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Superradiant instability of the Kerr brane
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  • Regular Article - Theoretical Physics
  • Open Access
  • Published: 29 September 2015

Superradiant instability of the Kerr brane

  • Akihiro Ishibashi1,
  • Paolo Pani2,3,
  • Leonardo Gualtieri2 &
  • …
  • Vitor Cardoso3,4 

Journal of High Energy Physics volume 2015, Article number: 209 (2015) Cite this article

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A preprint version of the article is available at arXiv.

Abstract

We consider linear gravitational perturbations of the Kerr brane, an exact solution of vacuum Einstein’s equations in dimensions higher than four and a low-energy solution of string theory. Decomposing the perturbations in tensor harmonics of the trans-verse Ricci-flat space, we show that tensor- and vector-type metric perturbations of the Kerr brane satisfy respectively a massive Klein-Gordon equation and a Proca equation on the four-dimensional Kerr space, where the mass term is proportional to the eigenvalue of the harmonics. Massive bosonic fields trigger a well-known superradiant instability on a Kerr black hole. We thus establish that Kerr branes in dimensions D ≥ 6 are gravi-tationally unstable due to superradiance. These solutions are also unstable against the Gregory-Laflamme instability and we discuss the conditions for either instability to occur and their rather different nature. When the transverse dimensions are compactified and much smaller than the Kerr horizon, only the superradiant instability is present, with a time scale much longer than the dynamical time scale. Our formalism can be also used to discuss other types of higher-dimensional black objects, taking advantage of recent progress in studying linear perturbations of four-dimensional black holes.

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References

  1. R. Gregory and R. Laflamme, The instability of charged black strings and p-branes, Nucl. Phys. B 428 (1994) 399 [hep-th/9404071] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

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

    Article  ADS  MathSciNet  MATH  Google Scholar 

  3. S.A. Teukolsky and W.H. Press, Perturbations of a rotating black hole. III — interaction of the hole with gravitational and electromagnetic radiation, Astrophys. J. 193 (1974) 443 [INSPIRE].

    Article  ADS  Google Scholar 

  4. R. Brito, V. Cardoso and P. Pani, Superradiance, Lect. Notes Phys. 906 (2015) 1 [arXiv:1501.06570] [INSPIRE].

    Article  Google Scholar 

  5. W.H. Press and S.A. Teukolsky, Floating orbits, superradiant scattering and the black-hole bomb, Nature 238 (1972) 211 [INSPIRE].

    Article  ADS  Google Scholar 

  6. V. Cardoso, Ó.J.C. Dias, J.P.S. Lemos and S. Yoshida, The black hole bomb and superradiant instabilities, Phys. Rev. D 70 (2004) 044039 [Erratum ibid. D 70 (2004) 049903] [hep-th/0404096] [INSPIRE].

  7. C.A.R. Herdeiro, J.C. Degollado and H.F. Rúnarsson, Rapid growth of superradiant instabilities for charged black holes in a cavity, Phys. Rev. D 88 (2013) 063003 [arXiv:1305.5513] [INSPIRE].

    ADS  Google Scholar 

  8. S. Hod, Analytic treatment of the charged black-hole-mirror bomb in the highly explosive regime, Phys. Rev. D 88 (2013) 064055 [arXiv:1310.6101] [INSPIRE].

    ADS  Google Scholar 

  9. J.C. Degollado and C.A.R. Herdeiro, Time evolution of superradiant instabilities for charged black holes in a cavity, Phys. Rev. D 89 (2014) 063005 [arXiv:1312.4579] [INSPIRE].

    ADS  Google Scholar 

  10. R. Li and J. Zhao, Numerical study of superradiant instability for charged stringy black hole-mirror system, Phys. Lett. B 740 (2015) 317 [arXiv:1412.1527] [INSPIRE].

    Article  ADS  Google Scholar 

  11. T. Damour, N. Deruelle and R. Ruffini, On quantum resonances in stationary geometries, Lett. Nuovo Cim. 15 (1976) 257 [INSPIRE].

