To go or not to go with the flow: Hawking radiation at strong coupling

Abstract

We construct the gravitational dual of a one-parameter class of states of strongly coupled SU(N) \( \mathcal{N} \) = 4 SYM at infinite N and asymptotic temperature T, on a fixed Schwarzschild black hole background with temperature TBH. The resulting bulk geometry is of the flowing type and allow us to measure Hawking radiation at strong coupling. The outgoing Hawking flux is a function of the dimensionless ratio τ ≡ T/TBH and appears to be non-monotonic in τ. At present, we have no field theory understanding for this behaviour.

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References

  1. [1]

    S.W. Hawking, Black hole explosions, Nature248 (1974) 30 [INSPIRE].

    ADS  Article  Google Scholar 

  2. [2]

    S.W. Hawking, Particle Creation by Black Holes, Commun. Math. Phys.43 (1975) 199 [Erratum ibid.46 (1976) 206] [INSPIRE].

  3. [3]

    G.W. Gibbons and M.J. Perry, Black Holes in Thermal Equilibrium, Phys. Rev. Lett.36 (1976) 985 [INSPIRE].

    ADS  Article  Google Scholar 

  4. [4]

    E.T. Akhmedov, H. Godazgar and F.K. Popov, Hawking radiation and secularly growing loop corrections, Phys. Rev.D 93 (2016) 024029 [arXiv:1508.07500] [INSPIRE].

  5. [5]

    J.M. Maldacena, The large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys.38 (1999) 1113 [hep-th/9711200] [INSPIRE].

    MathSciNet  Article  Google Scholar 

  6. [6]

    S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett.B 428 (1998) 105 [hep-th/9802109] [INSPIRE].

    ADS  Article  Google Scholar 

  7. [7]

    E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys.2 (1998) 253 [hep-th/9802150] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  8. [8]

    O. Aharony, S.S. Gubser, J.M. Maldacena, H. Ooguri and Y. Oz, Large N field theories, string theory and gravity, Phys. Rept.323 (2000) 183 [hep-th/9905111] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  9. [9]

    V.E. Hubeny, D. Marolf and M. Rangamani, Hawking radiation in large N strongly-coupled field theories, Class. Quant. Grav.27 (2010) 095015 [arXiv:0908.2270] [INSPIRE].

  10. [10]

    V.E. Hubeny, D. Marolf and M. Rangamani, Black funnels and droplets from the AdS C-metrics, Class. Quant. Grav.27 (2010) 025001 [arXiv:0909.0005] [INSPIRE].

  11. [11]

    V.E. Hubeny, D. Marolf and M. Rangamani, Hawking radiation from AdS black holes, Class. Quant. Grav.27 (2010) 095018 [arXiv:0911.4144] [INSPIRE].

  12. [12]

    M.M. Caldarelli, O.J.C. Dias, R. Monteiro and J.E. Santos, Black funnels and droplets in thermal equilibrium, JHEP05 (2011) 116 [arXiv:1102.4337] [INSPIRE].

    ADS  Article  Google Scholar 

  13. [13]

    D. Marolf, M. Rangamani and T. Wiseman, Holographic thermal field theory on curved spacetimes, Class. Quant. Grav.31 (2014) 063001 [arXiv:1312.0612] [INSPIRE].

  14. [14]

    S. Fischetti, J.E. Santos and B. Way, Dissonant Black Droplets and Black Funnels, Class. Quant. Grav.34 (2017) 155001 [arXiv:1611.09363] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  15. [15]

    J.E. Santos and B. Way, Black Funnels, JHEP12 (2012) 060 [arXiv:1208.6291] [INSPIRE].

    ADS  Article  Google Scholar 

  16. [16]

    J.E. Santos and B. Way, Black Droplets, JHEP08 (2014) 072 [arXiv:1405.2078] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  17. [17]

    P. Figueras, J. Lucietti and T. Wiseman, Ricci solitons, Ricci flow and strongly coupled CFT in the Schwarzschild Unruh or Boulware vacua, Class. Quant. Grav.28 (2011) 215018 [arXiv:1104.4489] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  18. [18]

    V.P. Frolov and D.N. Page, Proof of the generalized second law for quasistationary semiclassical black holes, Phys. Rev. Lett.71 (1993) 3902 [gr-qc/9302017] [INSPIRE].

  19. [19]

    S.W. Hawking, Black holes in general relativity, Commun. Math. Phys.25 (1972) 152 [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  20. [20]

    S.W. Hawking and G.F.R. Ellis, The Large Scale Structure of Space-Time, Cambridge Monographs on Mathematical Physics, Cambridge University Press, (2011).

