Download PDF

Soft hair of dynamical black hole and Hawking radiation

Open Access
Regular Article - Theoretical Physics
First Online:
Received:
Accepted:
  • 21 Downloads

Abstract

Soft hair of black hole has been proposed recently to play an important role in the resolution of the black hole information paradox. Recent work has emphasized that the soft modes cannot affect the black hole S-matrix due to Weinberg soft theorems. However as soft hair is generated by supertranslation of geometry which involves an angular dependent shift of time, it must have non-trivial quantum effects. We consider supertranslation of the Vaidya black hole and construct a non-spherical symmetric dynamical spacetime with soft hair. We show that this spacetime admits a trapping horizon and is a dynamical black hole. We find that Hawking radiation is emitted from the trapping horizon of the dynamical black hole. The Hawking radiation has a spectrum which depends on the soft hair of the black hole and this is consistent with the factorization property of the black hole S-matrix.

Keywords

Black Holes Space-Time Symmetries 
Download to read the full article text

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

References

  1. [1]
    J.D. Bekenstein, Black holes and entropy, Phys. Rev. D 7 (1973) 2333 [INSPIRE].ADSMathSciNetMATHGoogle Scholar
  2. [2]
    S.W. Hawking, Black hole explosions, Nature 248 (1974) 30 [INSPIRE].ADSCrossRefMATHGoogle Scholar
  3. [3]
    S.W. Hawking, Particle Creation by Black Holes, Commun. Math. Phys. 43 (1975) 199 [Erratum ibid. 46 (1976) 206] [INSPIRE].
  4. [4]
    R.M. Wald, Black hole entropy is the Noether charge, Phys. Rev. D 48 (1993) R3427 [gr-qc/9307038] [INSPIRE].
  5. [5]
    P.T. Chrusciel, J. Lopes Costa and M. Heusler, Stationary Black Holes: Uniqueness and Beyond, Living Rev. Rel. 15 (2012) 7 [arXiv:1205.6112] [INSPIRE].CrossRefMATHGoogle Scholar
  6. [6]
    S.D. Mathur, The Information paradox: A Pedagogical introduction, Class. Quant. Grav. 26 (2009) 224001 [arXiv:0909.1038] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  7. [7]
    D. Marolf, The Black Hole information problem: past, present and future, Rept. Prog. Phys. 80 (2017) 092001 [arXiv:1703.02143] [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    A. Strominger, On BMS Invariance of Gravitational Scattering, JHEP 07 (2014) 152 [arXiv:1312.2229] [INSPIRE].ADSCrossRefGoogle Scholar
  9. [9]
    T. He, V. Lysov, P. Mitra and A. Strominger, BMS supertranslations and Weinberg’s soft graviton theorem, JHEP 05 (2015) 151 [arXiv:1401.7026] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  10. [10]
    F. Cachazo and A. Strominger, Evidence for a New Soft Graviton Theorem, arXiv:1404.4091 [INSPIRE].
  11. [11]
    D. Kapec, V. Lysov, S. Pasterski and A. Strominger, Semiclassical Virasoro symmetry of the quantum gravity \( \mathcal{S} \) -matrix, JHEP 08 (2014) 058 [arXiv:1406.3312] [INSPIRE].
  12. [12]
    A. Strominger and A. Zhiboedov, Gravitational Memory, BMS Supertranslations and Soft Theorems, JHEP 01 (2016) 086 [arXiv:1411.5745] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  13. [13]
    A. Strominger, Lectures on the Infrared Structure of Gravity and Gauge Theory, arXiv:1703.05448 [INSPIRE].
  14. [14]
