Skip to main content
SpringerLink
Log in

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

  • Published:
Journal of High Energy Physics Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. S.W. Hawking, Black hole explosions, Nature 248 (1974) 30 [SPIRES].

    Article  ADS  MATH  Google Scholar 

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

    Article  ADS  MathSciNet  MATH  Google Scholar 

  3. W.G. Unruh, Notes on black hole evaporation, Phys. Rev. D 14 (1976) 870 [SPIRES].

    ADS  Google Scholar 

  4. F.J. Tipler, Do black holes really evaporate thermally?, Phys. Rev. Lett. 45 (1980) 949 [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  5. P. Hajicek and W. Israel, What, no black hole evaporation?, Phys. Lett. A 80 (1980) 9.

    Article  ADS  MathSciNet  Google Scholar 

  6. J.M. Bardeen, Black holes do evaporate thermally, Phys. Rev. Lett. 46 (1981) 382 [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  7. J.W. York Jr., Dynamical origin of black hole radiance, Phys. Rev. D 28 (1983) 2929 [SPIRES].

    ADS  MathSciNet  MATH  Google Scholar 

  8. P. Hajicek, Origin of Hawking radiation, Phys. Rev. D 36 (1987) 1065 [SPIRES].

    ADS  MathSciNet  Google Scholar 

  9. P.G. Grove, Observations on particle creation by static gravitational fields, Class. Quant. Grav. 7 (1990) 1353 [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  10. M. Visser, Hawking radiation without black hole entropy, Phys. Rev. Lett. 80 (1998) 3436 [gr-qc/9712016] [SPIRES].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  11. M. Visser, Acoustic black holes: horizons, ergospheres and Hawking radiation, Class. Quant. Grav. 15 (1998) 1767 [gr-qc/9712010] [SPIRES].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  12. M. Visser, Essential and inessential features of Hawking radiation, Int. J. Mod. Phys. D 12 (2003) 649 [hep-th/0106111] [SPIRES].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  13. J. Lindesay and P. Sheldon, Penrose diagram for a transient black hole, Class. Quant. Grav. 27 (2010) 215015 [arXiv:1005.4449] [SPIRES].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  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. M.K. Parikh and F. Wilczek, Hawking radiation as tunneling, Phys. Rev. Lett. 85 (2000) 5042 [hep-th/9907001] [SPIRES].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  16. M.K. Parikh, Energy conservation and Hawking radiation, hep-th/0402166 [SPIRES].

  17. M.K. Parikh, A secret tunnel through the horizon, Int. J. Mod. Phys. D 13 (2004) 2351 [hep-th/0405160] [SPIRES].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  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].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  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].

    Article  ADS  MathSciNet  Google Scholar 

  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].

    Article  ADS  MATH  Google Scholar 

  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].

    Article  ADS  MathSciNet  Google Scholar 

  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].

    Article  ADS  MathSciNet  Google Scholar 

  23. T. Clifton, Properties of black hole radiation from tunnelling, Class. Quant. Grav. 25 (2008) 175022 [arXiv:0804.2635] [SPIRES].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  24. R. Banerjee and B.R. Majhi, Hawking black body spectrum from tunneling mechanism, Phys. Lett. B 675 (2009) 243 [arXiv:0903.0250] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  25. T. Padmanabhan, Gravity and the thermodynamics of horizons, Phys. Rept. 406 (2005) 49 [gr-qc/0311036] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  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].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  27. M. Visser, Dirty black holes: thermodynamics and horizon structure, Phys. Rev. D 46 (1992) 2445 [hep-th/9203057] [SPIRES].

    ADS  MathSciNet  Google Scholar 

  28. T.A. Roman and P.G. Bergmann, Stellar collapse without singularities?, Phys. Rev. D 28 (1983) 1265 [SPIRES].

    ADS  MathSciNet  Google Scholar 

  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].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  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].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  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].

    ADS  Google Scholar 

  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. 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].

    Article  ADS  MATH  Google Scholar 

  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).