  21. [21]

    S. Hollands, A. Ishibashi and R.M. Wald, A higher dimensional stationary rotating black hole must be axisymmetric, Commun. Math. Phys.271 (2007) 699 [gr-qc/0605106] [INSPIRE].

  22. [22]

    S. Fischetti and D. Marolf, Flowing Funnels: Heat sources for field theories and the AdS3dual of CFT2Hawking radiation, Class. Quant. Grav.29 (2012) 105004 [arXiv:1202.5069] [INSPIRE].

    ADS  Article  Google Scholar 

  23. [23]

    S. Fischetti, D. Marolf and J.E. Santos, AdS flowing black funnels: Stationary AdS black holes with non-Killing horizons and heat transport in the dual CFT, Class. Quant. Grav.30 (2013) 075001 [arXiv:1212.4820] [INSPIRE].

  24. [24]

    P. Figueras and T. Wiseman, Stationary holographic plasma quenches and numerical methods for non-Killing horizons, Phys. Rev. Lett.110 (2013) 171602 [arXiv:1212.4498] [INSPIRE].

    ADS  Article  Google Scholar 

  25. [25]

    R. Emparan and M. Martinez, Black String Flow, JHEP09 (2013) 068 [arXiv:1307.2276] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  26. [26]

    M. Sun and Y.-C. Huang, Kerr Black string flow, Nucl. Phys.B 897 (2015) 98 [arXiv:1405.6906] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  27. [27]

    I. Amado and A. Yarom, Black brane steady states, JHEP10 (2015) 015 [arXiv:1501.01627] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  28. [28]

    E. Megias, Out-of-equilibrium energy flow and steady state configurations in AdS/CFT, PoSEPS-HEP2015 (2015) 366 [arXiv:1510.04219] [INSPIRE].

  29. [29]

    C.P. Herzog, M. Spillane and A. Yarom, The holographic dual of a Riemann problem in a large number of dimensions, JHEP08 (2016) 120 [arXiv:1605.01404] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  30. [30]

    E. Megias, Far-from-equilibrium energy flow and entanglement entropy, EPJ Web Conf.164 (2017) 01010 [arXiv:1701.00098] [INSPIRE].

  31. [31]

    J. Sonner and B. Withers, Universal spatial structure of nonequilibrium steady states, Phys. Rev. Lett.119 (2017) 161603 [arXiv:1705.01950] [INSPIRE].

    ADS  Article  Google Scholar 

  32. [32]

    M. Headrick, S. Kitchen and T. Wiseman, A new approach to static numerical relativity and its application to Kaluza-Klein black holes, Class. Quant. Grav.27 (2010) 035002 [arXiv:0905.1822] [INSPIRE].

  33. [33]

    T. Wiseman, Numerical construction of static and stationary black holes, in Black Holes in Higher Dimensions, Cambridge University Press, (2012), pp. 233–279.

  34. [34]

    Ó.J.C. Dias, J.E. Santos and B. Way, Numerical Methods for Finding Stationary Gravitational Solutions, Class. Quant. Grav.33 (2016) 133001 [arXiv:1510.02804] [INSPIRE].

  35. [35]

    P. Figueras and T. Wiseman, On the existence of stationary Ricci solitons, Class. Quant. Grav.34 (2017) 145007 [arXiv:1610.06178] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  36. [36]

    A. Donos and J.P. Gauntlett, The thermoelectric properties of inhomogeneous holographic lattices, JHEP01 (2015) 035 [arXiv:1409.6875] [INSPIRE].

    ADS  Article  Google Scholar 

  37. [37]

    A. Donos and J.P. Gauntlett, Minimally packed phases in holography, JHEP03 (2016) 148 [arXiv:1512.06861] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  38. [38]

    M.S. Costa, L. Greenspan, J. Penedones and J.E. Santos, Polarised Black Holes in ABJM, JHEP06 (2017) 024 [arXiv:1702.04353] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  39. [39]

    T. Crisford, G.T. Horowitz and J.E. Santos, Testing the Weak Gravity-Cosmic Censorship Connection, Phys. Rev.D 97 (2018) 066005 [arXiv:1709.07880] [INSPIRE].

  40. [40]

    G.T. Horowitz and J.E. Santos, Further evidence for the weak gravity — cosmic censorship connection, JHEP06 (2019) 122 [arXiv:1901.11096] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  41. [41]

    J.E. Santos, in preparation.

