Advertisement

Modifying horizon thermodynamics by surface tensions

  • Deyou ChenEmail author
  • Xiaoxiong Zeng
Research Article
  • 9 Downloads

Abstract

The modified first laws of thermodynamics at the black hole horizon and the cosmological horizon of the Schwarzschild de Sitter black hole and the apparent horizon of the Friedmann–Robertson–Walker cosmology are derived by the surface tensions, respectively. The corresponding Smarr relations are obeyed. For the black hole, the cosmological constant is first treated as a fixed constant, and then as a variable associated to the pressure. The law at the apparent horizon takes the same form as that at the cosmological horizon, but is different from that at the black hole horizon. The positive temperatures guarantee the appearance of the worked terms in the modified laws at the cosmological and apparent horizons. While they can disappear at the black hole horizon.

Keywords

Surface tensions Horizon thermodynamics Schwarzschild de Sitter black holes 

Notes

Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant No. 11875095).

References

  1. 1.
    Padmanabhan, T.: Classical and quantum thermodynamics of horizons in spherically symmetric spacetimes. Class. Quant. Grav. 19, 5387 (2002). arXiv:gr-qc/0204019 ADSMathSciNetCrossRefGoogle Scholar
  2. 2.
    Cai, R.G.: Connections between gravitational dynamics and thermodynamics. J. Phys. Conf. Ser. 484, 012003 (2014)CrossRefGoogle Scholar
  3. 3.
    Sarkar, S., Kothawala, D.: Hawking radiation as tunneling for spherically symmetric black holes: a generalized treatment. Phys. Lett. B 659, 683 (2008). arXiv:0709.4448 [gr-qc]ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    Padmanabhan, T., Kothawala, D.: Lanczos–Lovelock models of gravity. Phys. Rep. 531, 115 (2013). arXiv:1302.2151 [gr-qc]ADSMathSciNetCrossRefGoogle Scholar
  5. 5.
    Kothawala, D., Sarkar, S., Padmanabhan, T.: Einstein’s equations as a thermodynamic identity: the cases of stationary axisymmetric horizons and evolving spherically symmetric horizons. Phys. Lett. B 652, 338 (2007). arXiv:gr-qc/0701002 ADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    Akbar, M., Siddiqui, A.A.: Charged rotating BTZ black hole and thermodynamic behavior of field equations at its horizon. Phys. Lett. B 656, 217 (2007). arXiv:1302.2151 [gr-qc]ADSMathSciNetCrossRefGoogle Scholar
  7. 7.
    Kubiznak, D., Mann, R.B.: P-V criticality of charged AdS black holes. JHEP 1207, 033 (2012). arXiv:1205.0559 [hep-th]ADSMathSciNetCrossRefGoogle Scholar
  8. 8.
    Dolan, B.P.: Pressure and volume in the first law of black hole thermodynamics. Class. Quant. Grav. 28, 235017 (2011). arXiv:1106.6260 [gr-qc]ADSMathSciNetCrossRefGoogle Scholar
  9. 9.
    Gunasekaran, S., Kubiznak, D., Mann, R.B.: Extended phase space thermodynamics for charged and rotating black holes and Born–Infeld vacuum polarization. JHEP 1211, 110 (2012). arXiv:1208.6251 [hep-th]ADSCrossRefGoogle Scholar
  10. 10.
    Wei, S.W., Liu, Y.X.: Critical phenomena and thermodynamic geometry of charged Gauss–Bonnet AdS black holes. Phys. Rev. D 87, 044014 (2013). arXiv:1209.1707 [gr-qc]ADSCrossRefGoogle Scholar
  11. 11.
    Wei, S.W., Liu, Y.X.: Insight into the microscopic structure of an AdS black hole from thermodynamical phase transition. Phys. Rev. Lett. 115, 111302 (2015). arXiv:1502.00386 [gr-qc]ADSCrossRefGoogle Scholar
  12. 12.
    Hendi, S.H., Vahidinia, M.H.: Extended phase space thermodynamics and P-V criticality of black holes with nonlinear source. Phys. Rev. D 88, 084045 (2013). arXiv:1212.6128 [hep-th]ADSCrossRefGoogle Scholar
