Advertisement

Thermodynamics of Gauss–Bonnet black holes revisited

Regular Article - Theoretical Physics

Abstract

We investigate the Gauss–Bonnet black hole in five dimensional anti-de Sitter spacetimes (GBAdS). We analyze all thermodynamic quantities of the GBAdS, which is characterized by the Gauss–Bonnet coupling c and mass M, comparing with those of the Born–Infeld-AdS (BIAdS), Reissner–Norström-AdS black holes (RNAdS), Schwarzschild-AdS (SAdS), and BTZ black holes. For c<0 we cannot obtain the black hole with positively definite thermodynamic quantities of mass, temperature, and entropy, because the entropy does not satisfy the area law. On the other hand, for c>0, we find the BIAdS-like black hole, showing that the coupling c plays the role of a pseudo-charge. Importantly, we could not obtain the SAdS in the limit of c→0, which means that the GBAdS is basically different from the SAdS. In addition, we clarify the connections between thermodynamic and dynamical stability. Finally, we also conjecture that if a black hole is big and thus globally stable, its quasi-normal modes may take on analytic expressions.

PACS

04.70.Dy 04.50.Gh 04.70.-s 

References

  1. 1.
    D.G. Boulware, S. Deser, String generated gravity models. Phys. Rev. Lett. 55, 2656 (1985) CrossRefADSGoogle Scholar
  2. 2.
    R.C. Myers, J.Z. Simon, Black hole thermodynamics in lovelock gravity. Phys. Rev. D 38, 2434 (1988) CrossRefADSMathSciNetGoogle Scholar
  3. 3.
    D.J. Gross, E. Witten, Superstring modifications of Einstein’s equations. Nucl. Phys. B 277, 1 (1986) CrossRefADSMathSciNetGoogle Scholar
  4. 4.
    R.R. Metsaev, A.A. Tseytlin, Two loop beta function for the generalized bosonic sigma model. Phys. Lett. B 191, 354 (1987) CrossRefADSGoogle Scholar
  5. 5.
    C.G. Callan, R.C. Myers, M.J. Perry, Black holes in string theory. Nucl. Phys. B 311, 673 (1989) CrossRefADSMathSciNetGoogle Scholar
  6. 6.
    R.C. Myers, Higher derivative gravity, surface terms and string theory. Phys. Rev. D 36, 392 (1987) CrossRefADSMathSciNetGoogle Scholar
  7. 7.
    J.T. Wheeler, Symmetric solutions to the Gauss–Bonnet extended Einstein equations. Nucl. Phys. B 268, 737 (1986) CrossRefADSGoogle Scholar
  8. 8.
    Y.M. Cho, I.P. Neupane, Anti-de Sitter black holes, thermal phase transition and holography in higher curvature gravity. Phys. Rev. D 66, 024044 (2002). arXiv:hep-th/0202140 CrossRefADSMathSciNetGoogle Scholar
  9. 9.
    T. Torii, H. Maeda, Spacetime structure of static solutions in Gauss–Bonnet gravity: Neutral case. Phys. Rev. D 71, 124002 (2005). arXiv:hep-th/0504127 CrossRefADSMathSciNetGoogle Scholar
  10. 10.
    S.W. Hawking, D.N. Page, Thermodynamics of black holes in anti-de Sitter space. Commun. Math. Phys. 87, 577 (1983) CrossRefADSMathSciNetGoogle Scholar
  11. 11.
    E. Witten, Anti-de Sitter space, thermal phase transition, and confinement in gauge theories. Adv. Theor. Math. Phys. 2, 505 (1998) arXiv:hep-th/9803131 MATHMathSciNetGoogle Scholar
  12. 12.
    A. Chamblin, R. Emparan, C.V. Johnson, R.C. Myers, Charged AdS black holes and catastrophic holography. Phys. Rev. D 60, 064018 (1999). arXiv:hep-th/9902170 CrossRefADSMathSciNetGoogle Scholar
  13. 13.
    T.K. Dey, S. Mukherji, S. Mukhopadhyay, S. Sarkar, Phase transitions in higher derivative gravity and gauge theory: R-charged black holes. J. High. Energy Phys. 0709, 026 (2007). arXiv:0706.3996 [hep-th] CrossRefADSMathSciNetGoogle Scholar
  14. 14.