    Article  ADS  Google Scholar 

  12. S.L. Detweiler, Klein-Gordon equation and rotating black holes, Phys. Rev. D 22 (1980) 2323 [INSPIRE].

    ADS  Google Scholar 

  13. S.R. Dolan, Instability of the massive Klein-Gordon field on the Kerr spacetime, Phys. Rev. D 76 (2007) 084001 [arXiv:0705.2880] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  14. J.G. Rosa, The extremal black hole bomb, JHEP 06 (2010) 015 [arXiv:0912.1780] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  15. P. Pani, V. Cardoso, L. Gualtieri, E. Berti and A. Ishibashi, Black hole bombs and photon mass bounds, Phys. Rev. Lett. 109 (2012) 131102 [arXiv:1209.0465] [INSPIRE].

    Article  ADS  Google Scholar 

  16. P. Pani, V. Cardoso, L. Gualtieri, E. Berti and A. Ishibashi, Perturbations of slowly rotating black holes: massive vector fields in the Kerr metric, Phys. Rev. D 86 (2012) 104017 [arXiv:1209.0773] [INSPIRE].

    ADS  Google Scholar 

  17. H. Witek, V. Cardoso, A. Ishibashi and U. Sperhake, Superradiant instabilities in astrophysical systems, Phys. Rev. D 87 (2013) 043513 [arXiv:1212.0551] [INSPIRE].

    ADS  Google Scholar 

  18. R. Brito, V. Cardoso and P. Pani, Massive spin-2 fields on black hole spacetimes: instability of the Schwarzschild and Kerr solutions and bounds on the graviton mass, Phys. Rev. D 88 (2013) 023514 [arXiv:1304.6725] [INSPIRE].

    ADS  Google Scholar 

  19. H. Yoshino and H. Kodama, Bosenova and axiverse, arXiv:1505.00714 [INSPIRE].

  20. P. Pani and A. Loeb, Constraining primordial black-hole bombs through spectral distortions of the cosmic microwave background, Phys. Rev. D 88 (2013) 041301 [arXiv:1307.5176] [INSPIRE].

    ADS  Google Scholar 

  21. V. Cardoso, I.P. Carucci, P. Pani and T.P. Sotiriou, Black holes with surrounding matter in scalar-tensor theories, Phys. Rev. Lett. 111 (2013) 111101 [arXiv:1308.6587] [INSPIRE].

    Article  ADS  Google Scholar 

  22. V. Cardoso, I.P. Carucci, P. Pani and T.P. Sotiriou, Matter around Kerr black holes in scalar-tensor theories: scalarization and superradiant instability, Phys. Rev. D 88 (2013) 044056 [arXiv:1305.6936] [INSPIRE].

    ADS  Google Scholar 

  23. S.W. Hawking and H.S. Reall, Charged and rotating AdS black holes and their CFT duals, Phys. Rev. D 61 (2000) 024014 [hep-th/9908109] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  24. V. Cardoso and Ó.J.C. Dias, Small Kerr-anti-de Sitter black holes are unstable, Phys. Rev. D 70 (2004) 084011 [hep-th/0405006] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  25. V. Cardoso, Ó.J.C. Dias and S. Yoshida, Classical instability of Kerr-AdS black holes and the issue of final state, Phys. Rev. D 74 (2006) 044008 [hep-th/0607162] [INSPIRE].

    ADS  Google Scholar 

  26. N. Uchikata, S. Yoshida and T. Futamase, Scalar perturbations of Kerr-AdS black holes, Phys. Rev. D 80 (2009) 084020 [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  27. V. Cardoso, Ó. J.C. Dias, G.S. Hartnett, L. Lehner and J.E. Santos, Holographic thermalization, quasinormal modes and superradiance in Kerr-AdS, JHEP 04 (2014) 183 [arXiv:1312.5323] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  28. V. Cardoso and J.P.S. Lemos, New instability for rotating black branes and strings, Phys. Lett. B 621 (2005) 219 [hep-th/0412078] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  29. V. Cardoso and S. Yoshida, Superradiant instabilities of rotating black branes and strings, JHEP 07 (2005) 009 [hep-th/0502206] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  30. J.G. Rosa, Boosted black string bombs, JHEP 02 (2013) 014 [arXiv:1209.4211] [INSPIRE].