  42. [42]

    V. Balasubramanian, P. Kraus, A.E. Lawrence and S.P. Trivedi, Holographic probes of anti-de Sitter space-times, Phys. Rev.D 59 (1999) 104021 [hep-th/9808017] [INSPIRE].

    ADS  Google Scholar 

  43. [43]

    S. de Haro, S.N. Solodukhin and K. Skenderis, Holographic reconstruction of space-time and renormalization in the AdS/CFT correspondence, Commun. Math. Phys.217 (2001) 595 [hep-th/0002230] [INSPIRE].

    ADS  Article  Google Scholar 

  44. [44]

    C. Fefferman and C.R. Graham, Conformal invariants, in The Mathematical Heritage of Élie Cartan (Lyon, 1984), Astérisque98 (1985) 95.

  45. [45]

    C.R. Graham, Volume and area renormalizations for conformally compact Einstein metrics, in Proceedings, 19th Winter School on Geometry and Physics, (1999), math/9909042.

  46. [46]

    M.T. Anderson, Geometric aspects of the AdS/CFT correspondence, IRMA Lect. Math. Theor. Phys.8 (2005) 1 [hep-th/0403087] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  47. [47]

    C. Fefferman and C.R. Graham, The ambient metric, Ann. Math. Stud.178 (2011) 1 [arXiv:0710.0919] [INSPIRE].

    Google Scholar 

  48. [48]

    S.R. Green, S. Hollands, A. Ishibashi and R.M. Wald, Superradiant instabilities of asymptotically anti-de Sitter black holes, Class. Quant. Grav.33 (2016) 125022 [arXiv:1512.02644] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  49. [49]

    P. Figueras, K. Murata and H.S. Reall, Black hole instabilities and local Penrose inequalities, Class. Quant. Grav.28 (2011) 225030 [arXiv:1107.5785] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  50. [50]

    R. Gregory and R. Laflamme, Black strings and p-branes are unstable, Phys. Rev. Lett.70 (1993) 2837 [hep-th/9301052] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  51. [51]

    R. Penrose, Gravitational collapse: The role of general relativity, Riv. Nuovo Cim.1 (1969) 252 [INSPIRE].

    ADS  Google Scholar 

  52. [52]

    L. Lehner and F. Pretorius, Black Strings, Low Viscosity Fluids and Violation of Cosmic Censorship, Phys. Rev. Lett.105 (2010) 101102 [arXiv:1006.5960] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  53. [53]

    B.E. Niehoff, J.E. Santos and B. Way, Towards a violation of cosmic censorship, Class. Quant. Grav.33 (2016) 185012 [arXiv:1510.00709] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  54. [54]

    Ó.J.C. Dias, J.E. Santos and B. Way, Localised AdS5 × S5Black Holes, Phys. Rev. Lett.117 (2016) 151101 [arXiv:1605.04911] [INSPIRE].

  55. [55]

    G.T. Horowitz, J.E. Santos and B. Way, Evidence for an Electrifying Violation of Cosmic Censorship, Class. Quant. Grav.33 (2016) 195007 [arXiv:1604.06465] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  56. [56]

    T. Crisford and J.E. Santos, Violating the Weak Cosmic Censorship Conjecture in Four-Dimensional Anti-de Sitter Space, Phys. Rev. Lett.118 (2017) 181101 [arXiv:1702.05490] [INSPIRE].

    ADS  Article  Google Scholar 

  57. [57]

    D. Marolf and J.E. Santos, Phases of Holographic Hawking Radiation on spatially compact spacetimes, JHEP10 (2019) 250 [arXiv:1906.07681] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  58. [58]

    P.M. Chesler and L.G. Yaffe, Numerical solution of gravitational dynamics in asymptotically anti-de Sitter spacetimes, JHEP07 (2014) 086 [arXiv:1309.1439] [INSPIRE].

    ADS  Article  Google Scholar 

  59. [59]

    K. Balasubramanian and C.P. Herzog, Losing Forward Momentum Holographically, Class. Quant. Grav.31 (2014) 125010 [arXiv:1312.4953] [INSPIRE].

    ADS  Article  Google Scholar 

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Santos, J.E. To go or not to go with the flow: Hawking radiation at strong coupling. J. High Energ. Phys. 2020, 104 (2020). https://doi.org/10.1007/JHEP06(2020)104

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Keywords

  • AdS-CFT Correspondence
  • Black Holes
  • Nonperturbative Effects