Skip to main content
SpringerLink
Log in

The Fermion Tunneling from a Slowly Varying Charged Black Hole

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

According to the Dirac equation and the Rarita-Schwinger equation, the Hamilton-Jacobi equation in curved space-time for the spin 1/2 and 3/2 fermions have been derived. Therefore, we find the Hamilton-Jacobi equation is a fundamental equation in the semiclassical theory. By utilizing this Hamilton-Jacobi equation, we investigate the quantum tunneling radiation from slowly varying Reissner-Nordström (R-N) black hole. The results show that the Hawking temperature do not only related to the properties of slowly varying R-N black hole, but also depended on the time. Meanwhile, it finds that the Hamilton-Jacobi equation can help people more easily and effectively calculated thermodynamic properties black hole.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bekenstein, J.D.: Black Holes and Entropy. Phys. Rev. D 7, 2333 (1973)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  2. Carmeli, M., Kaye, M.: Gravitational field of a radiating rotating body. Ann. Phys. 103, 97 (1977)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  3. Aizawa, S.: A semigroup treatment of the Hamilton-Jacobi equation in one space variable. Hiroshima Math. J. 3, 367–386 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  4. Hawking, S.W.: Particle creation by black holes. Commun. Math. Phys. 43, 199 (1975)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  5. Angheben, M., Nadalini, M., Vanzo, L., Zerbini, S.: Hawking radiation as tunneling for extremal and rotating Black holes. J. High Energy Phys. 05, 014 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  6. Medved, A.J.M., Vagenas, E.: On Hawking radiation as tunneling with back-reaction. Mod. Phys. Lett. A 20, 2449 (2005)

    Article  ADS  MATH  Google Scholar 

  7. Yang, S.Z., Li, H.L., Jang, Q.Q.: The Hawking radiation of the charged particle via tunnelling from the axisymmetric Sen black hole. Int. J. Theor. Phys. 45, 965 (2007)

    Article  Google Scholar 

  8. Hemming, S., Keski-Vakkuri, E.: Hawking radiation from AdS black holes. Phys. Rev. D 64, 44006 (2001)

    Article  ADS  MathSciNet  Google Scholar 

  9. Liu, W.B.: Damour-Ruffini method and the non-thermal Hawking radiation of Reissner-Nordström black hole. Acta. Phys. Sin. 56, 6164 (2007)

    Google Scholar 

  10. Zeng, X.X., Zhang, H., Li, L.F.: Phase transition of holographic entanglement entropy in massive gravity. Phys. Lett. B 756, 170 (2015)

    Article  ADS  MATH  Google Scholar 

  11. Zeng, X.X., Liu, X.M., Li, L.F.: Phase structure of the Born-Infeld-anti-de Sitter black holes probed by non-local observables. Eur. Phys. J. C 76, 616 (2016)

    Article  ADS  Google Scholar 

  12. He, S., Li, L.F., Zeng, X.X.: Holographic Van der Waals-like phase transition in the Gauss-Bonnet gravity. Nucl. Phys. B 915, 243 (2016)

    Article  ADS  MATH  Google Scholar 

  13. Li, H.L., Yang, S.Z., Zu, X.T.: Holographic research on phase transitions for a five dimensional AdS black hole with conformally coupled scalar hair. Phys. Lett. B 764, 310 (2016)

    Article  ADS  Google Scholar 

  14. Li, H.-L., Feng, Z.-W., Yang, S.-Z., Zu, X.-T.: Wilson loop’s phase transition probed by non-local observable. Nucl. Phys. B 915, 243 (2016)

    MATH  Google Scholar 

  15. Ong, Y.C.: Zero mass remnant as an asymptotic state of hawking evaporation. J. High Energy Phys. 10, 195 (2018)

    Article  ADS  Google Scholar 

  16. Ong, Y.C.: Generalized uncertainty principle, black holes, and white dwarfs: a tale of two infinities. J. Cosmol. Astropart. 015, 09 (2018)

    Google Scholar 

  17. Parikh, M.K., Wilczek, F.: Hawking radiation as tunneling. Phys. Rev. Lett. 85, 5042 (2000)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  18. Parikh, M.: A secret tunnel through the horizon. Int. J. mod. Phys. D 13, 2351 (2004)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  19. Parikh, M.K.: A secret tunnel through the horizon. Int. J. Mod. Phys. D 13, 2351–2354 (2004)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  20. Kim, S.P.: Schwinger mechanism and Hawking radiation as quantum tunneling. J. Korean Phys. Soc. 53, 1095–1099 (2008)