    S.W. Hawking, M.J. Perry and A. Strominger, Soft Hair on Black Holes, Phys. Rev. Lett. 116 (2016) 231301 [arXiv:1601.00921] [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    S.W. Hawking, M.J. Perry and A. Strominger, Superrotation Charge and Supertranslation Hair on Black Holes, JHEP 05 (2017) 161 [arXiv:1611.09175] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  16. [16]
    A. Strominger, Black Hole Information Revisited, arXiv:1706.07143 [INSPIRE].
  17. [17]
    H. Bondi, M.G.J. van der Burg and A.W.K. Metzner, Gravitational waves in general relativity. 7. Waves from axisymmetric isolated systems, Proc. Roy. Soc. Lond. A 269 (1962) 21 [INSPIRE].
  18. [18]
    R.K. Sachs, Gravitational waves in general relativity. 8. Waves in asymptotically flat space-times, Proc. Roy. Soc. Lond. A 270 (1962) 103 [INSPIRE].
  19. [19]
    R.L. Arnowitt, S. Deser and C.W. Misner, The Dynamics of general relativity, Gen. Rel. Grav. 40 (2008) 1997 [gr-qc/0405109] [INSPIRE].
  20. [20]
    R.M. Wald and A. Zoupas, A General definition of ‘conserved quantities’ in general relativity and other theories of gravity, Phys. Rev. D 61 (2000) 084027 [gr-qc/9911095] [INSPIRE].
  21. [21]
    G. Barnich and C. Troessaert, BMS charge algebra, JHEP 12 (2011) 105 [arXiv:1106.0213] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  22. [22]
    Ya.B. Zel’dovich and A.G. Polnarev, Radiation of gravitational waves by a cluster of superdense stars, Sov. Astron. 18 (1974) 17.Google Scholar
  23. [23]
    V.B. Braginsky and L.P. Grishchuk, Kinematic Resonance and Memory Effect in Free Mass Gravitational Antennas, Sov. Phys. JETP 62 (1985) 427 [INSPIRE].Google Scholar
  24. [24]
    V.B. Braginsky and K.S. Thorne, Gravitational-wave bursts with memory and experimental prospects, Nature 327 (1987) 123.ADSCrossRefGoogle Scholar
  25. [25]
    L. Blanchet and T. Damour, Hereditary effects in gravitational radiation, Phys. Rev. D 46 (1992) 4304 [INSPIRE].ADSMathSciNetGoogle Scholar
  26. [26]
    M. Mirbabayi and M. Porrati, Dressed Hard States and Black Hole Soft Hair, Phys. Rev. Lett. 117 (2016) 211301 [arXiv:1607.03120] [INSPIRE].ADSCrossRefGoogle Scholar
  27. [27]
    B. Gabai and A. Sever, Large gauge symmetries and asymptotic states in QED, JHEP 12 (2016) 095 [arXiv:1607.08599] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  28. [28]
    C. Gomez and M. Panchenko, Asymptotic dynamics, large gauge transformations and infrared symmetries, arXiv:1608.05630 [INSPIRE].
  29. [29]
    R. Bousso and M. Porrati, Soft Hair as a Soft Wig, Class. Quant. Grav. 34 (2017) 204001 [arXiv:1706.00436] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  30. [30]
    W. Donnelly and S.B. Giddings, How is quantum information localized in gravity?, Phys. Rev. D 96 (2017) 086013 [arXiv:1706.03104] [INSPIRE].ADSGoogle Scholar
  31. [31]
    K. Srinivasan and T. Padmanabhan, Particle production and complex path analysis, Phys. Rev. D 60 (1999) 024007 [gr-qc/9812028] [INSPIRE].
  32. [32]
    M.K. Parikh and F. Wilczek, Hawking radiation as tunneling, Phys. Rev. Lett. 85 (2000) 5042 [hep-th/9907001] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  33. [33]
    J.-i. Koga, Asymptotic symmetries on Killing horizons, Phys. Rev. D 64 (2001) 124012 [gr-qc/0107096] [INSPIRE].
  34. [34]
    M. Hotta, K. Sasaki and T. Sasaki, Diffeomorphism on horizon as an asymptotic isometry of Schwarzschild black hole, Class. Quant. Grav. 18 (2001) 1823 [gr-qc/0011043] [INSPIRE].
