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Black hole superradiance from Kerr/CFT

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Abstract

The superradiant scattering of a scalar field with frequency and angular momentum (ω, m) by a near-extreme Kerr black hole with mass and spin (M, J) was derived in the seventies by Starobinsky, Churilov, Press and Teukolsky. In this paper we show that for frequencies scaled to the superradiant bound the full functional dependence on (ω, m, M, J) of the scattering amplitudes is precisely reproduced by a dual two-dimensional conformal field theory in which the black hole corresponds to a specific thermal state and the scalar field to a specific operator. This striking agreement corroborates a conjectured Kerr/CFT correspondence.

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References

  1. M. Guica, T. Hartman, W. Song and A. Strominger, The Kerr/CFT correspondence, Phys. Rev. D 80 (2009) 124008 [arXiv:0809.4266] [SPIRES].

    ADS  Google Scholar 

  2. J.D. Brown and M. Henneaux, Central charges in the canonical realization of asymptotic symmetries: an example from three-dimensional gravity, Commun. Math. Phys. 104 (1986) 207 [SPIRES].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  3. H. Lü, J. Mei and C.N. Pope, Kerr/CFT correspondence in diverse dimensions, JHEP 04 (2009) 054 [arXiv:0811.2225] [SPIRES].

    Article  Google Scholar 

  4. T. Azeyanagi, N. Ogawa and S. Terashima, Holographic duals of Kaluza-Klein black holes, JHEP 04 (2009) 061 [arXiv:0811.4177] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  5. T. Hartman, K. Murata, T. Nishioka and A. Strominger, CFT duals for extreme black holes, JHEP 04 (2009) 019 [arXiv:0811.4393] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  6. D.D.K. Chow, M. Cvetič, H. Lü and C.N. Pope, Extremal black hole/CFT correspondence in (gauged) supergravities, Phys. Rev. D 79 (2009) 084018 [arXiv:0812.2918] [SPIRES].

    ADS  Google Scholar 

  7. H. Isono, T.-S. Tai and W.-Y. Wen, Kerr/CFT correspondence and five-dimensional BMPV black holes, Int. J. Mod. Phys. A 24 (2009) 5659 [arXiv:0812.4440] [SPIRES].

    ADS  Google Scholar 

  8. T. Azeyanagi, N. Ogawa and S. Terashima, The Kerr/CFT correspondence and string theory, Phys. Rev. D 79 (2009) 106009 [arXiv:0812.4883] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  9. J.-J. Peng and S.-Q. Wu, Extremal kerr black hole/CFT correspondence in the five dimensional Gödel universe, Phys. Lett. B 673 (2009) 216 [arXiv:0901.0311] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  10. C.-M. Chen and J.E. Wang, Holographic duals of black holes in five-dimensional minimal supergravity, Class. Quant. Grav. 27 (2010) 075004 [arXiv:0901.0538] [SPIRES].

    Article  ADS  Google Scholar 

  11. F. Loran and H. Soltanpanahi, 5D extremal rotating black holes and CFT duals, Class. Quant. Grav. 26 (2009) 155019 [arXiv:0901.1595] [SPIRES].

    Article  ADS  Google Scholar 

  12. A.M. Ghezelbash, Kerr/CFT correspondence in the low energy limit of heterotic string theory, JHEP 08 (2009) 045 [arXiv:0901.1670] [SPIRES].

    Article  ADS  Google Scholar 

  13. H. Lü, J.-w. Mei, C.N. Pope and J.F. Vazquez-Poritz, Extremal static AdS black hole/CFT correspondence in gauged supergravities, Phys. Lett. B 673 (2009) 77 [arXiv:0901.1677] [SPIRES].

    ADS  Google Scholar 

  14. G. Compere, K. Murata and T. Nishioka, Central charges in extreme black hole/CFT correspondence, JHEP 05 (2009) 077 [arXiv:0902.1001] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  15. K. Hotta, Holographic RG flow dual to attractor flow in extremal black holes, Phys. Rev. D 79 (2009) 104018 [arXiv:0902.3529] [SPIRES].

    ADS  Google Scholar 

  16. D. Astefanesei and Y.K. Srivastava, CFT duals for attractor horizons, Nucl. Phys. B 822 (2009) 283 [arXiv:0902.4033] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  17. A.M. Ghezelbash, Kerr-Bolt spacetimes and Kerr/CFT correspondence, arXiv:0902.4662 [SPIRES].

  18. M.R. Garousi and A. Ghodsi, The RN/CFT correspondence, Phys. Lett. B 687 (2010) 79 [arXiv:0902.4387] [SPIRES].

    ADS  Google Scholar 

  19. T. Azeyanagi, G. Compere, N. Ogawa, Y. Tachikawa and S. Terashima, Higher-derivative corrections to the asymptotic Virasoro symmetry of 4D extremal black holes, Prog. Theor. Phys. 122 (2009) 355 [arXiv:0903.4176] [SPIRES].

