General Relativity and Gravitation

, Volume 39, Issue 10, pp 1519–1523

Symmetries, horizons, and black hole entropy

Open Access
Essay

Abstract

Black holes behave as thermodynamic systems, and a central task of any quantum theory of gravity is to explain these thermal properties. A statistical mechanical description of black hole entropy once seemed remote, but today we suffer an embarrassment of riches: despite counting very different states, many inequivalent approaches to quantum gravity obtain identical results. Such “universality” may reflect an underlying two-dimensional conformal symmetry near the horizon, which can be powerful enough to control the thermal characteristics independent of other details of the theory. This picture suggests an elegant description of the relevant degrees of freedom as Goldstone-boson-like excitations arising from symmetry breaking by the conformal anomaly.

References

  1. 1.
    Strominger, A., Vafa, C.: Phys. Lett. B 379, 99 (1996) hep-th/9601029Google Scholar
  2. 2.
    Skenderis, K.: Lect. Notes Phys. 541 325 (2000) hep-th/9901050Google Scholar
  3. 3.
    Mathur, S.D.: Fortsch. Phys. 53, 793 (2005) hep-th/0502050Google Scholar
  4. 4.
    Ashtekar, A., Baez, J., Corichi, A., Krasnov, K.: Phys. Rev. Lett. 80, 904 (1998) gr-qc/9710007Google Scholar
  5. 5.
    Livine, E.R., Terno, D.R.: Nucl. Phys. B 741, 131 (2006) gr-qc/0508085Google Scholar
  6. 6.
    Frolov, V.P., Fursaev, D.V.: Phys. Rev. D 56, 2212 (1997) hep-th/9703178Google Scholar
  7. 7.
    Rideout, D., Zohren, S.: Class Quant. Grav. 23, 6195 (2006) gr-qc/0606065Google Scholar
  8. 8.
    Hawking, S.W., Hunter, C.J.: Phys. Rev. D 59, 044025 (1999) hep-th/9808085Google Scholar
  9. 9.
    Bombelli L., Koul R.K., Lee J., Sorkin R.D. (1986). Phys. Rev. D 34: 373 CrossRefADSGoogle Scholar
  10. 10.
    Emparan, R.: JHEP 0606, 012 (2006) hep-th/0603081Google Scholar
  11. 11.
    Hawking S.W. (1974). Nature 248: 30 CrossRefADSGoogle Scholar
  12. 12.
    Birmingham, D., Gupta, K.S., Sen, S.: Phys. Lett. B 505, 191 (2001) hep-th/0102051Google Scholar
  13. 13.
    Medved, A.J.M., Martin, D., Visser, M.: Phys. Rev. D 70, 024009 (2004) gr-qc/0403026Google Scholar
  14. 14.
    Jacobson, T., Kang, G.: Class. Quant. Grav. 10, L201 (1993) gr-qc/9307002Google Scholar
  15. 15.
    Robinson, S.P., Wilczek, F.: Phys. Rev. Lett. 95, 011303 (2005) gr-qc/0502074Google Scholar
  16. 16.
    Iso, S., Morita, T., Umetsu, H.: hep-th/0701272Google Scholar
  17. 17.
    Cardy J.A. (1986). Nucl. Phys. B 270: 186 MATHCrossRefADSGoogle Scholar
  18. 18.
    Blöte H.W.J., Cardy J.A., Nightingale M.P. (1986). Phys. Rev. Lett. 56: 742 CrossRefADSGoogle Scholar
  19. 19.
    Brown J.D., Henneaux M. (1986). Commun. Math. Phys. 104: 207 MATHCrossRefADSGoogle Scholar
  20. 20.
    Carlip, S.: Class. Quant. Grav. 22, R85 (2005) gr-qc/0503022 (review)Google Scholar
  21. 21.
    Carlip, S.: Phys. Rev. Lett. 82, 2828 (1999) hep-th/9812013Google Scholar
  22. 22.
    Carlip, S.: Class. Quant. Grav. 16, 3327 (1999) gr-qc/9906126Google Scholar
  23. 23.
    Cvitan, M., Pallua, S., Prester, P.: Phys. Rev. D 70, 084043 (2004) hep-th/0406186Google Scholar
  24. 24.
    Dreyer, O., Ghosh, A., Wisniewski, J.: Class. Quant. Grav. 18, 1929 (2001) hep-th/0101117Google Scholar
  25. 25.
    Koga, J.: Phys. Rev. D 64, 124012 (2001) gr-qc/0107096Google Scholar
  26. 26.
    Carlip, S.: Class. Quant. Grav. 22, 1303 (2005) hep-th/0408123Google Scholar
  27. 27.
    Carlip, S.: gr-qc/0702107Google Scholar
  28. 28.
    Bergmann P.G., Komar A.B. (1960). Phys. Rev. Lett. 4: 432 CrossRefADSGoogle Scholar
  29. 29.
    Di Francesco, P., Mathieu, P., Sénéchal, D.: Conformal Field Theory. Springer, Heidelberg (1997)Google Scholar
  30. 30.
    Kaloper, N., Terning, J.: personal communicationGoogle Scholar
  31. 31.
    Carlip, S.: Class. Quant. Grav. 22, 3055 (2005) gr-qc/0501033Google Scholar
  32. 32.
    Aros, R., Romo, M., Zamorano, N.: hep-th/0612028Google Scholar
  33. 33.
    Emparan, R., Sachs, I.: Phys. Rev. Lett. 81, 2408 (1998) hep-th/9806122Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Department of PhysicsUniversity of CaliforniaDavisUSA

Personalised recommendations