  35. S.W. Hawking, Information loss in black holes, Phys. Rev. D 72 (2005) 084013 [hep-th/0507171] [SPIRES].

    ADS  MathSciNet  Google Scholar 

  36. A. Ashtekar and M. Bojowald, Black hole evaporation: a paradigm, Class. Quant. Grav. 22 (2005) 3349 [gr-qc/0504029] [SPIRES].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  37. S.A. Hayward, The disinformation problem for black holes, gr-qc/0504037, gr-qc/0504038 [SPIRES].

  38. S.A. Hayward, Formation and evaporation of regular black holes, Phys. Rev. Lett. 96 (2006) 031103 [gr-qc/0506126] [SPIRES].

    Article  ADS  Google Scholar 

  39. M. Visser, Acoustic propagation in fluids: an unexpected example of Lorentzian geometry, gr-qc/9311028 [SPIRES].

  40. C. Barceló, S. Liberati and M. Visser, Analogue gravity, Living Rev. Rel. 8 (2005) 12 [gr-qc/0505065] [SPIRES].

    Article  MATH  Google Scholar 

  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. 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. C. Barceló, S. Liberati, S. Sonego and M. Visser, Causal structure of acoustic spacetimes, New J. Phys. 6 (2004) 186 [gr-qc/0408022] [SPIRES].

    Article  ADS  Google Scholar 

  44. J. Macher and R. Parentani, Black-hole radiation in Bose-Einstein condensates, Phys. Rev. A 80 (2009) 043601 [arXiv:0905.3634] [SPIRES].

    Article  ADS  Google Scholar 

  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].

    ADS  Google Scholar 

  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].

    Article  ADS  MathSciNet  Google Scholar 

  47. J.D. Barrow, Sudden future singularities, Class. Quant. Grav. 21 (2004) L79 [gr-qc/0403084] [SPIRES].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  48. J.D. Barrow, More general sudden singularities, Class. Quant. Grav. 21 (2004) 5619 [gr-qc/0409062] [SPIRES].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  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].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  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].

    ADS  MathSciNet  Google Scholar 

  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].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  52. N.D. Birrell and P.C.W. Davies, Quantum fields in curved space, Cambridge University Press, Cambridge U.K. (1982) [SPIRES].

    Book  MATH  Google Scholar 

  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].

    ADS  MathSciNet  MATH  Google Scholar 

  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].

    ADS  MathSciNet  Google Scholar 

  55. W.G. Unruh, Where are the particles created in black hole evaporation?, PoS(QG-Ph)039 [SPIRES].

  56. A.B. Nielsen and M. Visser, Production and decay of evolving horizons, Class. Quant. Grav. 23 (2006) 4637 [gr-qc/0510083] [SPIRES].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  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].

    ADS  Google Scholar 

  58. G. Abreu and M. Visser, Tolman mass, generalized surface gravity, and entropy bounds, Phys. Rev. Lett. 105 (2010) 041302 [arXiv:1005.1132] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Instituto de Astrofísica de Andalucía, IAA-CSIC, Glorieta de Astronomía, 18008, Granada, Spain

    Carlos Barceló

  2. SISSA/International School for Advanced Studies, and INFN, Sezione di Trieste, Via Bonomea 265, 34136, Trieste, Italy

    Stefano Liberati

  3. Dipartimento di Fisica, Università di Udine, Via delle Scienze 208, 33100, Udine, Italy

    Sebastiano Sonego

  4. School of Mathematics, Statistics and Operations Research, Victoria University of Wellington, Wellington, New Zealand

    Matt Visser

Authors
  1. Carlos Barceló
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Stefano Liberati
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sebastiano Sonego
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Matt Visser
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Matt Visser.

Additional information

ArXiv ePrint: 1011.5911

Rights and permissions

Reprints and permissions

About this article

Cite this article

Barceló, C., Liberati, S., Sonego, S. et al. Hawking-like radiation from evolving black holes and compact horizonless objects. J. High Energ. Phys. 2011, 3 (2011). https://doi.org/10.1007/JHEP02(2011)003

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP02(2011)003

Keywords

Search

Navigation