv:1210.3590] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  28. G. Chapline, E. Hohlfeld, R. Laughlin and D. Santiago, Quantum phase transitions and the breakdown of classical general relativity, Int. J. Mod. Phys. A 18 (2003) 3587 [gr-qc/0012094] [INSPIRE].

    Article  ADS  Google Scholar 

  29. P.O. Mazur and E. Mottola, Gravitational condensate stars: an alternative to black holes, gr-qc/0109035 [INSPIRE].

  30. A. Davidson, Holographic shell model: stack data structure inside black holes, arXiv:1108.2650 [INSPIRE].

  31. S.D. Mathur and D. Turton, Comments on black holes I: the possibility of complementarity, arXiv:1208.2005 [INSPIRE].

  32. D.N. Page, Particle emission rates from a black hole: massless particles from an uncharged, nonrotating hole, Phys. Rev. D 13 (1976) 198 [INSPIRE].

    ADS  Google Scholar 

  33. W. Unruh and R.M. Wald, Acceleration radiation and generalized second law of thermodynamics, Phys. Rev. D 25 (1982) 942 [INSPIRE].

    ADS  Google Scholar 

  34. W.G. Unruh and R. Wald, How to mine energy from a black hole, Gen. Rel. Grav. 15 (1983) 195.

    Article  MathSciNet  ADS  Google Scholar 

  35. W. Unruh and R.M. Wald, Entropy bounds, acceleration radiation, and the generalized second law, Phys. Rev. D 27 (1983) 2271 [INSPIRE].

    ADS  Google Scholar 

  36. A.R. Brown, Tensile strength and the mining of black holes, arXiv:1207.3342 [INSPIRE].

  37. B. Czech, J.L. Karczmarek, F. Nogueira and M. Van Raamsdonk, Rindler quantum gravity, Class. Quant. Grav. 29 (2012) 235025 [arXiv:1206.1323] [INSPIRE].

    Article  ADS  Google Scholar 

  38. N. Itzhaki, Is the black hole complementarity principle really necessary?, hep-th/9607028 [INSPIRE].

  39. D.A. Lowe and L. Thorlacius, Comments on the black hole information problem, Phys. Rev. D 73 (2006) 104027 [hep-th/0601059] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  40. S. Hawking, Particle creation by black holes, Commun. Math. Phys. 43 (1975) 199 [Erratum ibid. 46 (1976) 206] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  41. G.T. Horowitz and J.M. Maldacena, The black hole final state, JHEP 02 (2004) 008 [hep-th/0310281] [INSPIRE].

    Article  MathSciNet  ADS  Google Scholar 

  42. S. Corley and T. Jacobson, Lattice black holes, Phys. Rev. D 57 (1998) 6269 [hep-th/9709166] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  43. T. Jacobson and D. Mattingly, Hawking radiation on a falling lattice, Phys. Rev. D 61 (2000) 024017 [hep-th/9908099] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  44. T. Jacobson, Trans Planckian redshifts and the substance of the space-time river, Prog. Theor. Phys. Suppl. 136 (1999) 1 [hep-th/0001085] [INSPIRE].

    Article  ADS  Google Scholar 

  45. A.E. Lawrence and E.J. Martinec, Black hole evaporation along macroscopic strings, Phys. Rev. D 50 (1994) 2680 [hep-th/9312127] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  46. V.P. Frolov and D. Fursaev, Mining energy from a black hole by strings, Phys. Rev. D 63 (2001) 124010 [hep-th/0012260] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  47. R. Price, K. Thorne and D.A. MacDonald eds., Black holes: the membrane paradigm, section VII.E.1, Yale University Press, New Haven U.S.A. (1986).

  48. A.J. Amsel, D. Marolf and A. Virmani, The physical process first law for bifurcate killing horizons, Phys. Rev. D 77 (2008) 024011 [arXiv:0708.2738] [INSPIRE].

    MathSciNet  ADS  Google Scholar 

  49. B. Carter, The general theory of mechanical, electromagnetic and thermodynamic properties of black holes, in General relativity: an Einstein centenary survey, S.W. Hawking and W. Israel eds., Cambridge University Press, Cambridge U.K. (1979).

  50. R.M. Wald, Quantum field theory in curved spacetime and black hole thermodynamics, University of Chicago Press, Chicago U.S.A. (1994).

    MATH  Google Scholar 

  51. T. Jacobson, On the nature of black hole entropy, in General relativity and relativistic astrophysics: eighth Canadian conference, C.P. Burgess and R.C. Myers eds., AIP Conf. Proc. 493 (2000) 85 [gr-qc/9908031] [INSPIRE].

  52. B.S. DeWitt, The Everett-Wheeler interpretation of quantum mechanics, in Battelle rencontres, 1967 lectures in mathematics and physics, C. DeWitt and J.A. Wheeler eds., W.A. Benjamin Inc., New York U.S.A. (1968).

  53. J.B. Hartle, Quantum mechanics of individual systems, Am. J. Phys. 36 (1968) 704.

    Article  ADS  Google Scholar 

  54. T. Banks, private communication.

  55. M. Srednicki, private communication.

  56. R. Bousso, Complementarity is not enough, arXiv:1207.5192 [INSPIRE].

  57. D. Harlow, Complementarity, not firewalls, arXiv:1207.6243.

  58. B.D. Chowdhury and A. Puhm, Is Alice burning or fuzzing?, arXiv:1208.2026 [INSPIRE].

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Correspondence to Joseph Polchinski.

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ArXiv ePrint: 1207.3123

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Almheiri, A., Marolf, D., Polchinski, J. et al. Black holes: complementarity or firewalls?. J. High Energ. Phys. 2013, 62 (2013).

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