    Article  ADS  Google Scholar 

  31. A. Arvanitaki, S. Dimopoulos, S. Dubovsky, N. Kaloper and J. March-Russell, String axiverse, Phys. Rev. D 81 (2010) 123530 [arXiv:0905.4720] [INSPIRE].

    ADS  Google Scholar 

  32. A. Arvanitaki and S. Dubovsky, Exploring the string axiverse with precision black hole physics, Phys. Rev. D 83 (2011) 044026 [arXiv:1004.3558] [INSPIRE].

    ADS  Google Scholar 

  33. J.E. McClintock and R.A. Remillard, Measuring the spins of stellar-mass black holes, arXiv:0902.3488 [INSPIRE].

  34. T. Johannsen, D. Psaltis and J.E. McClintock, Constraints on the size of extra dimensions from the orbital evolution of black-hole X-ray binaries, Astrophys. J. 691 (2009) 997 [arXiv:0803.1835] [INSPIRE].

    Article  ADS  Google Scholar 

  35. S.T. McWilliams, Constraining the braneworld with gravitational wave observations, Phys. Rev. Lett. 104 (2010) 141601 [arXiv:0912.4744] [INSPIRE].

    Article  ADS  Google Scholar 

  36. K. Yagi, N. Tanahashi and T. Tanaka, Probing the size of extra dimension with gravitational wave astronomy, Phys. Rev. D 83 (2011) 084036 [arXiv:1101.4997] [INSPIRE].

    ADS  Google Scholar 

  37. H. Kodama, A. Ishibashi and O. Seto, Brane world cosmology: gauge invariant formalism for perturbation, Phys. Rev. D 62 (2000) 064022 [hep-th/0004160] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  38. H. Kudoh, Origin of black string instability, Phys. Rev. D 73 (2006) 104034 [hep-th/0602001] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  39. H. Kodama, R.A. Konoplya and A. Zhidenko, Gravitational stability of simply rotating Myers-Perry black holes: tensorial perturbations, Phys. Rev. D 81 (2010) 044007 [arXiv:0904.2154] [INSPIRE].

    ADS  Google Scholar 

  40. P. Kanti, H. Kodama, R.A. Konoplya, N. Pappas and A. Zhidenko, Graviton emission in the bulk by a simply rotating black hole, Phys. Rev. D 80 (2009) 084016 [arXiv:0906.3845] [INSPIRE].

    ADS  Google Scholar 

  41. J. Doukas, H.T. Cho, A.S. Cornell and W. Naylor, Graviton emission from simply rotating Kerr-de Sitter black holes: transverse traceless tensor graviton modes, Phys. Rev. D 80 (2009) 045021 [arXiv:0906.1515] [INSPIRE].

    ADS  Google Scholar 

  42. H. Kodama and A. Ishibashi, A master equation for gravitational perturbations of maximally symmetric black holes in higher dimensions, Prog. Theor. Phys. 110 (2003) 701 [hep-th/0305147] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  43. A. Ishibashi and H. Kodama, Perturbations and stability of static black holes in higher dimensions, Prog. Theor. Phys. Suppl. 189 (2011) 165 [arXiv:1103.6148] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  44. T. Harmark, V. Niarchos and N.A. Obers, Instabilities of black strings and branes, Class. Quant. Grav. 24 (2007) R1 [hep-th/0701022] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  45. F.R. Tangherlini, Schwarzschild field in n dimensions and the dimensionality of space problem, Nuovo Cim. 27 (1963) 636 [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  46. C.-M. Yoo, S. Tanzawa and M. Sasaki, Gregory-Laflamme instability of a slowly rotating black string, Int. J. Mod. Phys. D 20 (2011) 963 [arXiv:1103.6081] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  47. E. Babichev and A. Fabbri, Instability of black holes in massive gravity, Class. Quant. Grav. 30 (2013) 152001 [arXiv:1304.5992] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  48. R. Brito, V. Cardoso and P. Pani, Partially massless gravitons do not destroy general relativity black holes, Phys. Rev. D 87 (2013) 124024 [arXiv:1306.0908] [INSPIRE].

