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A new look at hidden conformal symmetries of black holes

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Abstract

We propose a different approach to the analysis of symmetries in the near-horizon region of black holes. The idea is presented here for spherically symmetric black holes, for which we have shown that the generators of hidden symmetries can be extracted by solving the conformal Killing equation under certain assumptions. Our result is in agreement with that obtained in literature by the analysis of the wave equation in the near-horizon region.

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References

  1. J.M. Bardeen, B. Carter and S.W. Hawking, The four laws of black hole mechanics, Commun. Math. Phys. 31 (1973) 161 [SPIRES].

    Article  MATH  ADS  MathSciNet  Google Scholar 

  2. J.D. Bekenstein, Black holes and entropy, Phys. Rev. D7 (1973) 2333 [SPIRES].

    ADS  MathSciNet  Google Scholar 

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

    ADS  MathSciNet  Google Scholar 

  4. A. Strominger, Black hole entropy from near-horizon microstates, JHEP 02 (1998) 009 [hep-th/9712251] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  5. 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  MATH  ADS  MathSciNet  Google Scholar 

  6. S. Carlip, Black hole entropy from conformal field theory in any dimension, Phys. Rev. Lett. 82 (1999) 2828 [hep-th/9812013] [SPIRES].

    Article  MATH  ADS  MathSciNet  Google Scholar 

  7. S.N. Solodukhin, Conformal description of horizon’s states, Phys. Lett. B 454 (1999) 213 [hep-th/9812056] [SPIRES].

    ADS  MathSciNet  Google Scholar 

  8. I. Bredberg, C. Keeler, V. Lysov and A. Strominger, Cargèse lectures on the Kerr/CFT correspondence, Nucl. Phys. Proc. Suppl. 216 (2011) 194 [arXiv:1103.2355] [SPIRES].

    Article  ADS  Google Scholar 

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

    ADS  MathSciNet  Google Scholar 

  10. A. Castro, A. Maloney and A. Strominger, Hidden conformal symmetry of the Kerr black hole, Phys. Rev. D 82 (2010) 024008 [arXiv:1004.0996] [SPIRES].

    ADS  MathSciNet  Google Scholar 

  11. Y.-Q. Wang and Y.-X. Liu, Hidden conformal symmetry of the Kerr-Newman black hole, JHEP 08 (2010) 087 [arXiv:1004.4661] [SPIRES].

    Article  ADS  Google Scholar 

  12. S. Bertini, S.L. Cacciatori and D. Klemm, Conformal structure of the Schwarzschild black hole, arXiv:1106.0999 [SPIRES].

  13. C. Krishnan, Hidden conformal symmetries of five-dimensional black holes, JHEP 07 (2010) 039 [arXiv:1004.3537] [SPIRES].

    Article  ADS  Google Scholar 

  14. R. Zegers, Birkhoff’s theorem in Lovelock gravity, J. Math. Phys. 46 (2005) 072502 [gr-qc/0505016] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  15. J. Oliva and S. Ray, A new cubic theory of gravity in five dimensions: black hole, Birkhoff’s theorem and C-function, Class. Quant. Grav. 27 (2010) 225002 [arXiv:1003.4773] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  16. J. Oliva and S. Ray, Birkhoff’s theorem in higher derivative theories of gravity, arXiv:1104.1205 [SPIRES].

  17. L. Bonora, M. Cvitan, P. Dominis Prester, S. Pallua and I. Smolić, Gravitational Chern-Simons Lagrangian terms and spherically symmetric spacetimes, Class. Quant. Grav. 28 (2011) 195009 [arXiv:1105.4792] [SPIRES].

    Article  ADS  Google Scholar 

  18. T. Jacobson, When is g tt g rr  = −1?, Class. Quant. Grav. 24 (2007) 5717 [arXiv:0707.3222] [SPIRES].

    Article  MATH  ADS  Google Scholar 

  19. R.M. Wald, General relativity, Chicago University Press, Chicago U.S.A. (1984) [SPIRES].

    MATH  Google Scholar 

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Authors and Affiliations

  1. International School for Advanced Studies (SISSA/ISAS), Via Bonomea 265, 34136, Trieste, Italy

    Edgardo Franzin & Ivica Smolić

  2. Theoretical Physics Department, Faculty of Science, University of Zagreb, p.p. 331, HR-10002, Zagreb, Croatia

    Ivica Smolić

Authors
  1. Edgardo Franzin
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  2. Ivica Smolić
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Correspondence to Ivica Smolić.

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ArXiv ePrint: 1107.2756

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Franzin, E., Smolić, I. A new look at hidden conformal symmetries of black holes. J. High Energ. Phys. 2011, 81 (2011). https://doi.org/10.1007/JHEP09(2011)081

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  • DOI: https://doi.org/10.1007/JHEP09(2011)081

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