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Thermodynamic behavior of particular f(R,T)-gravity models

Abstract

We investigate the thermodynamics at the apparent horizon of the FRW universe in f(R, T) theory in the nonequilibrium description. The laws of thermodynamics are discussed for two particular models of the f(R, T) theory. The first law of thermodynamics is expressed in the form of the Clausius relation \(T_h d\hat S_h = \delta Q\), where δQ is the energy flux across the horizon and \(d\hat S\) is the entropy production term. Furthermore, the conditions for the generalized second law of thermodynamics to be preserved are established with the constraints of positive temperature and attractive gravity. We illustrate our results for some concrete models in this theory.

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References

  1. S. Perlmutter, G. Aldering, G. Goldhaber, R. A. Knop, P. Nugent, P. G. Castro, S. Deustua, S. Fabbro, A. Goobar, D. E. Groom, I. M. Hook, A. G. Kim, M. Y. Kim, J. C. Lee, N. J. Nunes, R. Pain, C. R. Pennypacker, R. Quimby, C. Lidman, R. S. Ellis, M. Irwin, R. G. McMahon, P. Ruiz-Lapuente, N. Walton, B. Schaefer, B. J. Boyle, A. V. Filippenko, T. Matheson, A. S. Fruchter, N. Panagia, H. J. M. Newberg, W. J. Couch, and The Supernova Cosmology Project, Astrophys. J. 517, 565 (1999).

    ADS  Article  Google Scholar 

  2. D. N. Spergel, R. Bean, O. Doré, M. R. Nolta, C. L. Bennett, J. Dunkley, G. Hinshaw, N. Jarosik, E. Komatsu, L. Page, H. V. Peiris, L. Verde, M. Halpern, R. S. Hill, A. Kogut, M. Limon, S. S. Meyer, N. Odegard, G. S. Tucker, J. L. Weiland, E. Wollack, and E. L. Wright, Astrophys. J., Suppl. Ser. 170, 377 (2007).

    ADS  Article  Google Scholar 

  3. M. Tegmark, M. A. Strauss, M. R. Blanton, K. Abazajian, S. Dodelson, H. Sandvik, X. Wang, D. H. Weinberg, I. Zehavi, N. A. Bahcall, F. Hoyle, D. Schlegel, R. Scoccimarro, M. S. Vogeley, A. Berlind, T. Budavari, A. Connolly, D. J. Eisenstein, D. Finkbeiner, J. A. Frieman, J. E. Gunn, L. Hui, B. Jain, D. Johnston, S. Kent, H. Lin, R. Nakajima, R. C. Nichol, J. P. Ostriker, A. Pope, R. Scranton, U. Seljak, R. K. Sheth, A. Stebbins, A. S. Szalay, I. Szapudi, Y. Xu, J. Annis, J. Brinkmann, S. Burles, F. J. Castander, I. Csabai, J. Loveday, M. Doi, M. Fukugita, B. Gillespie, G. Hennessy, D.W. Hogg, Ž. Ivezić, G. R. Knapp, D. Q. Lamb, B. C. Lee, R. H. Lupton, T. A. McKay, P. Kunszt, J. A. Munn, L. O’Connell, J. Peoples, J. R. Pier, M. Richmond, C. Rockosi, D. P. Schneider, C. Stoughton, D. L. Tucker, D. E. V. Berk, B. Yanny, and D. G. York, Phys. Rev. D: Part. Fields 69, 103501 (2004).