    Article  ADS  Google Scholar 

  21. Feng, Z.W., Li, H.L., Zu, X.T., Yang, S.Z.: Quantum corrections to the thermodynamics of Schwarzschild-Tangherlini black hole and the generalized uncertainty principle. Eur. Phys. J. C 76, 212 (2016)

    Article  ADS  Google Scholar 

  22. Kempf, A.: Non-pointlike particles in harmonic oscillators. J. Phys. A Math. Gen. 30, 2093 (1997)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  23. Srinivasan, K., Padmanabhan, T.: Particle production and complex path analysis. Phys. Rev. D 60, 24007 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  24. Scardigli, F.: Generalized uncertainty principle in quantum gravity from micro-black hole gedanken experiment. Phys. Lett. B 452, 39–44 (1999)

    Article  ADS  Google Scholar 

  25. Lin, K., Yang, S.Z.: Fermions tunneling from higher-dimensional black holes. Phys. Rev. D 79, 064035 (2009)

    Article  ADS  Google Scholar 

  26. Yang, S.Z., Lin, K.: Fermionss tunneling of higher-dimensional Kerr-Anti-de Sitter black hole with one rotational parameter. Phys. Lett. B 674, 127–130 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  27. Lin, K., Yang, S.Z.: Fermions tunneling from higher-dimensional black holes. Adv. High Energy Phys. 79, 064035 (2009)

    Google Scholar 

  28. Yang, S.Z.: Dynamics equation of spin particles in a strong gravitational field. J. Chin. West Normal Univ. (Nat. Sci.) 37, 126 (2016)

    Google Scholar 

  29. Feng, Z.W., Chen, Y., Zu, X.T.: Hawking radiation of vector particles via tunneling from 4-dimensional and 5-dimensional black holes. Astrophys. Space Sci. 359, 48 (2015)

    Article  ADS  Google Scholar 

  30. Magueijo, J., Smolin, L.: Gravity’s rainbow. Classical Quant. Grav. 21, 1725–1736 (2004)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  31. Feng, Z.W., Yang, S.Z.: Thermodynamic phase transition of a black hole in rainbow gravity. Phys. Lett. B 772, 737–742 (2017)

    Article  ADS  Google Scholar 

  32. Li, H.L., Feng, Z.W., Zu, X.T.: Quantum tunneling from a high dimensional Gödel black hole. Gen. Relativ. Gravit. 48, 18 (2016)

    Article  ADS  MATH  Google Scholar 

  33. Li, H.-L., Feng, Z.-W., Yang, S.-Z., Zu, X.-T.: The remnant and phase transition of a Finslerian black hole. Eur. Phys. J. C 78, 768 (2018)

    Article  ADS  Google Scholar 

  34. Zhang, J., Zhao, Z.: Hawking radiation of charged particles via tunneling from the Reissner-Nordström black hole. J. High Energy Phys. 10, 055 (2005)

    Article  ADS  Google Scholar 

  35. Zhao, Z., Huang, W.H.: Temperature of non-stationary Kerr-Newman black hole. Chin. Phys. Lett. 9, 333 (1992)

    Article  ADS  MathSciNet  Google Scholar 

  36. Jing, J.L., Pan, Q.Y.: Quasinormal modes of a stationary axisymmetric EMDA black hole. Chin. Phys. 15, 77 (2006)

    Article  ADS  Google Scholar 

  37. William, A.H., Lance, D.W.: Evolution of charged evaporating black holes. Phys. Rev. D 41, 1142 (1990)

    Google Scholar 

Download references

Acknowledgements

The authors would like to thank the anonymous reviewers for their helpful comments and suggestions, which helped to improve the quality of this paper. This work was supported by the National Natural Science Foundation of China (Grant Nos. 11573022 and 11847048) and the Fundamental Research Funds of China West Normal University (Grant Nos. 17E093 and 17YC518).

Author information

Authors and Affiliations

  1. Physics and Space Science College, China West Normal University, Nanchong, 637009, China

    Qun-Chao Ding, Zhong-Wen Feng & Shu-Zheng Yang

Authors
  1. Qun-Chao Ding
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhong-Wen Feng
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Shu-Zheng Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shu-Zheng Yang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ding, QC., Feng, ZW. & Yang, SZ. The Fermion Tunneling from a Slowly Varying Charged Black Hole. Int J Theor Phys 58, 1028–1035 (2019). https://doi.org/10.1007/s10773-018-3994-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10773-018-3994-x

Keywords

Search

Navigation