Advertisement

Journal of High Energy Physics

, Volume 2011, Issue 2, pp 1–30 | Cite as

Hawking-like radiation from evolving black holes and compact horizonless objects

  • Carlos Barceló
  • Stefano Liberati
  • Sebastiano Sonego
  • Matt Visser
Article

Abstract

Usually, Hawking radiation is derived assuming (i) that a future eternal event horizon forms, and (ii) that the subsequent exterior geometry is static. However, one may be interested in either considering quasi-black holes (objects in an ever-lasting state of approach to horizon formation, but never quite forming one), where (i) fails, or, following the evolution of a black hole during evaporation, where (ii) fails. We shall verify that as long as one has an approximately exponential relation between the affine parameters on the null generators of past and future null infinity, then subject to a suitable adiabatic condition being satisfied, a Planck-distributed flux of Hawking-like radiation will occur. This happens both for the case of an evaporating black hole, as well as for the more dramatic case of a collapsing object for which no horizon has yet formed (or even will ever form). In this article we shall cast the previous statement in a more precise and quantitative form, and subsequently provide several explicit calculations to show how the time-dependent Bogoliubov coefficients can be calculated.

Keywords

Black Holes Models of Quantum Gravity 2D Gravity Spacetime Singularities 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    S.W. Hawking, Black hole explosions, Nature 248 (1974) 30 [SPIRES].ADSCrossRefGoogle Scholar
  2. [2]
    S.W. Hawking, Particle creation by black holes, Commun. Math. Phys. 43 (1975) 199 [Erratum ibid. 46 (1976) 206] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  3. [3]
    W.G. Unruh, Notes on black hole evaporation, Phys. Rev. D 14 (1976) 870 [SPIRES].ADSGoogle Scholar
  4. [4]
    F.J. Tipler, Do black holes really evaporate thermally?, Phys. Rev. Lett. 45 (1980) 949 [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  5. [5]
    P. Hajicek and W. Israel, What, no black hole evaporation?, Phys. Lett. A 80 (1980) 9.MathSciNetADSGoogle Scholar
  6. [6]
    J.M. Bardeen, Black holes do evaporate thermally, Phys. Rev. Lett. 46 (1981) 382 [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  7. [7]
    J.W. York Jr., Dynamical origin of black hole radiance, Phys. Rev. D 28 (1983) 2929 [SPIRES].MathSciNetADSGoogle Scholar
  8. [8]
    P. Hajicek, Origin of Hawking radiation, Phys. Rev. D 36 (1987) 1065 [SPIRES].MathSciNetADSGoogle Scholar
  9. [9]
    P.G. Grove, Observations on particle creation by static gravitational fields, Class. Quant. Grav. 7 (1990) 1353 [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  10. [10]
    M. Visser, Hawking radiation without black hole entropy, Phys. Rev. Lett. 80 (1998) 3436 [gr-qc/9712016] [SPIRES].MathSciNetADSMATHCrossRefGoogle Scholar
  11. [11]
    M. Visser, Acoustic black holes: horizons, ergospheres and Hawking radiation, Class. Quant. Grav. 15 (1998) 1767 [gr-qc/9712010] [SPIRES].MathSciNetADSMATHCrossRefGoogle Scholar
  12. [12]
    M. Visser, Essential and inessential features of Hawking radiation, Int. J. Mod. Phys. D 12 (2003) 649 [hep-th/0106111] [SPIRES].MathSciNetADSGoogle Scholar
  13. [13]
    J. Lindesay and P. Sheldon, Penrose diagram for a transient black hole, Class. Quant. Grav. 27 (2010) 215015 [arXiv:1005.4449] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  14. [14]
    G.E. Volovik, Simulation of Panlevé-Gullstrand black hole in thin 3 He-A film, Pisma ZhETF 69 (1999) 662 [JETP Lett. 69 (1999) 705] [gr-qc/9901077] [SPIRES].Google Scholar
  15. [15]
    M.K. Parikh and F. Wilczek, Hawking radiation as tunneling, Phys. Rev. Lett. 85 (2000) 5042 [hep-th/9907001] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  16. [16]
    M.K. Parikh, Energy conservation and Hawking radiation, hep-th/0402166 [SPIRES].
  17. [17]
    M.K. Parikh, A secret tunnel through the horizon, Int. J. Mod. Phys. D 13 (2004) 2351 [hep-th/0405160] [SPIRES].MathSciNetADSGoogle Scholar