  13. 13.
    Cai, R.G., Cao, L.M., Li, L., Yang, R.Q.: P-V criticality in the extended phase space of Gauss–Bonnet black holes in AdS space. JHEP 1309, 005 (2013). arXiv:1306.6233 [gr-qc]ADSCrossRefGoogle Scholar
  14. 14.
    Altamirano, N., Kubiznak, D., Mann, R.B.: Reentrant phase transitions in rotating AdS black holes. Phys. Rev. D 88, 101502 (2013). arXiv:1306.5756 [hep-th]ADSCrossRefGoogle Scholar
  15. 15.
    Zou, D.C., Zhang, S.J., Wang, B.: Critical behavior of Born-Infeld AdS black holes in the extended phase space thermodynamics. Phys. Rev. D 89, 044002 (2014). arXiv:1311.7299 [hep-th]ADSCrossRefGoogle Scholar
  16. 16.
    Gim, Y., Kim, W., Yi, S.H.: The first law of thermodynamics in Lifshitz black holes revisited. JHEP 1407, 002 (2014). arXiv:1403.4704 [hep-th]ADSMathSciNetCrossRefGoogle Scholar
  17. 17.
    Johnson, C.V.: The extended thermodynamic phase structure of Taub–NUT and Taub–Bolt. Class. Quant. Grav. 31, 225005 (2014). arXiv:1406.4533 [hep-th]ADSMathSciNetCrossRefGoogle Scholar
  18. 18.
    Mirza, B., Sherkatghanad, Z.: Phase transitions of hairy black holes in massive gravity and thermodynamic behavior of charged AdS black holes in an extended phase space. Phys. Rev. D 90, 084006 (2014). arXiv:1409.6839 [gr-qc]ADSCrossRefGoogle Scholar
  19. 19.
    Suresh, J., Tharanath, R., Kuriakose, V.C.: A unified thermodynamic picture of Hoava–Lifshitz black hole in arbitrary space time. JHEP 1501, 019 (2015). arXiv:1408.0911 [gr-qc]ADSCrossRefGoogle Scholar
  20. 20.
    Dehghani, M.H., Kamrani, S., Sheykhi, A.: P-V criticality of charged dilatonic black holes. Phys. Rev. D 90, 104020 (2014). arXiv:1505.02386 [hep-th]ADSCrossRefGoogle Scholar
  21. 21.
    Xu, W., Zhao, L.: Critical phenomena of static charged AdS black holes in conformal gravity. Phys. Lett. B 736, 214 (2014). arXiv:1405.7665 [gr-qc]ADSMathSciNetCrossRefGoogle Scholar
  22. 22.
    Mustapha, A.A., Marques, G.T., Rodrigues, M.E.: Phantom black holes and critical phenomena. JCAP 1407, 036 (2014). arXiv:1405.5745 [gr-qc]Google Scholar
  23. 23.
    Armas, J., Obers, N.A., Sanchioni, M.: Gravitational tension, spacetime pressure and black hole volume. JHEP 1609, 124 (2016). arXiv:1512.09106 [hep-th]ADSMathSciNetCrossRefGoogle Scholar
  24. 24.
    Zhao, Z.X., Jing, J.L.: Ehrenfest scheme for complex thermodynamic systems in full phase space. JHEP 1411, 037 (2014). arXiv:1405.2640 [gr-qc]ADSCrossRefGoogle Scholar
  25. 25.
    Mo, J.X., Liu, W.B.: P-V criticality of topological black holes in Lovelock–Born–Infeld gravity. Eur. Phys. J. C 74, 2836 (2014). arXiv:1401.0785 [gr-qc]ADSCrossRefGoogle Scholar
  26. 26.
    Poshteh, M.B.J., Mirza, B., Sherkatghanad, Z.: Phase transition, critical behavior, and critical exponents of Myers–Perry black holes. Phys. Rev. D 88, 024005 (2013). arXiv:1306.4516 [gr-qc]ADSCrossRefGoogle Scholar
  27. 27.
    Hansen, D., Kubiznak, D., Mann, R.B.: Criticality and surface tension in rotating horizon thermodynamics. Class. Quant. Grav. 33, 165005 (2016). arXiv:1604.06312 [gr-qc]ADSMathSciNetCrossRefGoogle Scholar
  28. 28.
    Ghezelbash, A., Mann, R.B.: Action, mass and entropy of Schwarzschild–de Sitter black holes and the de Sitter/CFT correspondence. JHEP 0201, 005 (2002). arXiv:hep-th/0111217 ADSMathSciNetCrossRefGoogle Scholar
  29. 29.
    Balasubramanian, V., de Boer, J., Minic, D.: Mass, entropy and holography in asymptotically de Sitter spaces. Phys. Rev. D 65, 123508 (2002). arXiv:hep-th/0110108 ADSMathSciNetCrossRefGoogle Scholar