    Article  ADS  MATH  Google Scholar 

  20. X.-N. Wu and Y. Tian, Extremal isolated horizon/CFT correspondence, Phys. Rev. D 80 (2009) 024014 [arXiv:0904.1554] [SPIRES].

    ADS  Google Scholar 

  21. A.J. Amsel, G.T. Horowitz, D. Marolf and M.M. Roberts, No dynamics in the extremal Kerr throat, JHEP 09 (2009) 044 [arXiv:0906.2376] [SPIRES].

    Article  ADS  Google Scholar 

  22. O.J.C. Dias, H.S. Reall and J.E. Santos, Kerr-CFT and gravitational perturbations, JHEP 08 (2009) 101 [arXiv:0906.2380] [SPIRES].

    Article  ADS  Google Scholar 

  23. V. Balasubramanian, J. de Boer, M.M. Sheikh-Jabbari and J. Simon, What is a chiral 2D CFT? And what does it have to do with extremal black holes?, JHEP 02 (2010) 017 [arXiv:0906.3272] [SPIRES].

    Article  Google Scholar 

  24. Y. Matsuo, T. Tsukioka and C.-M. Yoo, Another realization of Kerr/CFT correspondence, Nucl. Phys. B 825 (2010) 231 [arXiv:0907.0303] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  25. G. Compere and S. Detournay, Boundary conditions for spacelike and timelike warped AdS 3 spaces in topologically massive gravity, JHEP 08 (2009) 092 [arXiv:0906.1243] [SPIRES].

    Article  ADS  Google Scholar 

  26. M. Guica, T. Hartman, W. Song and A. Strominger, unpublished, October (2008).

  27. J.M. Maldacena and A. Strominger, Black hole greybody factors and D-brane spectroscopy, Phys. Rev. D 55 (1997) 861 [hep-th/9609026] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  28. J.M. Maldacena and A. Strominger, Universal low-energy dynamics for rotating black holes, Phys. Rev. D 56 (1997) 4975 [hep-th/9702015] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  29. J.M. Maldacena, J. Michelson and A. Strominger, Anti-de Sitter fragmentation, JHEP 02 (1999) 011 [hep-th/9812073] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  30. T. Faulkner, H. Liu, J. McGreevy and D. Vegh, Emergent quantum criticality,Fermi surfaces and AdS 2, arXiv:0907.2694 [SPIRES].

  31. A.A. Starobinsky, Amplification of waves during reflection from a rotating “black hole”, Zh. Exp. Teor. Fiz. 64 (1973) 48 [Sov. Phys. JETP 37 (1973) 28].

    ADS  Google Scholar 

  32. A.A. Starobinsky and S.M. Churilov, Amplification of electromagnetic and gravitational waves scattered by a rotating “black hole”, Zh. Exp. Teor. Fiz. 65 (1973) 3 [Sov. Phys. JETP 38 (1973) 1].

    ADS  Google Scholar 

  33. S.A. Teukolsky, Perturbations of a rotating black hole. I. Fundamental equations for gravitational electromagnetic and neutrino field perturbations, Astrophys. J. 185 (1973) 635 [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  34. W.H. Press and S.A. Teukolsky, Perturbations of a rotating black hole. II. Dynamical stability of the Kerr metric, Astrophys. J. 185 (1973) 649 [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  35. S.A. Teukolsky and W.H. Press, Perturbations of a rotating black hole. III. Interaction of the hole with gravitational and electromagnet ic radiation, Astrophys. J. 193 (1974) 443 [SPIRES].

    Article  ADS  Google Scholar 

  36. J.A.H. Futterman, F.A. Handler and R.A. Matzner, Scattering from black holes, Cambridge University Press, Cambridge U.K. (1988) [SPIRES].

    Google Scholar 

  37. Ya. B. Zeldovich, Generation of waves by a rotating body, Zh. Exp. Teor. Fiz. Pisma 14 (1971) 270 [JETP Lett. 14 (1971) 180].

    Google Scholar 

  38. Ya. B. Zeldovich, Amplification of cylindrical electromagnetic waves from a rotating body, Zh. Exp. Teor. Fiz. 62 (1972) 2076 [Sov. Phys. JETP 35 (1972) 1085].

    Google Scholar 

  39. C.W. Misner, Stability of Kerr black holes against scalar perturbations, Bull. Amer. Phys. Soc. 17 (1972) 472.

    Google Scholar 

  40. C.W. Misner, Interpretation of gravitational-wave observations, Phys. Rev. Lett. 28 (1972) 994 [SPIRES].

    Article  ADS  Google Scholar 

  41. R.P. Kerr, Gravitational field of a spinning mass as an example of algebraically special metrics, Phys. Rev. Lett. 11 (1963) 237 [SPIRES].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  42. Kerrfest proceedings, online at http://www.phys.canterbury.ac.nz/kerrfest.

  43. M. Visser, The Kerr spacetime: a brief introduction, in The Kerr spacetime: rotating black holes in general relativity, D.L. Wiltshire, M. Visser and S.M. Scott eds., Cambridge University Press, Cambridge, U.K. (2009), arXiv:0706.0622 [SPIRES].