    ADS  Article  Google Scholar 

  4. D. J. Eisentein, I. Zehavi, D. W. Hogg, R. Scoccimarro, M. R. Blanton, R. C. Nichol, R. Scranton, H.-J. Seo, M. Tegmark, Z. Zheng, S. F. Anderson, J. Annis, N. Bahcall, J. Brinkmann, S. Burles, F. J. Castander, A. Connolly, I. Csabai, M. Doi, M. Fukugita, J. A. Frieman, K. Glazebrook, J. E. Gunn, J. S. Hendry, G. Hennessy, Z. Ivezić, S. Kent, G. R. Knapp, H. Lin, Y.-S. Loh, R. H. Lupton, B. Margon, T. A. McKay, A. Meiksin, J. A. Munn, A. Pope, M. W. Richmond, D. Schlegel, D. P. Schneider, K. Shimasaku, C. Stoughton, M. A. Strauss, M. Sub-baRao, A. S. Szalay, I. Szapudi, D. L. Tucker, B. Yanny, and D. G. York, Astrophys. J. 633, 560 (2005).

    ADS  Article  Google Scholar 

  5. B. Jain and A. Taylor, Phys. Rev. Lett. 91, 141302 (2003).

    ADS  Article  Google Scholar 

  6. M. Sharif and M. Zubair, Int. J. Mod. Phys. D 19, 1957 (2010).

    ADS  Article  MATH  Google Scholar 

  7. M. Sharif and M. Zubair, Astrophys. Space Sci. 330, 399 (2010); M. Sharif and M. Zubair, Astrophys. Space Sci. 339, 45 (2012).

    ADS  Article  MATH  Google Scholar 

  8. M. Li, X.-D. Li, S. Wang, and Y. Wang, Commun. Theor. Phys. 56, 525 (2011).

    ADS  Article  MATH  Google Scholar 

  9. A. De Felice and S. Tsujikawa, Living Rev. Relativ. 13, 3 (2010).

    ADS  Google Scholar 

  10. R. Ferraro and F. Fiorini, Phys. Rev. D: Part. Fields 75, 084031 (2007).

    MathSciNet  ADS  Article  Google Scholar 

  11. G. R. Bengochea and R. Ferraro, Phys. Rev. D: Part. Fields 79, 124019 (2009).

    ADS  Article  Google Scholar 

  12. T. Harko, F. S. N. Lobo, S. Nojiri, and S. D. Odintsov, Phys. Rev. D: Part. Fields 84, 024020 (2011).

    ADS  Article  Google Scholar 

  13. M. Sharif and M. Zubair, J. Phys. Soc. Jpn. 81, 114005 (2012); M. Sharif and M. Zubair, J. Phys. Soc. Jpn. 82, 014002 (2013).

