Rotating black droplet

  • Sebastian Fischetti
  • Jorge E. Santos


We construct the gravitational dual, in the Unruh state, of the “jammed” phase of a CFT at strong coupling and infinite N on a fixed five-dimensional rotating Myers-Perry black hole with equal angular momenta. When the angular momenta are all zero, the solution corresponds to the five-dimensional generalization of the solution first studied in [1]. In the extremal limit, when the angular momenta of the Myers-Perry black hole are maximum, the Unruh, Boulware and Hartle-Hawking states degenerate. We give a detailed analysis of the corresponding holographic stress energy tensor for all values of the angular momenta, finding it to be regular at the horizon in all cases. We compare our results with existent literature on thermal states of free field theories on black hole backgrounds.


Gauge-gravity correspondence AdS-CFT Correspondence Black Holes 


  1. [1]
    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].MathSciNetADSCrossRefGoogle Scholar
  2. [2]
    S. Hawking, Black hole explosions, Nature 248 (1974) 30 [INSPIRE].ADSCrossRefGoogle Scholar
  3. [3]
    N.D. Birrell and P.C.W. Davies, Quantum fields in curved space, Cambridge University Press, Cambridge U.K. (1982).MATHCrossRefGoogle Scholar
  4. [4]
    J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [Int. J. Theor. Phys. 38 (1999) 1113] [hep-th/9711200] [INSPIRE].
  5. [5]
    L. Randall and R. Sundrum, An alternative to compactification, Phys. Rev. Lett. 83 (1999) 4690 [hep-th/9906064] [INSPIRE].MathSciNetADSMATHCrossRefGoogle Scholar
  6. [6]
    T. Tanaka, Classical black hole evaporation in Randall-Sundrum infinite brane world, Prog. Theor. Phys. Suppl. 148 (2003) 307 [gr-qc/0203082] [INSPIRE].ADSCrossRefGoogle Scholar
  7. [7]
    R. Emparan, A. Fabbri and N. Kaloper, Quantum black holes as holograms in AdS brane worlds, JHEP 08 (2002) 043 [hep-th/0206155] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  8. [8]
    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].MathSciNetADSCrossRefGoogle Scholar
  9. [9]
    V.E. Hubeny, D. Marolf and M. Rangamani, Hawking radiation from AdS black holes, Class. Quant. Grav. 27 (2010) 095018 [arXiv:0911.4144] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  10. [10]
    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].MathSciNetADSCrossRefGoogle Scholar
  11. [11]
    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].MathSciNetADSCrossRefGoogle Scholar
  12. [12]
    M.M. Caldarelli, O.J. Dias, R. Monteiro and J.E. Santos, Black funnels and droplets in thermal equilibrium, JHEP 05 (2011) 116 [arXiv:1102.4337] [INSPIRE].ADSCrossRefGoogle Scholar
  13. [13]
    S. Fischetti and D. Marolf, Flowing Funnels: heat sources for field theories and the AdS 3 dual of CFT 2 Hawking radiation, Class. Quant. Grav. 29 (2012) 105004 [arXiv:1202.5069] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  14. [14]
    J.E. Santos and B. Way, Black funnels, JHEP 12 (2012) 060 [arXiv:1208.6291] [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    A.R. Steif, The quantum stress tensor in the three-dimensional black hole, Phys. Rev. D 49 (1994) 585 [gr-qc/9308032] [INSPIRE].MathSciNetADSGoogle Scholar
  16. [16]
    R. Myers and M. Perry, Black holes in higher dimensional space-times, Ann. Phys. 172 (1986) 304.MathSciNetADSMATHCrossRefGoogle Scholar
  17. [17]
    R.C. Myers, Myers-Perry black holes, arXiv:1111.1903 [INSPIRE].
  18. [18]
    P. Figueras and S. Tunyasuvunakool, CFTs in rotating black hole backgrounds, Class. Quantum Grav. 30 (2013) 125015 [arXiv:1304.1162] [INSPIRE]ADSCrossRefGoogle Scholar