    Google Scholar 

  44. J.M. Bardeen and G.T. Horowitz, The extreme Kerr throat geometry: a vacuum analog of AdS 2 × S 2, Phys. Rev. D 60 (1999) 104030 [hep-th/9905099] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  45. V.P. Frolov and K.S. Thorne, Renormalized stress-energy tensor near the horizon of a slowly evolving, rotating black hole, Phys. Rev. D 39 (1989) 2125 [SPIRES].

    MathSciNet  ADS  Google Scholar 

  46. M. Spradlin and A. Strominger, Vacuum states for AdS 2 black holes, JHEP 11 (1999) 021 [hep-th/9904143] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  47. W.-Y. Wen, Holographic descriptions of (near-)extremal black holes in five dimensional minimal supergravity, arXiv:0903.4030 [SPIRES].

  48. E. Berti, V. Cardoso and M. Casals, Eigenvalues and eigenfunctions of spin-weighted spheroidal harmonics in four and higher dimensions, Phys. Rev. D 73 (2006) 024013 [Erratum ibid. D 73 (2006) 109902] [gr-qc/0511111] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  49. M. Casals i Casanellas, Electromagnetic quantum field theory on Kerr-Newman black holes, arXiv:0802.1885 [SPIRES].

  50. S.S. Gubser, Can the effective string see higher partial waves?, Phys. Rev. D 56 (1997) 4984 [hep-th/9704195] [SPIRES].

    ADS  Google Scholar 

  51. M. Cvetič and F. Larsen, Greybody factors for rotating black holes in four dimensions, Nucl. Phys. B 506 (1997) 107 [hep-th/9706071] [SPIRES].

    Article  ADS  Google Scholar 

  52. S.S. Gubser, Absorption of photons and fermions by black holes in four dimensions, Phys. Rev. D 56 (1997) 7854 [hep-th/9706100] [SPIRES].

    ADS  Google Scholar 

  53. 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] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  54. S.P. Kim and D.N. Page, Schwinger pair production in dS 2 and AdS 2, Phys. Rev. D 78 (2008) 103517 [arXiv:0803.2555] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  55. B. Pioline and J. Troost, Schwinger pair production in AdS 2, JHEP 03 (2005) 043 [hep-th/0501169] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  56. D. Birmingham, I. Sachs and S.N. Solodukhin, Conformal field theory interpretation of black hole quasi-normal modes, Phys. Rev. Lett. 88 (2002) 151301 [hep-th/0112055] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  57. B. Mashhoon, Stability of charged rotating black holes in the eikonal approximation, Phys. Rev. D 31 (1985) 290.

    MathSciNet  ADS  Google Scholar 

  58. S. Hod, Near-extreme black holes and the universal relaxation bound, Class. Quant. Grav. 24 (2007) 4235 [arXiv:0705.2306] [SPIRES].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  59. R.C. Myers and M.J. Perry, Black holes in higher dimensional space-times, Ann. Phys. 172 (1986) 304 [SPIRES].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  60. A. Strominger and C. Vafa, Microscopic origin of the Bekenstein-Hawking entropy, Phys. Lett. B 379 (1996) 99 [hep-th/9601029] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  61. J.C. Breckenridge, R.C. Myers, A.W. Peet and C. Vafa, D-branes and spinning black holes, Phys. Lett. B 391 (1997) 93 [hep-th/9602065] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  62. J.C. Breckenridge et al., Macroscopic and microscopic entropy of near-extremal spinning black holes, Phys. Lett. B 381 (1996) 423 [hep-th/9603078] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  63. M. Cvetič and F. Larsen, General rotating black holes in string theory: greybody factors and event horizons, Phys. Rev. D 56 (1997) 4994 [hep-th/9705192] [SPIRES].

    ADS  Google Scholar 

  64. J.P. Gauntlett, R.C. Myers and P.K. Townsend, Black holes of D = 5 supergravity, Class. Quant. Grav. 16 (1999) 1 [hep-th/9810204] [SPIRES].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  65. O.J.C. Dias, R. Emparan and A. Maccarrone, Microscopic theory of black hole superradiance, Phys. Rev. D 77 (2008) 064018 [arXiv:0712.0791] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  66. T. Azeyanagi, N. Ogawa and S. Terashima, The Kerr/CFT correspondence and string theory, Phys. Rev. D 79 (2009) 106009 [arXiv:0812.4883] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  67. R.C. Myers and M.J. Perry, Black holes in higher dimensional space-times, Ann. Phys. 172 (1986) 304 [SPIRES].

    Article  MathSciNet  ADS  MATH  Google Scholar 

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Correspondence to Thomas Hartman.

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Bredberg, I., Hartman, T., Song, W. et al. Black hole superradiance from Kerr/CFT. J. High Energ. Phys. 2010, 19 (2010). https://doi.org/10.1007/JHEP04(2010)019

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