Origin of Hawking radiation: firewall or atmosphere?

Research Article


The Unruh vacuum not admitting any outgoing flux at the horizon implies that the origin of the outgoing Hawking radiation is the atmosphere of a near-horizon quantum region without resort to the firewall; however, the existence of the firewall of superplanckian excitations at the horizon can be supported by the infinite Tolman temperature at the horizon. In an exactly soluble model, we explicitly show that the firewall necessarily emerges out of the Unruh vacuum so that the Tolman temperature in the Unruh vacuum is divergent in essence due to the infinitely blueshifted negative ingoing flux crossing the horizon rather than the outgoing flux. We also show that the outgoing Hawking radiation in the Unruh vacuum indeed originates from the atmosphere, not just at the horizon, which is of no relevance to the infinite blueshift. Consequently, the firewall from the infinite Tolman temperature and the Hawking radiation from the atmosphere turn out to be compatible, once we waive the claim that the Hawking radiation in the Unruh vacuum originates from the infinitely blueshifted outgoing excitations at the horizon.


Boulware vacuum Israel-Hartle-Hawking vacuum Unruh vacuum Tolman temperature Stefan-Boltzmann law Firewall 



I have benefited from discussions with M. Eune, Y. Gim, and E. J. Son, and especially thank W. Israel for introducing his helpful paper for improvement of the present work.


