Journal of High Energy Physics

, 2013:62 | Cite as

Black holes: complementarity or firewalls?

  • Ahmed Almheiri
  • Donald Marolf
  • Joseph PolchinskiEmail author
  • James Sully


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.


Black Holes Gauge-gravity correspondence 


  1. [1]
    S. Hawking, Breakdown of predictability in gravitational collapse, Phys. Rev. D 14 (1976) 2460 [INSPIRE].MathSciNetADSGoogle Scholar
  2. [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].MathSciNetADSGoogle Scholar
  3. [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].MathSciNetADSCrossRefGoogle Scholar
  4. [4]
    L. Susskind and L. Thorlacius, Gedanken experiments involving black holes, Phys. Rev. D 49 (1994) 966 [hep-th/9308100] [INSPIRE].MathSciNetADSGoogle Scholar
  5. [5]
    J. Preskill, unpublished, quoted in ref. [2].Google Scholar
  6. [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].MathSciNetADSCrossRefGoogle Scholar
  7. [7]
    P. Hayden and J. Preskill, Black holes as mirrors: quantum information in random subsystems, JHEP 09 (2007) 120 [arXiv:0708.4025] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  8. [8]
    Y. Sekino and L. Susskind, Fast scramblers, JHEP 10 (2008) 065 [arXiv:0808.2096] [INSPIRE].ADSCrossRefGoogle Scholar
  9. [9]
    J.L. Barbon and J.M. Magan, Chaotic fast scrambling at black holes, Phys. Rev. D 84 (2011) 106012 [arXiv:1105.2581] [INSPIRE].ADSGoogle Scholar
  10. [10]
    N. Lashkari, D. Stanford, M. Hastings, T. Osborne and P. Hayden, Towards the fast scrambling conjecture, arXiv:1111.6580 [INSPIRE].
  11. [11]
    S.B. Giddings, Models for unitary black hole disintegration, Phys. Rev. D 85 (2012) 044038 [arXiv:1108.2015] [INSPIRE].ADSGoogle Scholar
  12. [12]
    S.B. Giddings, Black holes, quantum information and unitary evolution, Phys. Rev. D 85 (2012) 124063 [arXiv:1201.1037] [INSPIRE].ADSGoogle Scholar
  13. [13]
    S.B. Giddings and Y. Shi, Quantum information transfer and models for black hole mechanics, arXiv:1205.4732 [INSPIRE].
  14. [14]
    S.D. Mathur, The information paradox: a pedagogical introduction, Class. Quant. Grav. 26 (2009) 224001 [arXiv:0909.1038] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  15. [15]
    S.D. Mathur, The information paradox and the infall problem, Class. Quant. Grav. 28 (2011) 125010 [arXiv:1012.2101] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  16. [16]
    S.D. Mathur and C.J. Plumberg, Correlations in Hawking radiation and the infall problem, JHEP 09 (2011) 093 [arXiv:1101.4899] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  17. [17]
    S.D. Mathur, What the information paradox is not, arXiv:1108.0302 [INSPIRE].
  18. [18]
    B. Czech, K. Larjo and M. Rozali, Black holes as Rubiks cubes, JHEP 08 (2011) 143 [arXiv:1106.5229] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  19. [19]
    S.G. Avery, Qubit models of black hole evaporation, arXiv:1109.2911 [INSPIRE].
  20. [20]
    S.D. Mathur, Black holes and beyond, Annals Phys. 327 (2012) 2760 [arXiv:1205.0776] [INSPIRE].MathSciNetADSCrossRefzbMATHGoogle Scholar
  21. [21]
    D.N. Page, Average entropy of a subsystem, Phys. Rev. Lett. 71 (1993) 1291 [gr-qc/9305007] [INSPIRE].MathSciNetADSCrossRefzbMATHGoogle Scholar
  22. [22]
    D.N. Page, Black hole information, hep-th/9305040 [INSPIRE].
  23. [23]
    Y. Nomura, J. Varela and S.J. Weinberg, Complementarity endures: no firewall for an infalling observer, arXiv:1207.6626 [INSPIRE].
  24. [24]
    L. Susskind, Singularities, firewalls and complementarity, arXiv:1208.3445 [INSPIRE].
  25. [25]
    S. Hawking and D.N. Page, Thermodynamics of black holes in anti-de Sitter space, Commun. Math. Phys. 87 (1983) 577 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  26. [26]
    J.M. Maldacena, Eternal black holes in anti-de Sitter, JHEP 04 (2003) 021 [hep-th/0106112] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  27. [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].MathSciNetADSCrossRefGoogle Scholar
