Advertisement

International Journal of Theoretical Physics

, Volume 57, Issue 11, pp 3429–3435 | Cite as

The Entropy Inside a Charged Black Hole Under Hawking Radiation

  • Shan-Zhong Han
  • Jian-Zhi Yang
  • Xin-Yang Wang
  • Wen-Biao Liu
Article

Abstract

Christodoulou and Rovelli have revealed that black holes have big interiors that grow asymptotically linearly with advanced time. Even if the Hawking radiation is taken into account, such interiors remain large. Based on these findings, we investigate the relation between the entropy contained in the maximum interior volume of a charged black hole and the Bekenstein-Hawking entropy using an improved method. We find that, in the early stages of the radiation, the variation of the entropy is proportional to the variation of the Bekenstein-Hawking entropy. As the radiation progresses, the magnitude of the ratio will be gradually decreasing

Keywords

Black hole thermodynamics Volume Entropy Information paradox Reissner-Nordstrom black hole Hawking radiation 

Notes

Acknowledgments

Shan-Zhong Han is grateful to Jie Jiang for his useful opinions and suggestions.This work is supported by the National Natural Science Foundation of China(Grant No.11235003).

References

  1. 1.
    Marolf, D.: The Black Hole information problem: past, present, and future. Rept.Prog.Phys. 80(9), 092001 (2017). arXiv:1703.02143 [gr-qc]ADSCrossRefGoogle Scholar
  2. 2.
    Hawking, S.W.: Breakdown of predictability in gravitational collapse. Phys. Rev. D 14, 2460 (1976)ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    Page, D.N.: Average entropy of a subsystem. Phys. Rev. Lett. 71, 1291 (1993). [gr-qc/9305007]ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    Parikh, M.K.: The Volume of black holes. Phys. Rev. D 73, 124021 (2006). [hep-th/0508108]ADSMathSciNetCrossRefGoogle Scholar
  5. 5.
    Grumiller, D.: The Volume of 2-D black holes. J. Phys. Conf. Ser. 33, 361 (2006). [gr-qc/0509077]ADSCrossRefGoogle Scholar
  6. 6.
    DiNunno, B.S., Matzner, R.A.: The Volume Inside a Black Hole. Gen. Rel. Grav. 42, 63 (2010). arXiv:0801.1734 [gr-qc]ADSMathSciNetCrossRefGoogle Scholar
  7. 7.
    Ballik, W., Lake, K. arXiv:1005.1116 [gr-qc]
  8. 8.
    Cvetic, M., Gibbons, G.W., Kubiznak, D., Pope, C.N.: Black Hole Enthalpy and an Entropy Inequality for the Thermodynamic Volume. Phys. Rev. D 84, 024037 (2011). arXiv:1012.2888 [hep-th]ADSCrossRefGoogle Scholar
  9. 9.
    Ballik, W., Lake, K.: Vector volume and black holes. Phys. Rev. D 88(10), 104038 (2013). arXiv:1310.1935 [gr-qc]ADSCrossRefGoogle Scholar
  10. 10.
    Christodoulou, M., Rovelli, C.: How big is a black hole? Phys. Rev. D 91(6), 064046 (2015). arXiv:1411.2854 [gr-qc]ADSCrossRefGoogle Scholar
  11. 11.
    Bengtsson, I., Jakobsson, E.: Black holes: Their large interiors. Mod. Phys. Lett. A 30(21), 1550103 (2015). arXiv:1502.01907 [gr-qc]ADSMathSciNetCrossRefGoogle Scholar
  12. 12.
    Ong, Y.C.: Never Judge a Black Hole by Its Area. JCAP 1504(04), 003 (2015). arXiv:1503.01092 [gr-qc]ADSMathSciNetCrossRefGoogle Scholar
  13. 13.
    Bhaumik, N., Majhi, B.R.: Interior volume of (1 + D) dimensional Schwarzschild black hole, arXiv:1607.03704 [gr-qc]
  14. 14.
    Christodoulou, M., De Lorenzo, T.: Volume inside old black holes. Phys. Rev. D 94(10), 104002 (2016). arXiv:1604.07222 [gr-qc]ADSCrossRefGoogle Scholar
  15. 15.
    Zhang, B.: Entropy in the interior of a black hole and thermodynamics. Phys. Rev. D 92(8), 081501 (2015). arXiv:1510.02182 [gr-qc]ADSCrossRefGoogle Scholar
  16. 16.
    Ong, Y.C.: The Persistence of the Large Volumes in Black Holes. Gen. Rel. Grav. 47(8), 88 (2015). arXiv:1503.08245 [gr-qc]ADSMathSciNetCrossRefGoogle Scholar
  17. 17.
    Massar, S.: The Semiclassical back reaction to black hole evaporation. Phys. Rev. D 52, 5857 (1995). [gr-qc/9411039]ADSCrossRefGoogle Scholar
  18. 18.
    Chen, P., Ong, Y.C., Yeom, D.h.: Phys. Rept. 603, 1 (2015).  https://doi.org/10.1016/j.physrep.2015.10.007. arXiv:1412.8366 [gr-qc]ADSMathSciNetCrossRefGoogle Scholar
  19. 19.
    Zhang, B., You, L.: Phys. Lett. B 765, 226 (2017).  https://doi.org/10.1016/j.physletb.2016.12.027. arXiv:1612.07865 [gr-qc]ADSCrossRefGoogle Scholar
  20. 20.
    Zhang, B.: Phys. Lett. B 773, 644 (2017).  https://doi.org/10.1016/j.physletb.2017.09.035. arXiv:1709.07275 [gr-qc]ADSCrossRefGoogle Scholar
  21. 21.
    Ashtekar, A., Bojowald, M.: Class. Quant. Grav. 22, 3349 (2005).  https://doi.org/10.1088/0264-9381/22/16/014 [gr-qc/0504029]ADSMathSciNetCrossRefGoogle Scholar
  22. 22.
    Ronald, J., AdlerPisin ChenDavid, I.: Santiago, the generalized uncertainty principle and black hole remnants. Gen. Relativ. Gravit. 33, 2101 (2001)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of PhysicsBeijing Normal UniversityBeijingChina

Personalised recommendations