  1. 1.
    Hawking, S.W.: Particle creation by black holes. Commun. Math. Phys. 43, 199–220 (1975)ADSMathSciNetCrossRefGoogle Scholar
  2. 2.
    Susskind, L., Thorlacius, L., Uglum, J.: The Stretched horizon and black hole complementarity. Phys. Rev. D 48, 3743–3761 (1993). [arXiv:hep-th/9306069]ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    Almheiri, A., Marolf, D., Polchinski, J., Sully, J.: Black holes: complementarity or firewalls? JHEP 02, 062 (2013). [arXiv:1207.3123]ADSMathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Braunstein, S.L., Pirandola, S., Zyczkowski, K.: Better late than never: information retrieval from black holes. Phys. Rev. Lett. 110, 101301 (2013). [arXiv:0907.1190]ADSCrossRefGoogle Scholar
  5. 5.
    Page, D.N.: Information in black hole radiation. Phys. Rev. Lett. 71, 3743–3746 (1993). [arXiv:hep-th/9306083]ADSMathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Bousso, R.: Complementarity is not enough. Phys. Rev. D 87, 124023 (2013). [arXiv:1207.5192]ADSCrossRefGoogle Scholar
  7. 7.
    Nomura, Y., Varela, J., Weinberg, S.J.: Complementarity endures: no firewall for an infalling observer. JHEP 03, 059 (2013). [arXiv:1207.6626]ADSCrossRefGoogle Scholar
  8. 8.
    Susskind, L.: Singularities, Firewalls, and Complementarity. [arXiv:1208.3445]
  9. 9.
    Hossenfelder, S.: Comment on the Black Hole Firewall. [arXiv:1210.5317]
  10. 10.
    Giddings, S.B.: Nonviolent information transfer from black holes: a field theory parametrization. Phys. Rev. D 88, 024018 (2013). [arXiv:1302.2613]ADSCrossRefGoogle Scholar
  11. 11.
    Almheiri, A., Marolf, D., Polchinski, J., Stanford, D., Sully, J.: An apologia for firewalls. JHEP 1309, 018 (2013). [arXiv:1304.6483]ADSCrossRefGoogle Scholar
  12. 12.
    Hutchinson, J., Stojkovic, D.: Icezones Instead of Firewalls: Extended Entanglement Beyond the Event Horizon and Unitary Evaporation of a Black Hole. [arXiv:1307.5861]
  13. 13.
    Freivogel, B.: Energy and information near Black hole horizons. JCAP 1407, 041 (2014). [arXiv:1401.5340]ADSCrossRefGoogle Scholar
  14. 14.
    Unruh, W.G.: Notes on black hole evaporation. Phys. Rev. D 14, 870 (1976)ADSCrossRefGoogle Scholar
  15. 15.
    Unruh, W.G.: Dumb holes and the effects of high frequencies on black hole evaporation. [arXiv:gr-qc/9409008]
  16. 16.
    Casadio, R., Mersini-Houghton, L.: Short distance signatures in cosmology: why not in black holes? Int. J. Mod. Phys. A 19, 1395–1412 (2004). [arXiv:hep-th/0208050]ADSMathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    Israel, W.: Shenanigans at the Black Hole Horizon: Pair Creation or Boulware Accretion? [arXiv:1504.02419]
  18. 18.
    Giddings, S.B.: Hawking radiation, the Stefan–Boltzmann law, and unitarization. Phys. Lett. B 754, 39–42 (2016). [arXiv:1511.08221]ADSCrossRefGoogle Scholar
  19. 19.
    Page, D.N.: Particle emission rates from a black hole: massless particles from an uncharged, nonrotating hole. Phys. Rev. D 13, 198–206 (1976)ADSCrossRefGoogle Scholar
  20. 20.
    Giddings, S.B.: Black hole information, unitarity, and nonlocality. Phys. Rev. D 74, 106005 (2006). [arXiv:hep-th/0605196]ADSMathSciNetCrossRefGoogle Scholar
  21. 21.
    Tolman, R.C.: On the weight of heat and thermal equilibrium in general relativity. Phys. Rev. 35, 904–924 (1930)ADSCrossRefMATHGoogle Scholar
  22. 22.
    Hartle, J.B., Hawking, S.W.: Path integral derivation of black hole radiance. Phys. Rev. D 13, 2188–2203 (1976)ADSCrossRefGoogle Scholar
  23. 23.
    Israel, W.: Thermo field dynamics of black holes. Phys. Lett. A 57, 107–110 (1976)ADSMathSciNetCrossRefGoogle Scholar
  24. 24.
    Gim, Y., Kim, W.: A quantal Tolman temperature. Eur. Phys. J. C 75, 549 (2015). [arXiv:1508.00312]ADSCrossRefGoogle Scholar
  25. 25.
    Deser, S., Duff, M.J., Isham, C.J.: Nonlocal conformal anomalies. Nucl. Phys. B 111, 45 (1976)ADSMathSciNetCrossRefMATHGoogle Scholar
  26. 26.
    Christensen, S.M., Fulling, S.A.: Trace anomalies and the Hawking effect. Phys. Rev. D 15, 2088–2104 (1977)ADSCrossRefGoogle Scholar
  27. 27.
    Wald, R.M.: Gravitation, thermodynamics, and quantum theory. Class. Quant. Grav. 16, A177–A190 (1999). [arXiv:gr-qc/9901033]ADSMathSciNetCrossRefMATHGoogle Scholar
  28. 28.
    Eune, M., Gim, Y., Kim, W.: Something special at the event horizon. Mod. Phys. Lett. A 29, 1450215 (2014). [arXiv:1401.3501]ADSMathSciNetCrossRefMATHGoogle Scholar
  29. 29.
    Callan Jr., C.G., Giddings, S.B., Harvey, J.A., Strominger, A.: Evanescent black holes. Phys. Rev. D 45, 1005–1009 (1992). [arXiv:hep-th/9111056]ADSMathSciNetCrossRefGoogle Scholar
  30. 30.
    Boulware, D.G.: Quantum field theory in Schwarzschild and Rindler spaces. Phys. Rev. D 11, 1404 (1975)ADSMathSciNetCrossRefGoogle Scholar
  31. 31.
    Boschi-Filho, H., Natividade, C.P.: Anomalies in curved space-time at finite temperature. Phys. Rev. D 46, 5458–5466 (1992)ADSMathSciNetCrossRefMATHGoogle Scholar
  32. 32.
    Visser, M.: Gravitational vacuum polarization. 3: energy conditions in the (\(1+1\)) Schwarzschild space-time. Phys. Rev. D 54, 5123–5128 (1996). [arXiv:gr-qc/9604009]ADSMathSciNetCrossRefGoogle Scholar
  33. 33.
    Singleton, D., Wilburn, S.: Hawking radiation, unruh radiation and the equivalence principle. Phys. Rev. Lett. 107, 081102 (2011). [arXiv:1102.5564]ADSCrossRefGoogle Scholar
  34. 34.
    Hawking, S.W.: Information preservation and weather forecasting for black holes. [arXiv:1401.5761]
  35. 35.
    Visser, M.: Physical observability of horizons. Phys. Rev. D 90, 127502 (2014). [arXiv:1407.7295]ADSCrossRefGoogle Scholar
  36. 36.
    Mersini-Houghton, L.: Backreaction of Hawking radiation on a gravitationally collapsing star I: black holes? Phys. Lett. B 738, 61–67 (2014). [arXiv:1406.1525]ADSCrossRefGoogle Scholar
  37. 37.
    Mersini-Houghton, L., Pfeiffer, H.P.: Back-Reaction of the Hawking Radiation Flux on a Gravitationally Collapsing Star II. [arXiv:1409.1837]
  38. 38.
    Nomura, Y., Salzetta, N.: Why Firewalls Need Not Exist. [arXiv:1602.07673]

Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Department of PhysicsSogang UniversitySeoulSouth Korea

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