  35. [35]
    L. Donnay, G. Giribet, H.A. Gonzalez and M. Pino, Supertranslations and Superrotations at the Black Hole Horizon, Phys. Rev. Lett. 116 (2016) 091101 [arXiv:1511.08687] [INSPIRE].ADSCrossRefGoogle Scholar
  36. [36]
    A. Averin, G. Dvali, C. Gomez and D. Lüst, Gravitational Black Hole Hair from Event Horizon Supertranslations, JHEP 06 (2016) 088 [arXiv:1601.03725] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  37. [37]
    C. Eling and Y. Oz, On the Membrane Paradigm and Spontaneous Breaking of Horizon BMS Symmetries, JHEP 07 (2016) 065 [arXiv:1605.00183] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  38. [38]
    L. Donnay, G. Giribet, H.A. González and M. Pino, Extended Symmetries at the Black Hole Horizon, JHEP 09 (2016) 100 [arXiv:1607.05703] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  39. [39]
    R.-G. Cai, S.-M. Ruan and Y.-L. Zhang, Horizon supertranslation and degenerate black hole solutions, JHEP 09 (2016) 163 [arXiv:1609.01056] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  40. [40]
    H. Afshar, D. Grumiller, W. Merbis, A. Perez, D. Tempo and R. Troncoso, Soft hairy horizons in three spacetime dimensions, Phys. Rev. D 95 (2017) 106005 [arXiv:1611.09783] [INSPIRE].ADSGoogle Scholar
  41. [41]
    M. Hotta, J. Trevison and K. Yamaguchi, Gravitational Memory Charges of Supertranslation and Superrotation on Rindler Horizons, Phys. Rev. D 94 (2016) 083001 [arXiv:1606.02443] [INSPIRE].ADSMathSciNetGoogle Scholar
  42. [42]
    S. Kolekar and J. Louko, Gravitational memory for uniformly accelerated observers, Phys. Rev. D 96 (2017) 024054 [arXiv:1703.10619] [INSPIRE].ADSGoogle Scholar
  43. [43]
    S. Kolekar and J. Louko, Quantum memory for Rindler supertranslations, arXiv:1709.07355 [INSPIRE].
  44. [44]
    G. Barnich and C. Troessaert, Symmetries of asymptotically flat 4 dimensional spacetimes at null infinity revisited, Phys. Rev. Lett. 105 (2010) 111103 [arXiv:0909.2617] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  45. [45]
    R. Sachs, Asymptotic symmetries in gravitational theory, Phys. Rev. 128 (1962) 2851 [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  46. [46]
    S.A. Hayward, General laws of black hole dynamics, Phys. Rev. D 49 (1994) 6467 [INSPIRE].ADSMathSciNetGoogle Scholar
  47. [47]
    A. Ashtekar, C. Beetle and S. Fairhurst, Isolated horizons: A generalization of black hole mechanics, Class. Quant. Grav. 16 (1999) L1 [gr-qc/9812065] [INSPIRE].
  48. [48]
    A. Ashtekar and B. Krishnan, Dynamical horizons: Energy, angular momentum, fluxes and balance laws, Phys. Rev. Lett. 89 (2002) 261101 [gr-qc/0207080] [INSPIRE].
  49. [49]
    I. Booth and S. Fairhurst, The First law for slowly evolving horizons, Phys. Rev. Lett. 92 (2004) 011102 [gr-qc/0307087] [INSPIRE].
  50. [50]
    A. Ashtekar and B. Krishnan, Isolated and dynamical horizons and their applications, Living Rev. Rel. 7 (2004) 10 [gr-qc/0407042] [INSPIRE].
  51. [51]
    I. Booth, Black hole boundaries, Can. J. Phys. 83 (2005) 1073 [gr-qc/0508107] [INSPIRE].
  52. [52]
    S.A. Hayward, Dynamics of black holes, arXiv:0810.0923 [INSPIRE].
  53. [53]
    E. Gourgoulhon and J.L. Jaramillo, New theoretical approaches to black holes, New Astron. Rev. 51 (2008) 791 [arXiv:0803.2944] [INSPIRE].ADSCrossRefGoogle Scholar
  54. [54]