  28. [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].ADSCrossRefGoogle Scholar
  29. [29]
    P.O. Mazur and E. Mottola, Gravitational condensate stars: an alternative to black holes, gr-qc/0109035 [INSPIRE].
  30. [30]
    A. Davidson, Holographic shell model: stack data structure inside black holes, arXiv:1108.2650 [INSPIRE].
  31. [31]
    S.D. Mathur and D. Turton, Comments on black holes I: the possibility of complementarity, arXiv:1208.2005 [INSPIRE].
  32. [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].ADSGoogle Scholar
  33. [33]
    W. Unruh and R.M. Wald, Acceleration radiation and generalized second law of thermodynamics, Phys. Rev. D 25 (1982) 942 [INSPIRE].ADSGoogle Scholar
  34. [34]
    W.G. Unruh and R. Wald, How to mine energy from a black hole, Gen. Rel. Grav. 15 (1983) 195.MathSciNetADSCrossRefGoogle Scholar
  35. [35]
    W. Unruh and R.M. Wald, Entropy bounds, acceleration radiation, and the generalized second law, Phys. Rev. D 27 (1983) 2271 [INSPIRE].ADSGoogle Scholar
  36. [36]
    A.R. Brown, Tensile strength and the mining of black holes, arXiv:1207.3342 [INSPIRE].
  37. [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].ADSCrossRefGoogle Scholar
  38. [38]
    N. Itzhaki, Is the black hole complementarity principle really necessary?, hep-th/9607028 [INSPIRE].
  39. [39]
    D.A. Lowe and L. Thorlacius, Comments on the black hole information problem, Phys. Rev. D 73 (2006) 104027 [hep-th/0601059] [INSPIRE].MathSciNetADSGoogle Scholar
  40. [40]
    S. Hawking, Particle creation by black holes, Commun. Math. Phys. 43 (1975) 199 [Erratum ibid. 46 (1976) 206] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  41. [41]
    G.T. Horowitz and J.M. Maldacena, The black hole final state, JHEP 02 (2004) 008 [hep-th/0310281] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  42. [42]
    S. Corley and T. Jacobson, Lattice black holes, Phys. Rev. D 57 (1998) 6269 [hep-th/9709166] [INSPIRE].MathSciNetADSGoogle Scholar
  43. [43]
    T. Jacobson and D. Mattingly, Hawking radiation on a falling lattice, Phys. Rev. D 61 (2000) 024017 [hep-th/9908099] [INSPIRE].MathSciNetADSGoogle Scholar
  44. [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].ADSCrossRefGoogle Scholar
  45. [45]
    A.E. Lawrence and E.J. Martinec, Black hole evaporation along macroscopic strings, Phys. Rev. D 50 (1994) 2680 [hep-th/9312127] [INSPIRE].MathSciNetADSGoogle Scholar
  46. [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].MathSciNetADSGoogle Scholar
  47. [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).Google Scholar
  48. [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].MathSciNetADSGoogle Scholar
  49. [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).Google Scholar
  50. [50]
    R.M. Wald, Quantum field theory in curved spacetime and black hole thermodynamics, University of Chicago Press, Chicago U.S.A. (1994).zbMATHGoogle Scholar
  51. [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. [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).Google Scholar
  53. [53]
    J.B. Hartle, Quantum mechanics of individual systems, Am. J. Phys. 36 (1968) 704.ADSCrossRefGoogle Scholar
  54. [54]
    T. Banks, private communication.Google Scholar
  55. [55]
    M. Srednicki, private communication.Google Scholar
  56. [56]
    R. Bousso, Complementarity is not enough, arXiv:1207.5192 [INSPIRE].
  57. [57]
    D. Harlow, Complementarity, not firewalls, arXiv:1207.6243.
  58. [58]
    B.D. Chowdhury and A. Puhm, Is Alice burning or fuzzing?, arXiv:1208.2026 [INSPIRE].

Copyright information

© SISSA, Trieste, Italy 2013

Authors and Affiliations

  • Ahmed Almheiri
    • 1
  • Donald Marolf
    • 1
    • 2
  • Joseph Polchinski
    • 2
    Email author
  • James Sully
    • 1
  1. 1.Department of PhysicsUniversity of CaliforniaSanta BarbaraU.S.A
  2. 2.Kavli Institute for Theoretical PhysicsUniversity of CaliforniaSanta BarbaraU.S.A

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