  30. 30.
    Kubiznak, D., Simovic, F.: Thermodynamics of horizons: de Sitter black holes. Class. Quant. Grav. 33, 245001 (2016). arXiv:1507.08630 [hep-th]ADSCrossRefGoogle Scholar
  31. 31.
    Sekiwa, Y.: Thermodynamics of de Sitter black holes: thermal cosmological constant. Phys. Rev. D 73, 084009 (2006). arXiv:hep-th/0602269 ADSMathSciNetCrossRefGoogle Scholar
  32. 32.
    Gomberoff, A., Teitelboim, C.: de Sitter black holes with either of the two horizons as a boundary. Phys. Rev. D 67, 104024 (2003)ADSMathSciNetCrossRefGoogle Scholar
  33. 33.
    Cai, R.G., Ji, J.Y., Soh, K.S.: Action and entropy of black holes in spacetimes with a cosmological constant. Class. Quant. Grav. 15, 2783 (1998)ADSMathSciNetCrossRefGoogle Scholar
  34. 34.
    Wang, B.B., Huang, C.G.: Thermodynamics of Reissner–Nordstrom–de Sitter black hole in York’s formalism. Class. Quant. Grav. 19, 2491 (2002)ADSMathSciNetCrossRefGoogle Scholar
  35. 35.
    Urano, M., Tomimatsu, A., Saida, H.: Mechanical first law of black hole spacetimes with cosmological constant and its application to Schwarzschild–de Sitter spacetime. Class. Quant. Grav. 26, 105010 (2009). arXiv:0903.4230 [gr-qc]ADSMathSciNetCrossRefGoogle Scholar
  36. 36.
    Zhao, H.H., Zhang, L.C., Ma, M.S., Zhao, R.: P-V criticality of higher dimensional charged topological dilaton de Sitter black holes. Phys. Rev. D 90, 064018 (2014)ADSCrossRefGoogle Scholar
  37. 37.
    Gibbons, G.W., Hawking, S.W.: Cosmological event horizons, thermodynamics, and particle creation. Phys. Rev. D 15, 2738 (1977)ADSMathSciNetCrossRefGoogle Scholar
  38. 38.
    Misner, C.W., Sharp, D.H.: Relativistic equations for adiabatic, spherically symmetric gravitational collapse. Phys. Rev. B 571, 136 (1964)MathSciNetzbMATHGoogle Scholar
  39. 39.
    Cahill, M., McVittie, G.: Spherical symmetry and mass–energy in general relativity. I. general theory. J. Math. Phys. 11, 1382 (1970)ADSMathSciNetCrossRefGoogle Scholar
  40. 40.
    Hayward, S.A.: Quasi-local gravitational energy. Phys. Rev. D 49, 831 (1994). arXiv:gr-qc/9303030 ADSMathSciNetCrossRefGoogle Scholar
  41. 41.
    Hu, Y.P., Zhang, H.S.: Misner–Sharp mass and the unified first law in massive gravity. Phys. Rev. D 92, 024006 (2015). arXiv:1502.00069 [hep-th]ADSMathSciNetCrossRefGoogle Scholar
  42. 42.
    Cai, R.G., Kim, S.P.: First law of thermodynamics and Friedmann equations of Friedmann–Robertson–Walker universe. JHEP 0502, 050 (2005). arXiv:hep-th/0501055 ADSMathSciNetCrossRefGoogle Scholar
  43. 43.
    Gong, Y.G., Wang, A.Z.: Friedmann equations and thermodynamics of apparent horizons. Phys. Rev. Lett. 99, 211301 (2007). arXiv:0704.0793 [hep-th]ADSMathSciNetCrossRefGoogle Scholar
  44. 44.
    Cai, R.G., Cao, L.M., Hu, Y.P.: Corrected entropy-area relation and modified Friedmann equations. JHEP 0808, 090 (2008). arXiv:0807.1232 [hep-th]ADSMathSciNetCrossRefGoogle Scholar
  45. 45.
    Li, L.F., Zhu, J.Y.: Thermodynamics in loop quantum cosmology. Adv. High Energy Phys. 2009, 905705 (2009). arXiv:0812.3544 [gr-qc]CrossRefGoogle Scholar
  46. 46.
    Zhu, T., Ren, J.R., Singleton, D.: Hawking-like radiation as tunneling from the apparent horizon in a FRW universe. Int. J. Mod. Phys. D 19, 159 (2010). arXiv:0902.2542 [hep-th]ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of ScienceXihua UniversityChengduChina
  2. 2.School of Material Science and EngineeringChongqing Jiaotong UniversityChongqingChina

Personalised recommendations