  18. [18]
    S. Shankaranarayanan, T. Padmanabhan and K. Srinivasan, Hawking radiation in different coordinate settings: complex paths approach, Class. Quant. Grav. 19 (2002) 2671 [gr-qc/0010042] [SPIRES].MathSciNetADSMATHCrossRefGoogle Scholar
  19. [19]
    M. Angheben, M. Nadalini, L. Vanzo and S. Zerbini, Hawking radiation as tunneling for extremal and rotating black holes, JHEP 05 (2005) 014 [hep-th/0503081] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  20. [20]
    A.J.M. Medved and E.C. Vagenas, On Hawking radiation as tunneling with back-reaction, Mod. Phys. Lett. A 20 (2005) 2449 [gr-qc/0504113] [SPIRES].ADSGoogle Scholar
  21. [21]
    M. Arzano, A.J.M. Medved and E.C. Vagenas, Hawking radiation as tunneling through the quantum horizon, JHEP 09 (2005) 037 [hep-th/0505266] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  22. [22]
    S.P. Robinson and F. Wilczek, A relationship between Hawking radiation and gravitational anomalies, Phys. Rev. Lett. 95 (2005) 011303 [gr-qc/0502074] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  23. [23]
    T. Clifton, Properties of black hole radiation from tunnelling, Class. Quant. Grav. 25 (2008) 175022 [arXiv:0804.2635] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  24. [24]
    R. Banerjee and B.R. Majhi, Hawking black body spectrum from tunneling mechanism, Phys. Lett. B 675 (2009) 243 [arXiv:0903.0250] [SPIRES].MathSciNetADSGoogle Scholar
  25. [25]
    T. Padmanabhan, Gravity and the thermodynamics of horizons, Phys. Rept. 406 (2005) 49 [gr-qc/0311036] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  26. [26]
    S. Hossenfelder, D.J. Schwarz and W. Greiner, Particle production in time-dependent gravitational fields: the expanding mass shell, Class. Quant. Grav. 20 (2003) 2337 [gr-qc/0210110] [SPIRES].MathSciNetADSMATHCrossRefGoogle Scholar
  27. [27]
    M. Visser, Dirty black holes: thermodynamics and horizon structure, Phys. Rev. D 46 (1992) 2445 [hep-th/9203057] [SPIRES].MathSciNetADSGoogle Scholar
  28. [28]
    T.A. Roman and P.G. Bergmann, Stellar collapse without singularities?, Phys. Rev. D 28 (1983) 1265 [SPIRES].MathSciNetADSGoogle Scholar
  29. [29]
    C. Barceló, S. Liberati, S. Sonego and M. Visser, Quasi-particle creation by analogue black holes, Class. Quant. Grav. 23 (2006) 5341 [gr-qc/0604058] [SPIRES].ADSMATHCrossRefGoogle Scholar
  30. [30]
    C. Barceló, S. Liberati, S. Sonego and M. Visser, Hawking-like radiation does not require a trapped region, Phys. Rev. Lett. 97 (2006) 171301 [gr-qc/0607008] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  31. [31]
    C. Barceló, S. Liberati, S. Sonego and M. Visser, Fate of gravitational collapse in semiclassical gravity, Phys. Rev. D 77 (2008) 044032 [arXiv:0712.1130] [SPIRES].ADSGoogle Scholar
  32. [32]
    M. Visser, C. Barceló, S. Liberati and S. Sonego, Small, dark and heavy: but is it a black hole?, PoS(BHs, GR and Strings)010 [arXiv:0902.0346] [SPIRES].
  33. [33]
    C. Barceló, S. Liberati, S. Sonego and M. Visser, Revisiting the semiclassical gravity scenario for gravitational collapse, AIP Conf. Proc. 1122 (2009) 99 [arXiv:0909.4157] [SPIRES].ADSCrossRefGoogle Scholar
  34. [34]
    S.W. Hawking, abstract of The information paradox for black holes: “The way the information gets out seems to be that a true event horizon never forms, just an apparent horizon.”, talk given at GR17, Dublin, Ireland (2004).Google Scholar
  35. [35]
    S.W. Hawking, Information loss in black holes, Phys. Rev. D 72 (2005) 084013 [hep-th/0507171] [SPIRES].MathSciNetADSGoogle Scholar
  36. [36]
    A. Ashtekar and M. Bojowald, Black hole evaporation: a paradigm, Class. Quant. Grav. 22 (2005) 3349 [gr-qc/0504029] [SPIRES].MathSciNetADSMATHCrossRefGoogle Scholar
  37. [37]
    S.A. Hayward, The disinformation problem for black holes, gr-qc/0504037, gr-qc/0504038 [SPIRES].
  38. [38]
    S.A. Hayward, Formation and evaporation of regular black holes, Phys. Rev. Lett. 96 (2006) 031103 [gr-qc/0506126] [SPIRES].ADSCrossRefGoogle Scholar
  39. [39]