    Y.S. Myung, Phase transition between non-extremal and extremal Reissner–Nordstrom black holes. Mod. Phys. Lett. A 23, 667 (2008). arXiv:0710.2568 [gr-qc] MATHCrossRefADSMathSciNetGoogle Scholar
  15. 15.
    T.K. Dey, S. Mukherji, S. Mukhopadhyay, S. Sarkar, Phase transitions in higher derivative gravity. J. High. Energy Phys. 0704, 014 (2007). arXiv:hep-th/0609038 CrossRefADSMathSciNetGoogle Scholar
  16. 16.
    Y.S. Myung, Y.-W. Kim, Y.-J. Park, Thermodynamics of Einstein–Born–Infeld black holes in three dimensions. Phys. Rev. D 78, 044020 (2008). arXiv:0804.0301 [gr-qc] CrossRefADSMathSciNetGoogle Scholar
  17. 17.
    Y.S. Myung, Y.-W. Kim, Y.-J. Park, Thermodynamics and phase transitions in the Born–Infeld-anti-de Sitter black holes. Phys. Rev. D. 78, 084002 (2008). arXiv:0805.0187 [gr-qc] CrossRefADSMathSciNetGoogle Scholar
  18. 18.
    K.D. Kokkotas, B.G. Schmidt, Quasi-normal modes of stars and black holes. Living Rev. Relativ. 2, 2 (1999). arXiv:gr-qc/9909058 ADSMathSciNetGoogle Scholar
  19. 19.
    D. Birmingham, I. Sachs, S.N. Solodukhin, Conformal field theory interpretation of black hole quasi-normal modes. Phys. Rev. Lett. 88, 151301 (2002). arXiv:hep-th/0112055 CrossRefADSMathSciNetGoogle Scholar
  20. 20.
    D. Birmingham, S. Mokhtari, Exact gravitational quasi-normal frequencies of topological black holes. Phys. Rev. D 74, 084026 (2006). arXiv:hep-th/0609028 CrossRefADSMathSciNetGoogle Scholar
  21. 21.
    G.T. Horowitz, V.E. Hubeny, Quasinormal modes of AdS black holes and the approach to thermal equilibrium. Phys. Rev. D 62, 024027 (2000). arXiv:hep-th/9909056 CrossRefADSMathSciNetGoogle Scholar
  22. 22.
    G. Siopsis, Analytic calculation of quasi-normal modes. arXiv:0804.2713 [hep-th]
  23. 23.
    Y.S. Myung, H.W. Lee, Unitarity issue in BTZ black holes. Mod. Phys. Lett. A 21, 1737 (2006). arXiv:hep-th/0506031 MATHCrossRefADSMathSciNetGoogle Scholar
  24. 24.
    S. Musiri, G. Siopsis, Asymptotic form of quasi-normal modes of large AdS black holes. Phys. Lett. B 576, 309 (2003). arXiv:hep-th/0308196 MATHCrossRefADSMathSciNetGoogle Scholar
  25. 25.
    E. Berti, V. Cardoso, Quasinormal modes and thermodynamic phase transitions. Phys. Rev. D 77, 087501 (2008). arXiv:0802.1889 [hep-th] CrossRefADSGoogle Scholar
  26. 26.
    J. Grain, A. Barrau, Eur. Phys. J. C 53, 641 (2008). arXiv:hep-th/0701265 CrossRefADSMathSciNetGoogle Scholar
  27. 27.
    T. Hirayama, Negative modes of Schwarzschild black hole in Einstein–Gauss–Bonnet Theory. arXiv:0804.3694 [gr-qc]
  28. 28.
    R. Myers, Superstring gravity and black holes. Nucl. Phys. B 289, 701 (1987) CrossRefADSGoogle Scholar
  29. 29.
    S. Nojiri, S.D. Odintsov, Anti-de Sitter black hole thermodynamics in higher derivative gravity and new confining–deconfining phases in dual CFT. Phys. Lett. B 521, 87 (2001) [Erratum: Phys. Lett. B 542, 301 (2002)]. arXiv:hep-th/0109122 MATHCrossRefADSMathSciNetGoogle Scholar
  30. 30.
    R.G. Cai, Gauss–Bonnet black holes in AdS spaces. Phys. Rev. D 65, 084014 (2002). arXiv:hep-th/0109133 CrossRefADSMathSciNetGoogle Scholar
  31. 31.
    M. Cvetic, S. Nojiri, S.D. Odintsov, Black hole thermodynamics and negative entropy in de Sitter and anti-de Sitter Einstein–Gauss–Bonnet gravity. Nucl. Phys. B 628, 295 (2002). arXiv:hep-th/0112045 MATHCrossRefADSMathSciNetGoogle Scholar
  32. 32.
    I.P. Neupane, Black hole entropy in string-generated gravity models. Phys. Rev. D 67, 061501 (2003). arXiv:hep-th/0212092 CrossRefADSMathSciNetGoogle Scholar
  33. 33.
    I.P. Neupane, Thermodynamic and gravitational instability on hyperbolic spaces. Phys. Rev. D 69, 084011 (2004). arXiv:hep-th/0302132 CrossRefADSGoogle Scholar
