Advertisement

International Journal of Theoretical Physics

, Volume 48, Issue 9, pp 2672–2678 | Cite as

Generalized Second Law of Thermodynamics in Extended Theories of Gravity

  • M. Akbar
Article

Abstract

By employing the general expression for temperature \(T_{h}=|\kappa|/2\pi =\frac{1}{2\pi \tilde{r}_{A}}(1-\frac{\dot{\tilde{r}}_{A}}{2H\tilde{r}_{A}})\) associated with the apparent horizon of FRW universe and assuming a region of an expanding universe enclosed by the apparent horizon as a thermal system in equilibrium, we are able to show that the generalized second law of thermodynamics holds in Gauss-Bonnet and more general Lovelock gravities.

Keywords

Apparent horizon Generalized second law Extended theories of gravity 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Cai, R.G., Kim, S.P.: J. High Energy Phys. 02, 050 (2005). arXiv:hep-th/0501055 CrossRefADSMathSciNetGoogle Scholar
  2. 2.
    Gibbons, G.W., Hawking, S.W.: Phys. Rev. D 15, 2738 (1977) CrossRefADSMathSciNetGoogle Scholar
  3. 3.
    Akbar, M., Cai, R.G.: Phys. Rev. D 75, 084003 (2007) CrossRefADSGoogle Scholar
  4. 4.
    Eling, C., Guedens, R., Jacobson, T.: Phys. Rev. Lett. 96, 121301 (2006) CrossRefADSMathSciNetGoogle Scholar
  5. 5.
    Akbar, M., Cai, R.G.: Phys. Lett. B 648, 243 (2007) CrossRefADSMathSciNetGoogle Scholar
  6. 6.
    Cai, R.G., Cao, L.M., Hu, Y.P.: 0807.1232 [hep-th]
  7. 7.
    Cai, R.G., Cao, L.M.: Phys. Rev. D 75, 064008 (2007) CrossRefADSMathSciNetGoogle Scholar
  8. 8.
    Akbar, M., Cai, R.G.: Phys. Lett. B 635, 7 (2006). arXiv:hep-th/0602156 CrossRefADSMathSciNetGoogle Scholar
  9. 9.
    Kothawala, D., Sarkar, S., Padmanabhan, T.: arXiv:gr-qc/0701002
  10. 10.
    Padmanabhan, T.: Class. Quantum Gravity 19, 5387 (2002). arXiv:gr-qc/0204019 MATHCrossRefADSMathSciNetGoogle Scholar
  11. 11.
    Padmanabhan, T.: Phys. Rep. 406, 49 (2005). arXiv:gr-qc/0311036 CrossRefADSMathSciNetGoogle Scholar
  12. 12.
    Paranjape, A., Sarkar, S., Padmanabhan, T.: Phys. Rev. D 74, 104015 (2006). arXiv:hep-th/0607240 CrossRefADSMathSciNetGoogle Scholar
  13. 13.
    Akbar, M., Siddiqui, A.A.: Phys. Lett. B 656, 217 (2007) CrossRefADSMathSciNetGoogle Scholar
  14. 14.
    Akbar, M.: Chin. Phys. Lett. 24(5), 1158 (2007). hep-th/0702029 CrossRefADSGoogle Scholar
  15. 15.
    Cai, R.G., Cao, L.M.: hep-th/0612144
  16. 16.
    Sheykhi, A., Wang, B., Cai, R.G.: Nucl. Phys. B 779, 1 (2007). hep-th/0701198 MATHCrossRefADSMathSciNetGoogle Scholar
  17. 17.
    Sheykhi, A., Wang, B., Cai, R.G.: hep-th/0701261
  18. 18.
    Cai, R.G.: 0712.2142 [hep-th]
  19. 19.
    Wu, S.F., Wang, B., Yang, G.H., Zhang, P.M.: Class. Quantum Gravity 25, 235018 (2008). 0801.2688 [hep-th] CrossRefADSMathSciNetGoogle Scholar
  20. 20.
    Mohseni Sadjadi, H.: Phys. Lett. B 645, 108 (2007) CrossRefADSMathSciNetGoogle Scholar
  21. 21.
    Mohseni Sadjadi, H.: Phys. Rev. D 76, 104024 (2007) CrossRefADSMathSciNetGoogle Scholar
  22. 22.
    Barrow, J.D.: Nucl. Phys. B 310, 743 (1988) CrossRefADSMathSciNetGoogle Scholar
  23. 23.
    Giovannini, M.: Phys. Rev. D 59, 121301 (1999) CrossRefADSGoogle Scholar
  24. 24.
    Zimdahl, W., Pavon, D.: Phys. Rev. D 61, 108301 (2000) CrossRefADSGoogle Scholar
  25. 25.
    Setare, M.R.: Phys. Lett. B 641, 130 (2006) CrossRefADSMathSciNetGoogle Scholar
  26. 26.
    Akbar, M.: Chin. Phys. Lett. 25, 4199 (2008). 0808.0169 [gr-qc] CrossRefADSGoogle Scholar
  27. 27.
    Wald, R.M.: Phys. Rev. D 48, 3427 (1993) CrossRefADSMathSciNetGoogle Scholar
  28. 28.
    Cai, R.G.: Phys. Rev. D 65, 084014 (2002) CrossRefADSMathSciNetGoogle Scholar
  29. 29.
    Cai, R.G., Guo, Q.: Phys. Rev. D 69, 104025 (2004) CrossRefADSMathSciNetGoogle Scholar
  30. 30.
    Cai, R.G., Soh, K.S.: Phys. Rev. D 59, 044013 (1999) CrossRefADSMathSciNetGoogle Scholar
  31. 31.
    Wang, P.: Phys. Rev. D 72, 024030 (2005) CrossRefADSMathSciNetGoogle Scholar
  32. 32.
    Frolov, A.V., Kofman, L.: J. Cosmol. Astropart. Phys. 0305, 009 (2003) CrossRefADSMathSciNetGoogle Scholar
  33. 33.
    Bousso, R.: Phys. Rev. D 71, 064024 (2005). arXiv:hep-th/0412197 CrossRefADSMathSciNetGoogle Scholar
  34. 34.
    Lovelock, D.: J. Math. Phys. 12, 498 (1971) MATHCrossRefADSMathSciNetGoogle Scholar
  35. 35.
    Boulware, D.G., Deser, S.: Phys. Rev. Lett. 55, 2656 (1985) CrossRefADSGoogle Scholar
  36. 36.
    Wheeler, J.T.: Nucl. Phys. B 268, 737 (1986) CrossRefADSGoogle Scholar
  37. 37.
    Wheeler, J.T.: Nucl. Phys. B 273, 732 (1986) MATHCrossRefADSGoogle Scholar
  38. 38.
    Myers, R.C., Simon, J.Z.: Phys. Rev. D 38, 2434 (1988) CrossRefADSMathSciNetGoogle Scholar
  39. 39.
    Cai, R.G.: Phys. Lett. B 582, 237 (2004). hep-th/0311240 CrossRefADSMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Centre for Advanced Mathematics and PhysicsNational University of Sciences and TechnologyRawalpindiPakistan

Personalised recommendations