  19. [19]
    S.A. Fulling and P.C.W. Davies, Radiation from a moving mirror in two dimensional space-time: Conformal anomaly, Proc. Roy. Soc. Lond. A 348 (1976) 393.MathSciNetADSGoogle Scholar
  20. [20]
    H. Casimir, On the attraction between two perfectly conducting plates, Indag. Math. 10 (1948) 261.Google Scholar
  21. [21]
    H. Epstein, V. Glaser, and A. Jaffe, Nonpositivity of the energy density in quantized field theories, Nuovo Cim. 36 (1965) 1016.MathSciNetCrossRefGoogle Scholar
  22. [22]
    P. Davies, S. Fulling and W. Unruh, Energy momentum tensor near an evaporating black hole, Phys. Rev. D 13 (1976) 2720 [INSPIRE].ADSGoogle Scholar
  23. [23]
    D.N. Page, Thermal stress tensors in static Einstein spaces, Phys. Rev. D 25 (1982) 1499 [INSPIRE].MathSciNetADSGoogle Scholar
  24. [24]
    J. Bekenstein and L. Parker, Path integral evaluation of Feynman propagator in curved space-time, Phys. Rev. D 23 (1981) 2850 [INSPIRE].MathSciNetADSGoogle Scholar
  25. [25]
    P. Candelas, Vacuum polarization in Schwarzschild space-time, Phys. Rev. D 21 (1980) 2185 [INSPIRE].MathSciNetADSGoogle Scholar
  26. [26]
    S. Christensen and S. Fulling, Trace anomalies and the Hawking effect, Phys. Rev. D 15 (1977) 2088 [INSPIRE].ADSGoogle Scholar
  27. [27]
    F. Tangherlini, Schwarzschild field in n dimensions and the dimensionality of space problem, Nuovo Cim. 27 (1963) 636 [INSPIRE].MathSciNetMATHCrossRefGoogle Scholar
  28. [28]
    S.B. Giddings, E. Katz and L. Randall, Linearized gravity in brane backgrounds, JHEP 03 (2000) 023 [hep-th/0002091] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  29. [29]
    S.P. Trivedi, Semiclassical extremal black holes, Phys. Rev. D 47 (1993) 4233 [hep-th/9211011] [INSPIRE].MathSciNetADSGoogle Scholar
  30. [30]
    D.J. Loranz, W.A. Hiscock and P.R. Anderson, Thermal divergences on the event horizons of two-dimensional black holes, Phys. Rev. D 52 (1995) 4554 [gr-qc/9504044] [INSPIRE].MathSciNetADSGoogle Scholar
  31. [31]
    R. Balbinot, S. Fagnocchi, A. Fabbri, S. Farese and J. Navarro-Salas, On the quantum stress tensor for extreme 2D Reissner-Nordstrom black holes, Phys. Rev. D 70 (2004) 064031 [hep-th/0405263] [INSPIRE].MathSciNetADSGoogle Scholar
  32. [32]
    S. Farese, Regularity of the stress-energy tensor for extremal Reissner-Nordstrom black holes, J. Phys. Conf. Ser. 33 (2006) 451 [hep-th/0512181] [INSPIRE].ADSCrossRefGoogle Scholar
  33. [33]
    P.R. Anderson, W.A. Hiscock and D.J. Loranz, Semiclassical stability of the extreme Reissner-Nordstrom black hole, Phys. Rev. Lett. 74 (1995) 4365 [gr-qc/9504019] [INSPIRE].MathSciNetADSMATHCrossRefGoogle Scholar
  34. [34]
    D.M. DeTurck, Deforming metrics in the direction of their Ricci tensors, J. Diff. Geom. 18 (1983) 157.MathSciNetMATHGoogle Scholar
  35. [35]
    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].MathSciNetADSCrossRefGoogle Scholar
  36. [36]
    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].ADSMATHCrossRefGoogle Scholar
  37. [37]
    R. Gregory, Black string instabilities in Anti-de Sitter space, Class. Quant. Grav. 17 (2000) L125 [hep-th/0004101] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  38. [38]
    E. Poisson and W. Israel, Internal structure of black holes, Phys. Rev. D 41 (1990) 1796 [INSPIRE].MathSciNetADSGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2013

Authors and Affiliations

  1. 1.Department of PhysicsUniversity of California Santa BarbaraSanta BarbaraU.S.A.

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