  34. 34.
    T. Clunan, S.F. Ross, D.J. Smith, On Gauss–Bonnet black hole entropy. Class. Quantum Gravity 21, 3447 (2004). arXiv:gr-qc/0402044 MATHCrossRefADSMathSciNetGoogle Scholar
  35. 35.
    P.C.W. Davies, The thermodynamic theory of black holes. Proc. R. Soc. Lond. A 353, 499 (1977) ADSCrossRefGoogle Scholar
  36. 36.
    D. Pavon, Phase transition in Reissner–Nordström black holes. Phys. Rev. D 43, 2495 (1991) CrossRefADSGoogle Scholar
  37. 37.
    J. Jing, Q. Pan, Quasinormal modes and second order thermodynamic phase transition for Reissner–Nordström black hole. Phys. Lett. B 660, 13 (2008). arXiv:0802.0043 [gr-qc] CrossRefADSGoogle Scholar
  38. 38.
    Y.S. Myung, Y.-W. Kim, Y.-J. Park, Ruppeiner geometry and 2D dilaton gravity in the thermodynamics of black holes. Phys. Lett. B 663, 342 (2008). arXiv:0802.2152 [hep-th] CrossRefADSMathSciNetGoogle Scholar
  39. 39.
    Y.S. Myung, Phase transition between the BTZ black hole and AdS space. Phys. Lett. B 638, 515 (2006). arXiv:gr-qc/0603051 CrossRefADSMathSciNetGoogle Scholar
  40. 40.
    T. Harmark, V. Niarchos, N.A. Obers, Instabilities of black strings and branes. Class. Quantum Gravity 24, R1 (2007). arXiv:hep-th/0701022 MATHCrossRefADSMathSciNetGoogle Scholar
  41. 41.
    S.S. Gubser, I. Mitra, Instability of charged black holes in anti-de Sitter space. arXiv:hep-th/0009126
  42. 42.
    S.S. Gubser, I. Mitra, The evolution of unstable black holes in anti-de Sitter space. J. High. Energy Phys. 0108, 018 (2001). arXiv:hep-th/0011127 CrossRefADSMathSciNetGoogle Scholar
  43. 43.
    H.S. Reall, Classical and thermodynamic stability of black branes. Phys. Rev. D 64, 044005 (2001). arXiv:hep-th/0104071 CrossRefADSMathSciNetGoogle Scholar
  44. 44.
    R.K. Kaul, P. Majumdar, Quantum black hole entropy. Phys. Lett. B 439, 267 (1998). arXiv:gr-qc/9801080 CrossRefADSMathSciNetGoogle Scholar
  45. 45.
    R.K. Kaul, P. Majumdar, Logarithmic correction to the Bekenstein–Hawking entropy. Phys. Rev. Lett. 84, 5255 (2000). arXiv:gr-qc/0002040 CrossRefADSMathSciNetGoogle Scholar
  46. 46.
    S. Carlip, Logarithmic corrections to black hole entropy from the Cardy formula. Class. Quantum Gravity 17, 4175 (2000) arXiv:gr-qc/0005017 MATHCrossRefADSMathSciNetGoogle Scholar
  47. 47.
    T.R. Govindarajan, R.K. Kaul, V. Suneeta, Logarithmic correction to the Bekenstein–Hawking entropy of the BTZ black. Class. Quantum Gravity 18, 2877 (2001). arXiv:gr-qc/0104010 MATHCrossRefADSMathSciNetGoogle Scholar
  48. 48.
    D. Birmingham, S. Sen, An exact black hole entropy bound. Phys. Rev. D 63, 047501 (2001). arXiv:hep-th/0008051 CrossRefADSMathSciNetGoogle Scholar
  49. 49.
    R. Banerjee, B.R. Majhi, Quantum tunneling and back reaction. Phys. Lett. B 662, 62 (2008). arXiv:0801.0200 [hep-th] CrossRefADSMathSciNetGoogle Scholar
  50. 50.
    R. Banerjee, B.R. Majhi, Quantum tunneling beyond semiclassical approximation. J. High Energy Phys. 0806, 095 (2008). arXiv:0805.2220 [hep-th] CrossRefADSMathSciNetGoogle Scholar
  51. 51.
    S. Das, P. Majumdar, R.K. Bhaduri, General logarithmic corrections to black hole entropy. Class. Quantum Gravity 19, 2355 (2002). arXiv:hep-th/0111001 MATHCrossRefADSMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag / Società Italiana di Fisica 2008

Authors and Affiliations

  1. 1.Institute of Basic Science and School of Computer Aided ScienceInje UniversityGimhaeSouth Korea
  2. 2.Department of PhysicsSogang UniversitySeoulSouth Korea

Personalised recommendations