Skip to main content
Log in

Extremal and nonextremal Kerr/CFT correspondences

  • Published:
Journal of High Energy Physics Aims and scope Submit manuscript

Abstract

I rederive the Kerr/CFT correspondence without first taking the near-horizon extremal Kerr limit. This method extends easily to nonextremal black holes, for which the temperature and central charge behave poorly at the horizon but the entropy remains finite. A computation yields one-half of the standard Bekenstein-Hawking entropy, with hints that the other half may be related to a conformal field theory at the inner horizon. I then present an alternative approach, based on a stretched Killing horizon, in which the full entropy is obtained and the temperature and central charge remain well-behaved even in the nonextremal case.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

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

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  MATH  Google Scholar 

  3. S. Carlip, Entropy from conformal field theory at Killing horizons, Class. Quant. Grav. 16 (1999) 3327 [gr-qc/9906126] [SPIRES].

    Article  MathSciNet  ADS  MATH  Google Scholar 

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

    MathSciNet  ADS  Google Scholar 

  5. S. Carlip, Symmetries, Horizons and Black Hole Entropy, Gen. Rel. Grav. 39 (2007) 1519 [arXiv:0705.3024] [SPIRES].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  6. M. Guica and A. Strominger, Microscopic Realization of the Kerr/CFT Correspondence, JHEP 02 (2011) 010 [arXiv:1009.5039] [SPIRES].

    Article  ADS  MathSciNet  Google Scholar 

  7. A. Castro and F. Larsen, Near Extremal Kerr Entropy from AdS 2 Quantum Gravity, JHEP 12 (2009) 037 [arXiv:0908.1121] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  8. J. Rasmussen, A near-NHEK/CFT correspondence, Int. J. Mod. Phys. A 25 (2010) 5517 [arXiv:1004.4773] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  9. 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 

  10. J. Koga, Asymptotic symmetries on Killing horizons, Phys. Rev. D 64 (2001) 124012 [gr-qc/0107096] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  11. S. Silva, Black hole entropy and thermodynamics from symmetries, Class. Quant. Grav. 19 (2002) 3947 [hep-th/0204179] [SPIRES].

    Article  ADS  MATH  Google Scholar 

  12. G. Barnich and F. Brandt, Covariant theory of asymptotic symmetries, conservation laws and central charges, Nucl. Phys. B 633 (2002) 3 [hep-th/0111246] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  13. G. Compere, Symmetries and conservation laws in Lagrangian gauge theories with applications to the mechanics of black holes and to gravity in three dimensions, arXiv:0708.3153 [SPIRES].

  14. 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 

  15. V.P. Frolov and I.D. Novikov, Black Hole Physics, Kluwer (1998).

  16. C. Teitelboim, How commutators of constraints reflect the space-time structure, Ann. Phys. 79 (1973) 542 [SPIRES].

    Article  ADS  Google Scholar 

  17. J.L. Cardy, Operator Content of Two-Dimensional Conformally Invariant Theories, Nucl. Phys. B 270 (1986) 186 [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  18. H.W.J. Bloete, J.L. Cardy and M.P. Nightingale, Conformal Invariance, the Central Charge and Universal Finite Size Amplitudes at Criticality, Phys. Rev. Lett. 56 (1986) 742 [SPIRES].

    Article  ADS  Google Scholar 

  19. R. Bousso, A. Maloney and A. Strominger, Conformal vacua and entropy in de Sitter space, Phys. Rev. D 65 (2002) 104039 [hep-th/0112218] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  20. P. Di Francesco, P. Mathieu and D. Sénéchal, Conformal Field Theory, Springer (1997).

  21. A.J.M. Medved, D. Martin and M. Visser, Dirty black holes: Symmetries at stationary non-static horizons, Phys. Rev. D 70 (2004) 024009 [gr-qc/0403026] [SPIRES].

    MathSciNet  ADS  Google Scholar 

  22. A. Ori, Oscillatory null singularity inside realistic spinning black holes, Phys. Rev. Lett. 83 (1999) 5423 [gr-qc/0103012] [SPIRES].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  23. 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].

    MathSciNet  ADS  Google Scholar 

  24. M.-I. Park, Hamiltonian dynamics of bounded spacetime and black hole entropy: Canonical method, Nucl. Phys. B 634 (2002) 339 [hep-th/0111224] [SPIRES].

    Article  ADS  Google Scholar 

  25. G. Date, Isolated Horizon, Killing Horizon and Event Horizon, Class. Quant. Grav. 18 (2001) 5219 [gr-qc/0107039] [SPIRES].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  26. K.S. Thorne, D.A. MacDonald and R.H. Price, Black Holes: The Membrane Paradigm, Yale University Press, Yale U.S.A. (1986).

    Google Scholar 

  27. O. Dreyer, A. Ghosh and J. Wisniewski, Black hole entropy calculations based on symmetries, Class. Quant. Grav. 18 (2001) 1929 [hep-th/0101117] [SPIRES].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  28. S. Carlip, Black hole entropy and the problem of universality, J. Phys. Conf. Ser. 67 (2007) 012022 [gr-qc/0702094] [SPIRES].

    Article  ADS  Google Scholar 

  29. J.N. Goldberg, Dirac brackets for general relativity on a null cone, Found. Phys. 15 (1985) 439.

    Article  MathSciNet  ADS  Google Scholar 

  30. C.G. Torre, Null Surface Geometrodynamics, Class. Quant. Grav. 3 (1986) 773 [SPIRES].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  31. R.M. Wald, General Relativity, University of Chicago Press, Chicago U.S.A. (1984).

    MATH  Google Scholar 

  32. T. Regge and C. Teitelboim, Role of Surface Integrals in the Hamiltonian Formulation of General Relativity, Ann. Phys. 88 (1974) 286 [SPIRES].

    Article  MathSciNet  ADS  MATH  Google Scholar 

  33. J.D. Brown, S.R. Lau and J.W. York, Jr., Action and Energy of the Gravitational Field, gr-qc/0010024 [SPIRES].

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to S. Carlip.

Additional information

ArXiv ePrint: 1101.5136

Rights and permissions

Reprints and permissions

About this article

Cite this article

Carlip, S. Extremal and nonextremal Kerr/CFT correspondences. J. High Energ. Phys. 2011, 76 (2011). https://doi.org/10.1007/JHEP04(2011)076

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP04(2011)076

Keywords

Navigation