Advertisement

General Relativity and Gravitation

, Volume 37, Issue 8, pp 1411–1417 | Cite as

Near extremal Schwarzschild-de Sitter black hole area spectrum from quasi-normal modes

  • M. R. Setare
Letter

Abstract

Using the quasi-normal modes frequency of near extremal Schwar-zschild-de Sitter black holes, we obtain area and entropy spectrum for the black hole horizon. By using Bohr-Sommerfeld quantization for an adiabatic invariant I = ∫dEω(E), where E is the energy of the system and ω(E) is the vibrational frequency, we arrive at an equally spaced mass spectrum. In the other terms, we extend directly the Kunstatter’s approach kun [6] to determine mass and entropy spectrum of near extremal Schwarzschild-de Sitter black holes which are asymptotically de Sitter rather than asymptotically flat. We show the mass and area spectrum is equally spaced only for a fixed l. For different l there are multiplets with different values of spacing.

Keywords

Extremal Schwarzschild-de Sitter black hole Bohr-Sommerfeld quantization 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bekenstein, J.D.: Lett. Nuovo Cimento 11, 467 (1974)Google Scholar
  2. 2.
    Bekenstein, J.D., Mukhanov, V.F.: Phys. Lett. B360, 7 (1995)Google Scholar
  3. 3.
    Kastrup, H.A.: Phys. Lett. B 385, 75 (1996)CrossRefGoogle Scholar
  4. 4.
    Bekenstein, J.D.: [gr-qc/9808028]Google Scholar
  5. 5.
    Hod, S.: Phys. Rev. Lett. 81, 4293 (1998)CrossRefGoogle Scholar
  6. 6.
    Dreyer, O.: Phys. Rev. Lett. 90, 081301 (2003)CrossRefPubMedGoogle Scholar
  7. 7.
    Kunstatter, G.: Phys. Rev. Lett. 90, 161301 (2003)CrossRefPubMedGoogle Scholar
  8. 8.
    Motl, L.: Adv. Theor. Math. Phys. 6, 1135 (2003)Google Scholar
  9. 9.
    Corichi, A.: [gr-qc/0212126]Google Scholar
  10. 10.
    Abdalla, E., Castello-Branco, K.H.C., Lima-Santos, A.: [gr-qc/0301130]Google Scholar
  11. 11.
    Cardoso, V., Lemos, J.P.S.: Phys. Rev. D67, 084020 (2003)Google Scholar
  12. 12.
    Hod, S.: Phys. Rev. D 67, 081501 (2003)CrossRefGoogle Scholar
  13. 13.
    Berti, E., Kokkotas, K.D.: [hep-th/0303029]Google Scholar
  14. 14.
    Polychronakos, A.P.: [hep-th/0304135]Google Scholar
  15. 15.
    Cardoso, V., Konoplya, R., Lemos, J.P.S.: [gr-qc/0305037]Google Scholar
  16. 16.
    Birmingham, D.: [hep-th/0306004]Google Scholar
  17. 17.
    Padmanabhan, T., Patel, A.: [gr-qc/0309053]Google Scholar
  18. 18.
    Setare, M.R.: Class. Quant. Grav. 21, 1453 (2004)CrossRefGoogle Scholar
  19. 19.
    Setare, M.R.: Phys. Rev. D 69, 044016 (2004)CrossRefGoogle Scholar
  20. 20.
    Regge, T., Wheeler, J.A.: Phys. Rev. 108, 1063 (1957)CrossRefGoogle Scholar
  21. 21.
    Chandrasekhar, S., Detweiler, S.: Proc. R. Soc. London, Ser. A 344, 441 (1975)Google Scholar
  22. 22.
    Horowitz, G.T., Hubeny, V.: Phys. Rev D 62, 024027 (2000)CrossRefGoogle Scholar
  23. 23.
    Cardoso, V., Lemos, J.P.S.: Phys. Rev. D 63, 124015 (2001)CrossRefGoogle Scholar
  24. 24.
    Chan, J.S.F., Mann, R.B.: Phys. Rev. D 59, 064025 (1999)CrossRefGoogle Scholar
  25. 25.
    Birmingham, D., Sachs, I., Solodukhin, S.N.: Phys. Rev. Lett. 88, 151301 (2002)CrossRefPubMedGoogle Scholar
  26. 26.
    Birmingham, D., Sachs, I., Solodukhin, S.N.: [hep-th/0212308]Google Scholar
  27. 27.
    Konoplya, R.A.: Phys. Rev. D 66, 044009 (2002)CrossRefGoogle Scholar
  28. 28.
    Konoplya, R.A.: Phys. Rev. D 66, 084007 (2002)CrossRefGoogle Scholar
  29. 29.
    Starinets, A.O.: Phys. Rev. D 66, 124013 (2002)CrossRefGoogle Scholar
  30. 30.
    Abdalla, E., Castello-Branco, K.H.C., Lima-Santos, A.: [hep-th/0208065]Google Scholar
  31. 31.
    Aros, R., Martinez, C., Troncoso, R., Zanelli, J.: Phys. Rev. D 67, 044014 (2003)CrossRefGoogle Scholar
  32. 32.
    Fernando, S.: [hep-th/0306214]Google Scholar
  33. 33.
    Moss, I.G., Norman, J.P.: Class. Quant. Grav. 19, 2323 (2002)CrossRefGoogle Scholar
  34. 34.
    Birmingham, D., Carlip, S.: [hep-th/0311090]Google Scholar
  35. 35.
    Motl, L.: [gr-qc/0212096]Google Scholar
  36. 36.
    Ling, Y., Zhang, H.: Phys. Rev. D 68, 101501 (2003)CrossRefGoogle Scholar
  37. 37.
    Konoplya, R.A.: Phys. Lett. B 550, 117 (2002)CrossRefGoogle Scholar
  38. 38.
    Kim, W.T., Oh, J.J.: Phys. Lett. B 514, 155 (2001)CrossRefGoogle Scholar
  39. 39.
    Bekenstein, J.D.: [gr-qc/9710076]Google Scholar
  40. 40.
    Poshl, G., Teller, E.: Z. Phys. 83, 143 (1933)CrossRefGoogle Scholar
  41. 41.
    Ferrari, V., Mashhoon, B.: Phys. Rev. D 30, 295 (1984)CrossRefGoogle Scholar
  42. 42.
    Castello-Branco, K.H.C., Abdalla, E.: [gr-qc/0309090]Google Scholar
  43. 43.
    Medved, A.J.M., Martin, D.: [gr-qc/0311086]Google Scholar
  44. 44.
    Poshl, G., Teller, E.: Z. Phys. 83, 114 (1933)Google Scholar
  45. 45.
    Abbott, L.F., Deser, S.: Nucl. Phys. B 195, 76 (1982)CrossRefGoogle Scholar
  46. 46.
    Andersson, N., Howls, C.J.: [gr-qc/0307020]Google Scholar

Copyright information

© Springer-Verlag 2005

Authors and Affiliations

  1. 1.Physics Dept. Inst. for Studies in TheorPhysics and Mathematics (IPM)TehranIran

Personalised recommendations