    M. Visser, Acoustic propagation in fluids: an unexpected example of Lorentzian geometry, gr-qc/9311028 [SPIRES].
  40. [40]
    C. Barceló, S. Liberati and M. Visser, Analogue gravity, Living Rev. Rel. 8 (2005) 12 [gr-qc/0505065] [SPIRES].Google Scholar
  41. [41]
    C. Barceló, S. Liberati, S. Sonego and M. Visser, Minimal conditions for the existence of a Hawking-like flux, arXiv:1011.5593 [SPIRES].
  42. [42]
    B.L. Hu, Hawking-Unruh thermal radiance as relativistic exponential scaling of quantum noise, in Thermal field theory and applications, Y.X. Gui, F.C. Khanna and Z.B. Su eds., World Scientific, Singapore (1996), pg. 249–260 [gr-qc/9606073] [SPIRES].Google Scholar
  43. [43]
    C. Barceló, S. Liberati, S. Sonego and M. Visser, Causal structure of acoustic spacetimes, New J. Phys. 6 (2004) 186 [gr-qc/0408022] [SPIRES].ADSCrossRefGoogle Scholar
  44. [44]
    J. Macher and R. Parentani, Black-hole radiation in Bose-Einstein condensates, Phys. Rev. A 80 (2009) 043601 [arXiv:0905.3634] [SPIRES].ADSGoogle Scholar
  45. [45]
    R. Brout, S. Massar, R. Parentani and P. Spindel, Hawking radiation without transplanckian frequencies, Phys. Rev. D 52 (1995) 4559 [hep-th/9506121] [SPIRES].ADSGoogle Scholar
  46. [46]
    R. Brout, S. Massar, R. Parentani and P. Spindel, A primer for black hole quantum physics, Phys. Rept. 260 (1995) 329 [arXiv:0710.4345] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  47. [47]
    J.D. Barrow, Sudden future singularities, Class. Quant. Grav. 21 (2004) L79 [gr-qc/0403084] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  48. [48]
    J.D. Barrow, More general sudden singularities, Class. Quant. Grav. 21 (2004) 5619 [gr-qc/0409062] [SPIRES].MathSciNetADSMATHCrossRefGoogle Scholar
  49. [49]
    C. Cattoën and M. Visser, Necessary and sufficient conditions for big bangs, bounces, crunches, rips, sudden singularities and extremality events, Class. Quant. Grav. 22 (2005) 4913 [gr-qc/0508045] [SPIRES].ADSMATHCrossRefGoogle Scholar
  50. [50]
    C.G. Callan Jr., S.B. Giddings, J.A. Harvey and A. Strominger, Evanescent black holes, Phys. Rev. D 45 (1992) 1005 [hep-th/9111056] [SPIRES].MathSciNetADSGoogle Scholar
  51. [51]
    S.W. Hawking and J.M. Stewart, Naked and thunderbolt singularities in black hole evaporation, Nucl. Phys. B 400 (1993) 393 [hep-th/9207105] [SPIRES].MathSciNetADSCrossRefGoogle Scholar
  52. [52]
    N.D. Birrell and P.C.W. Davies, Quantum fields in curved space, Cambridge University Press, Cambridge U.K. (1982) [SPIRES].MATHGoogle Scholar
  53. [53]
    C. Barceló, L.J. Garay and G. Jannes, Sensitivity of Hawking radiation to superluminal dispersion relations, Phys. Rev. D 79 (2009) 024016 [arXiv:0807.4147] [SPIRES].ADSGoogle Scholar
  54. [54]
    R. Schützhold and W.G. Unruh, On the origin of the particles in black hole evaporation, Phys. Rev. D 78 (2008) 041504 [arXiv:0804.1686] [SPIRES].ADSGoogle Scholar
  55. [55]
    W.G. Unruh, Where are the particles created in black hole evaporation?, PoS(QG-Ph)039 [SPIRES].
  56. [56]
    A.B. Nielsen and M. Visser, Production and decay of evolving horizons, Class. Quant. Grav. 23 (2006) 4637 [gr-qc/0510083] [SPIRES].MathSciNetADSMATHCrossRefGoogle Scholar
  57. [57]
    G. Abreu and M. Visser, Kodama time: geometrically preferred foliations of spherically symmetric spacetimes, Phys. Rev. D 82 (2010) 044027 [arXiv:1004.1456] [SPIRES].ADSGoogle Scholar
  58. [58]
    G. Abreu and M. Visser, Tolman mass, generalized surface gravity, and entropy bounds, Phys. Rev. Lett. 105 (2010) 041302 [arXiv:1005.1132] [SPIRES].MathSciNetADSCrossRefGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2011

Authors and Affiliations

  • Carlos Barceló
    • 1
  • Stefano Liberati
    • 2
  • Sebastiano Sonego
    • 3
  • Matt Visser
    • 4
  1. 1.Instituto de Astrofísica de Andalucía, IAA-CSICGranadaSpain
  2. 2.SISSA/International School for Advanced Studies, and INFNSezione di TriesteTriesteItaly
  3. 3.Dipartimento di FisicaUniversità di UdineUdineItaly
  4. 4.School of Mathematics, Statistics and Operations ResearchVictoria University of WellingtonWellingtonNew Zealand

Personalised recommendations