Advertisement

Foundations of Physics

, Volume 32, Issue 12, pp 1877–1889 | Cite as

How Far Can the Generalized Second Law Be Generalized?

  • P. C. W. Davies
  • Tamara M. Davis
Article

Abstract

Jacob Bekenstein's identification of black hole event horizon area with entropy proved to be a landmark in theoretical physics. In this paper we trace the subsequent development of the resulting generalized second law of thermodynamics (GSL), especially its extension to incorporate cosmological event horizons. In spite of the fact that cosmological horizons do not generally have well-defined thermal properties, we find that the GSL is satisfied for a wide range of models. We explore in particular the case of an asymptotically de Sitter universe filled with a gas of small black holes as a means of casting light on the relative entropic ‘worth’ of black hole versus cosmological horizon area. We present some numerical solutions of the generalized total entropy as a function of time for certain cosmological models, in all cases confirming the validity of the GSL.

entropy horizons de Sitter space cosmological constant black holes thermodynamics 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

REFERENCES

  1. 1.
    J. D. Bekenstein, Phys. Rev. D 7, 2333 (1973).Google Scholar
  2. 2.
    S. W. Hawking, Phys. Rev. Lett 26, 1344 (1971).Google Scholar
  3. 3.
    S. W. Hawking, Commun. Math. Phys. 43, 199 (1975).Google Scholar
  4. 4.
    S. W. Hawking, Phys. Rev. D 13(2), 191–197 (1976).Google Scholar
  5. 5.
    P. C. W. Davies, S. A. Fulling, and W. G. Unruh, Phys. Rev. D 13(10), 2720–2733 (1976).Google Scholar
  6. 6.
    G. W. Gibbons and S. W. Hawking, Phys. Rev. D 15, 10 (1977).Google Scholar
  7. 7.
    C. H. Lineweaver, “Cosmological parametersz,” in Proceedings COSMO-01, Rovaniemi, Finland, preprint astro-ph/0112381 (2001).Google Scholar
  8. 8.
    J. L. Sievers et al., “Cosmological parameters from cosmic background imager observations and comparisons with Boomerang, DASI and MAXIMAz,” submitted to Astrophys. J., preprint astro-ph/0205387 (2002).Google Scholar
  9. 9.
    T. Kiang, Chinese Astronomy and Astrophysics 21(1), 1–18 (1997).Google Scholar
  10. 10.
    N. D. Birrell and P. C. W. Davies, Quantum Fields in Curved Space (Cambridge University Press, Cambridge, 1982).Google Scholar
  11. 11.
    P. C. W. Davies, Class. Quantum Grav. 5, 1349–1355 (1988a).Google Scholar
  12. 12.
    P. C. W. Davies, Class. Quantum Grav. 4, L225–L228 (1987).Google Scholar
  13. 13.
    J. D. Barrow, Phys. Lett. B 183, 285 (1987).Google Scholar
  14. 14.
    P. C. W. Davies, Ann. Inst. Henri Poincaré 49(3), 297–306 (1988b).Google Scholar
  15. 15.
    B. Carter, in Les Astre Occlus (Gordon & Breach, New York, 1973).Google Scholar
  16. 16.
    P. C. W. Davies, Phys. Rev. D 30(4), 737–742 (1984).Google Scholar
  17. 17.
    P. C. W. Davies, L. H. Ford, and D. N. Page, Phys. Rev. D 34(6), 1700 (1986).Google Scholar
  18. 18.
    T. M. Davis, P. C. W. Davies, and C. H. Lineweaver, in preparation (2003).Google Scholar
  19. 19.
    T. Shiromizu, K. Nakao, H. Kodama, and K. Maeda, Phys. Rev. D 47, R3099 (1993).Google Scholar
  20. 20.
    S. A. Hayward, T. Shiromizu, and K. Nakao, Phys. Rev. D 49, 5080 (1994).Google Scholar
  21. 21.
    W. Boucher, G. W. Gibbons, and G. Horowitz, Phys. Rev. D 30, 2447 (1984).Google Scholar
  22. 22.
    K. Maeda, T. Koike, M. Narita, and A. Ishibashi, “Upper bound for entropy in asymptotically de Sitter space time,” preprint gr-qc/9712029 (1997).Google Scholar

Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • P. C. W. Davies
    • 1
  • Tamara M. Davis
    • 2
  1. 1.Australian Centre for AstrobiologyMacquarie UniversitySydneyAustralia
  2. 2.Department of AstrophysicsUniversity of New South WalesSydneyAustralia

Personalised recommendations