    ADS  Google Scholar 

  49. B. Kol and E. Sorkin, On black-brane instability in an arbitrary dimension, Class. Quant. Grav. 21 (2004) 4793 [gr-qc/0407058] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  50. T.J.M. Zouros and D.M. Eardley, Instabilities of massive scalar perturbations of a rotating black hole, Annals Phys. 118 (1979) 139 [INSPIRE].

    Article  ADS  Google Scholar 

  51. P. Pani, Advanced methods in black-hole perturbation theory, Int. J. Mod. Phys. A 28 (2013) 1340018 [arXiv:1305.6759] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  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].

    Article  ADS  MathSciNet  Google Scholar 

  53. V. Cardoso and Ó.J.C. Dias, Rayleigh-Plateau and Gregory-Laflamme instabilities of black strings, Phys. Rev. Lett. 96 (2006) 181601 [hep-th/0602017] [INSPIRE].

    Article  ADS  Google Scholar 

  54. J. Camps, R. Emparan and N. Haddad, Black brane viscosity and the Gregory-Laflamme instability, JHEP 05 (2010) 042 [arXiv:1003.3636] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  55. D. Ida, K.-Y. Oda and S.C. Park, Rotating black holes at future colliders: greybody factors for brane fields, Phys. Rev. D 67 (2003) 064025 [Erratum ibid. D 69 (2004) 049901] [hep-th/0212108] [INSPIRE].

  56. D. Ida, K.-Y. Oda and S.C. Park, Rotating black holes at future colliders. II. Anisotropic scalar field emission, Phys. Rev. D 71 (2005) 124039 [hep-th/0503052] [INSPIRE].

    ADS  Google Scholar 

  57. D. Ida, K.-Y. Oda and S.C. Park, Rotating black holes at future colliders. III. Determination of black hole evolution, Phys. Rev. D 73 (2006) 124022 [hep-th/0602188] [INSPIRE].

    ADS  Google Scholar 

  58. Ó. J.C. Dias, G.S. Hartnett and J.E. Santos, Quasinormal modes of asymptotically flat rotating black holes, Class. Quant. Grav. 31 (2014) 245011 [arXiv:1402.7047] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

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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.

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Authors and Affiliations

  1. Department of Physics, Kinki University, Higashi-Osaka, 577-8502, Japan

    Akihiro Ishibashi

  2. Dipartimento di Fisica, Università di Roma “La Sapienza” & Sezione INFN Roma1, P.A. Moro 5, 00185, Roma, Italy

    Paolo Pani & Leonardo Gualtieri

  3. CENTRA, Departamento de F´ısica, Instituto Superior Técnico, Universidade de Lisboa — UL, Av. Rovisco Pais 1, 1049, Lisboa, Portugal

    Paolo Pani & Vitor Cardoso

  4. Perimeter Institute for Theoretical Physics, Waterloo, Ontario, N2J 2W9, Canada

    Vitor Cardoso

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  1. Akihiro Ishibashi
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  2. Paolo Pani
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Correspondence to Akihiro Ishibashi.

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ArXiv ePrint: 1507.07079

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Ishibashi, A., Pani, P., Gualtieri, L. et al. Superradiant instability of the Kerr brane. J. High Energ. Phys. 2015, 209 (2015). https://doi.org/10.1007/JHEP09(2015)209

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  • Received: 31 July 2015

  • Accepted: 31 August 2015

  • Published: 29 September 2015

  • DOI: https://doi.org/10.1007/JHEP09(2015)209

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Keywords

  • Classical Theories of Gravity
  • Black Holes
  • Black Holes in String Theory
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