    V. Faraoni, Evolving black hole horizons in General Relativity and alternative gravity, Galaxies 1 (2013) 114 [arXiv:1309.4915] [INSPIRE].ADSCrossRefGoogle Scholar
  55. [55]
    R.M. Wald, General Relativity, University of Chicago Press (1984).Google Scholar
  56. [56]
    A.B. Nielsen and J.H. Yoon, Dynamical surface gravity, Class. Quant. Grav. 25 (2008) 085010 [arXiv:0711.1445] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  57. [57]
    L. Vanzo, G. Acquaviva and R. Di Criscienzo, Tunnelling Methods and Hawking’s radiation: achievements and prospects, Class. Quant. Grav. 28 (2011) 183001 [arXiv:1106.4153] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  58. [58]
    H. Kodama, Conserved Energy Flux for the Spherically Symmetric System and the Back Reaction Problem in the Black Hole Evaporation, Prog. Theor. Phys. 63 (1980) 1217 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  59. [59]
    S.A. Hayward, Unified first law of black hole dynamics and relativistic thermodynamics, Class. Quant. Grav. 15 (1998) 3147 [gr-qc/9710089] [INSPIRE].
  60. [60]
    R. Kerner and R.B. Mann, Tunnelling, temperature and Taub-NUT black holes, Phys. Rev. D 73 (2006) 104010 [gr-qc/0603019] [INSPIRE].
  61. [61]
    M. Visser, Essential and inessential features of Hawking radiation, Int. J. Mod. Phys. D 12 (2003) 649 [hep-th/0106111] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  62. [62]
    R. Di Criscienzo, M. Nadalini, L. Vanzo, S. Zerbini and G. Zoccatelli, On the Hawking radiation as tunneling for a class of dynamical black holes, Phys. Lett. B 657 (2007) 107 [arXiv:0707.4425] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  63. [63]
    S.A. Hayward, R. Di Criscienzo, L. Vanzo, M. Nadalini and S. Zerbini, Local Hawking temperature for dynamical black holes, Class. Quant. Grav. 26 (2009) 062001 [arXiv:0806.0014] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  64. [64]
    J.B. Hartle and S.W. Hawking, Path Integral Derivation of Black Hole Radiance, Phys. Rev. D 13 (1976) 2188 [INSPIRE].ADSGoogle Scholar
  65. [65]
    B. Chatterjee, A. Ghosh and P. Mitra, Tunnelling from black holes in the Hamilton Jacobi approach, Phys. Lett. B 661 (2008) 307 [arXiv:0704.1746] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  66. [66]
    S. Stotyn, K. Schleich and D. Witt, Observer Dependent Horizon Temperatures: A Coordinate-Free Formulation of Hawking Radiation as Tunneling, Class. Quant. Grav. 26 (2009) 065010 [arXiv:0809.5093] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  67. [67]
    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
  68. [68]
    V. Iyer and R.M. Wald, Some properties of Noether charge and a proposal for dynamical black hole entropy, Phys. Rev. D 50 (1994) 846 [gr-qc/9403028] [INSPIRE].
  69. [69]
    D. Carney, L. Chaurette, D. Neuenfeld and G.W. Semenoff, Infrared quantum information, Phys. Rev. Lett. 119 (2017) 180502 [arXiv:1706.03782] [INSPIRE].ADSCrossRefGoogle Scholar
  70. [70]
    D. Carney, L. Chaurette, D. Neuenfeld and G.W. Semenoff, Dressed infrared quantum information, Phys. Rev. D 97 (2018) 025007 [arXiv:1710.02531] [INSPIRE].ADSGoogle Scholar

Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Physics Division, National Center for Theoretical SciencesNational Tsing-Hua UniversityHsinchuTaiwan
  2. 2.Department of PhysicsNational Tsing-Hua UniversityHsinchuTaiwan

Personalised recommendations