Entropy spectrum of a Kerr anti-de Sitter black hole

  • Deyou Chen
  • Haitang YangEmail author
Regular Article - Theoretical Physics


The entropy spectrum of a spherically symmetric black hole was derived without the quasinormal modes in the work of Majhi and Vagenas. Extending this work to rotating black holes, we quantize the entropy and the horizon area of a Kerr anti-de Sitter black hole by two methods. The spectra of entropy and area are obtained via the Bohr–Sommerfeld quantization rule and the adiabatic invariance in the first way. By addressing the wave function of emitted (absorbed) particles, the entropy and the area are quantized in the second one. Both results show that the entropy and the area spectra are equally spaced.


Black Hole Event Horizon Quasinormal Mode Loop Quantum Gravity Horizon Area 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This work is supported in part by the Natural Science Foundation of China (Grant No. 11178018 and No. 11175039).


  1. 1.
    J.D. Bekenstein, The quantum mass spectrum of the Kerr black hole. Lett. Nuovo Cimento 11, 467 (1974) ADSCrossRefGoogle Scholar
  2. 2.
    S. Hod, Bohr’s correspondence principle and the area spectrum of quantum black holes. Phys. Rev. Lett. 81, 4293 (1998) MathSciNetADSzbMATHCrossRefGoogle Scholar
  3. 3.
    O. Dreyer, Quasinormal modes, the area spectrum, and black hole entropy. Phys. Rev. Lett. 90, 081301 (2003) ADSCrossRefGoogle Scholar
  4. 4.
    G. Kunstatter, D-dimensional black hole entropy spectrum from quasi-normal modes. Phys. Rev. Lett. 90, 161301 (2003) MathSciNetADSCrossRefGoogle Scholar
  5. 5.
    M.R. Setare, Area spectrum of extremal Reissner–Nordstrom black holes from quasi-normal modes. Phys. Rev. D 69, 044016 (2004) MathSciNetADSCrossRefGoogle Scholar
  6. 6.
    M.R. Setare, Non-rotating BTZ black hole area spectrum from quasi-normal modes. Class. Quantum Gravity 21, 1453 (2004) MathSciNetADSzbMATHCrossRefGoogle Scholar
  7. 7.
    M.R. Setare, Near extremal Schwarzschild-de Sitter black hole area spectrum from quasi-normal modes. Gen. Relativ. Gravit. 37, 1411 (2005) MathSciNetADSzbMATHCrossRefGoogle Scholar
  8. 8.
    M. Maggiore, The physical interpretation of the spectrum of black hole quasinormal modes. Phys. Rev. Lett. 100, 141301 (2008) MathSciNetADSCrossRefGoogle Scholar
  9. 9.
    E.C. Vagenas, Area spectrum of rotating black holes via the new interpretation of quasinormal modes. J. High Energy Phys. 0811, 073 (2008) MathSciNetADSCrossRefGoogle Scholar
  10. 10.
    A.J.M. Medved, On the Kerr quantum area spectrum. Class. Quantum Gravity 25, 205014 (2008) MathSciNetADSCrossRefGoogle Scholar
  11. 11.
    D. Kothawala, T. Padmanabhan, S. Sarkar, Is gravitational entropy quantized? Phys. Rev. D 78, 104018 (2008) MathSciNetADSCrossRefGoogle Scholar
  12. 12.
    R. Banerjee, B.R. Majhi, E.C. Vagenas, Quantum tunneling and black hole spectroscopy. Phys. Lett. B 686, 279 (2010) ADSCrossRefGoogle Scholar
  13. 13.
    A. Lopez-Ortega, Area spectrum of the D-dimensional de Sitter spacetime. Phys. Lett. B 682, 85 (2009) MathSciNetADSCrossRefGoogle Scholar
  14. 14.
    S. Fernando, Spinning dilaton black holes in 2+1 dimensions: quasi-normal modes and the area spectrum. Phys. Rev. D 79, 124026 (2009) MathSciNetADSCrossRefGoogle Scholar
  15. 15.
    K. Ropotenko, Quantization of the black hole area as quantization of the angular momentum component. Phys. Rev. D 80, 044022 (2009) MathSciNetADSCrossRefGoogle Scholar
  16. 16.