    ADS  Article  Google Scholar 

  14. K. Bamba, S. Capozziello, S. Nojiri, and S. D. Odintsov, Astrophys. Space Sci. 345, 155 (2012).

    ADS  Article  Google Scholar 

  15. J. M. Bardeen, B. Carter, and S. W. Hawking, Commun. Math. Phys. 31, 161 (1973).

    MathSciNet  ADS  Article  MATH  Google Scholar 

  16. S. W. Hawking, Commun. Math. Phys. 43, 199 (1975).

    MathSciNet  ADS  Article  Google Scholar 

  17. J. D. Bekenstein, Phys. Rev. D: Part. Fields 7, 2333 (1973).

    MathSciNet  ADS  Article  Google Scholar 

  18. T. Jacobson, Phys. Rev. Lett. 75, 1260 (1995).

    MathSciNet  ADS  Article  MATH  Google Scholar 

  19. T. Padmanabhan, Phys. Rep. 406, 49 (2005).

    MathSciNet  ADS  Article  Google Scholar 

  20. R. G. Cai and S. P. Kim, J. High Energy Phys. (online) 02, 050 (2005).

    MathSciNet  ADS  Article  Google Scholar 

  21. C. Eling, R. Guedens, and T. Jacobson, Phys. Rev. Lett. 96, 121301 (2006).

    MathSciNet  ADS  Article  Google Scholar 

  22. M. Akbar and R. G. Cai, Phys. Rev. D: Part. Fields 75, 084003 (2007).

    ADS  Article  Google Scholar 

  23. S. A. Hayward, S. Mukohyama, and M. Ashworth, Phys. Lett. A 256, 347 (1999).

    MathSciNet  ADS  Article  Google Scholar 

  24. A. Sheykhi, B. Wang, and R. G. Cai, Phys. Rev. D: Part. Fields 76, 023515 (2007).

    MathSciNet  ADS  Article  Google Scholar 

  25. M. Akbar and R. G. Cai, Phys. Lett. B 648, 243 (2007).

    MathSciNet  ADS  Article  MATH  Google Scholar 

  26. R. G. Cai and L. M. Cao, Phys. Rev. D: Part. Fields 75, 064008 (2007).

    MathSciNet  ADS  Article  Google Scholar 

  27. S.-F. Wu, B. Wang, G.-H. Yang, and P.-M. Zhang, Classical Quantum Gravity 25, 235018 (2008).

    MathSciNet  ADS  Article  Google Scholar 

  28. Y. Gong and A. Wang, Phys. Rev. Lett. 99, 211301 (2007).

    MathSciNet  ADS  Article  Google Scholar 

  29. C. Eling, J. High Energy Phys. (online) 11, 048 (2008).

    MathSciNet  ADS  Article  Google Scholar 

  30. E. Elizalde and P. J. Silva, Phys. Rev. D: Part. Fields 78, 061501 (2008).

    MathSciNet  ADS  Article  Google Scholar 

  31. S.-F. Wu, X.-H. Ge, P.-M. Zhang, and G.-H. Yang, Phys. Rev. D: Part. Fields 81, 044034 (2010).

    ADS  Article  Google Scholar 

  32. K. Bamba and C. Q. Geng, Phys. Lett. B 679, 282 (2009).

    MathSciNet  ADS  Article  Google Scholar 

  33. K. Bamba and C. Q. Geng, J. Cosmol. Astropart. Phys. 06, 014 (2010); K. Bamba and C. Q. Geng, J. Cosmol. Astropart. Phys. 11, 008 (2011).

    MathSciNet  ADS  Article  Google Scholar 

  34. M. Sharif and M. Zubair, J. Cosmol. Astropart. Phys. 03, 028 (2012); M. Sharif and M. Zubair, J. Cosmol. Astropart. Phys. 05, E01 (2012).

    ADS  Article  Google Scholar 

  35. L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Volume 2: The Classical Theory of Fields (Fizmatlit, Moscow, 2001; Butterworth-Heinemann, Oxford, 2002).

    Google Scholar 

  36. R. M. Wald, Phys. Rev. D: Part. Fields 48, 3427 (1993).

    MathSciNet  ADS  Article  Google Scholar 

  37. R. Brustein, D. Gorbonos, and M. Hadad, Phys. Rev. D: Part. Fields 79, 044025 (2009).

    MathSciNet  ADS  Article  Google Scholar 

  38. C. W. Misner and D. H. Sharp, Phys. Rev. Sect. B 136, 571 (1964).

    MathSciNet  ADS  Article  Google Scholar 

  39. G. Izquierdo and D. Pavon, Phys. Lett. B 633, 420 (2006).

    MathSciNet  ADS  Article  MATH  Google Scholar 

  40. C. Corda, Eur. Phys. J. C 65, 257 (2010).

    ADS  Article  Google Scholar 

  41. S. Nojiri and S. D. Odintsov, Phys. Rev. D: Part. Fields 72, 023003 (2005).

    ADS  Article  Google Scholar 

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Sharif, M., Zubair, M. Thermodynamic behavior of particular f(R,T)-gravity models. J. Exp. Theor. Phys. 117, 248–257 (2013). https://doi.org/10.1134/S1063776113100075

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  • DOI: https://doi.org/10.1134/S1063776113100075

Keywords

  • Gravity Model
  • Horizon Entropy
  • Wald Entropy
  • Gravitational Coupling Constant
  • Clausius Relation