    S.W. Wei, R. Li, Y.X. Liu, J.R. Ren, Quantization of black hole entropy from quasinormal modes. J. High Energy Phys. 0903, 076 (2009) MathSciNetGoogle Scholar
  17. 17.
    Y. Kwon, S. Nam, Area spectra of the rotating BTZ black hole from quasi-normal modes. arXiv:1001.5106 [hep-th]
  18. 18.
    Y.S. Myung, Area spectrum of slowly rotating black holes. arXiv:1003.3519 [hep-th]
  19. 19.
    D. Chen, H. Yang, X.T. Zu, Area spectra of near extremal black holes. Eur. Phys. J. C 69, 289 (2010) ADSCrossRefGoogle Scholar
  20. 20.
    M.R. Setare, E.C. Vagenas, Area spectrum of Kerr and extremal Kerr black holes from Quasinormal modes. Mod. Phys. Lett. A 20, 1923 (2005) MathSciNetADSzbMATHCrossRefGoogle Scholar
  21. 21.
    E. Berti, V. Cardoso, A.O. Starinets, Quasinormal modes of black holes and black branes. arXiv:0905.2975 [gr-qc]
  22. 22.
    S.W. Wei, Y.X. Liu, K. Yang, Y. Zhong, Entropy/area spectra of the charged black hole from quasinormal modes. Phys. Rev. D 81, 104042 (2010) ADSCrossRefGoogle Scholar
  23. 23.
    W. Li, L. Xu, J. Lu, Area spectrum of near-extremal SdS black holes via the new interpretation of quasinormal modes. Phys. Lett. B 676, 177 (2009) MathSciNetADSCrossRefGoogle Scholar
  24. 24.
    P. Gonzalez, E. Papantonopoulos, J. Saavedra, Quasi-normal modes of scalar perturbations, mass and area spectrum of Chern-Simons black holes. J. High Energy Phys. 08, 050 (2010) MathSciNetADSCrossRefGoogle Scholar
  25. 25.
    B.R. Majhi, E.C. Vagenas, Black hole spectroscopy via adiabatic invariance. Phys. Lett. B 701, 623 (2011) ADSCrossRefGoogle Scholar
  26. 26.
    B. Carter, Killing horizons and orthogonally transitive groups in space-time. Commun. Math. Phys. 10, 280 (1968) zbMATHGoogle Scholar
  27. 27.
    Z.Z. Ma, Euler numbers of four-dimensional rotating black holes with the Euclidean signature. Phys. Rev. D 67, 024027 (2003) MathSciNetADSCrossRefGoogle Scholar
  28. 28.
    G.W. Gibbons, M.J. Perry, Black holes and thermal Green functions. Proc. R. Soc. Lond. A 358, 467 (1978) MathSciNetADSCrossRefGoogle Scholar
  29. 29.
    M.K. Parikh, F. Wilczek, Hawking radiation as tunneling. Phys. Rev. Lett. 85, 5042 (2000) MathSciNetADSCrossRefGoogle Scholar
  30. 30.
    J.Y. Zhang, Z. Zhao, Hawking radiation of charged particles via tunneling from the Reissner–Nordstrom black hole. J. High Energy Phys. 10, 055 (2005) ADSCrossRefGoogle Scholar
  31. 31.
    K. Umetsu, Hawking radiation from Kerr–Newman black hole and tunneling mechanism. Int. J. Mod. Phys. A 25, 4123 (2010) MathSciNetADSzbMATHCrossRefGoogle Scholar
  32. 32.
    R. Kerner, R.B. Mann, Fermions tunnelling from black holes. Class. Quantum Gravity 25, 095014 (2008) MathSciNetADSCrossRefGoogle Scholar
  33. 33.
    R. Kerner, R.B. Mann, Charged fermions tunnelling from Kerr–Newman black holes. Phys. Lett. B 665, 277 (2008) MathSciNetADSCrossRefGoogle Scholar
  34. 34.
    D. Chen, H. Yang, X.T. Zu, Fermion tunneling from anti-de Sitter spaces. Eur. Phys. J. C 56, 119 (2008) MathSciNetADSzbMATHCrossRefGoogle Scholar
  35. 35.
    X.X. Zeng, X.M. Liu, W.B. Liu, Periodicity and area spectrum of black holes. arXiv:1203.5947 [gr-qc]
  36. 36.
    R.K. Kaul, P. Majumdar, Logarithmic correction to the Bekenstein–Hawking entropy. Phys. Rev. Lett. 84, 5255 (2000) MathSciNetADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag / Società Italiana di Fisica 2012

Authors and Affiliations

  1. 1.Institute of Theoretical PhysicsChina West Normal UniversityNanchongChina
  2. 2.Department of PhysicsSichuan UniversityChengduChina

Personalised recommendations