Advertisement

The Fermion Tunneling from a Slowly Varying Charged Black Hole

  • Qun-Chao Ding
  • Zhong-Wen Feng
  • Shu-Zheng YangEmail author
Article

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.

Keywords

Hamilton-Jacobi equationl Slowly varying Reissner-Nordström black hole Hawking radiation 

Notes

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).

References

  1. 1.
    Bekenstein, J.D.: Black Holes and Entropy. Phys. Rev. D 7, 2333 (1973)ADSMathSciNetCrossRefGoogle Scholar
  2. 2.
    Carmeli, M., Kaye, M.: Gravitational field of a radiating rotating body. Ann. Phys. 103, 97 (1977)ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    Aizawa, S.: A semigroup treatment of the Hamilton-Jacobi equation in one space variable. Hiroshima Math. J. 3, 367–386 (1973)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Hawking, S.W.: Particle creation by black holes. Commun. Math. Phys. 43, 199 (1975)ADSMathSciNetCrossRefGoogle Scholar
  5. 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)ADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    Medved, A.J.M., Vagenas, E.: On Hawking radiation as tunneling with back-reaction. Mod. Phys. Lett. A 20, 2449 (2005)ADSCrossRefGoogle Scholar
  7. 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)CrossRefGoogle Scholar
  8. 8.
    Hemming, S., Keski-Vakkuri, E.: Hawking radiation from AdS black holes. Phys. Rev. D 64, 44006 (2001)ADSMathSciNetCrossRefGoogle Scholar
  9. 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. 10.
    Zeng, X.X., Zhang, H., Li, L.F.: Phase transition of holographic entanglement entropy in massive gravity. Phys. Lett. B 756, 170 (2015)ADSCrossRefGoogle Scholar
  11. 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)ADSCrossRefGoogle Scholar
  12. 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)ADSCrossRefGoogle Scholar
  13. 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)ADSCrossRefGoogle Scholar
  14. 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)zbMATHGoogle Scholar
  15. 15.
    Ong, Y.C.: Zero mass remnant as an asymptotic state of hawking evaporation. J. High Energy Phys. 10, 195 (2018)ADSCrossRefGoogle Scholar
  16. 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. 17.
    Parikh, M.K., Wilczek, F.: Hawking radiation as tunneling. Phys. Rev. Lett. 85, 5042 (2000)ADSMathSciNetCrossRefGoogle Scholar
  18. 18.
    Parikh, M.: A secret tunnel through the horizon. Int. J. mod. Phys. D 13, 2351 (2004)ADSMathSciNetCrossRefGoogle Scholar
  19. 19.
    Parikh, M.K.: A secret tunnel through the horizon. Int. J. Mod. Phys. D 13, 2351–2354 (2004)ADSMathSciNetCrossRefGoogle Scholar
  20. 20.
    Kim, S.P.: Schwinger mechanism and Hawking radiation as quantum tunneling. J. Korean Phys. Soc. 53, 1095–1099 (2008)ADSCrossRefGoogle Scholar
  21. 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)ADSCrossRefGoogle Scholar
  22. 22.
    Kempf, A.: Non-pointlike particles in harmonic oscillators. J. Phys. A Math. Gen. 30, 2093 (1997)ADSMathSciNetCrossRefGoogle Scholar
  23. 23.
    Srinivasan, K., Padmanabhan, T.: Particle production and complex path analysis. Phys. Rev. D 60, 24007 (1999)ADSMathSciNetCrossRefGoogle Scholar
  24. 24.
    Scardigli, F.: Generalized uncertainty principle in quantum gravity from micro-black hole gedanken experiment. Phys. Lett. B 452, 39–44 (1999)ADSCrossRefGoogle Scholar
  25. 25.
    Lin, K., Yang, S.Z.: Fermions tunneling from higher-dimensional black holes. Phys. Rev. D 79, 064035 (2009)ADSCrossRefGoogle Scholar
  26. 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)ADSMathSciNetCrossRefGoogle Scholar
  27. 27.
    Lin, K., Yang, S.Z.: Fermions tunneling from higher-dimensional black holes. Adv. High Energy Phys. 79, 064035 (2009)Google Scholar
  28. 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. 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)ADSCrossRefGoogle Scholar
  30. 30.
    Magueijo, J., Smolin, L.: Gravity’s rainbow. Classical Quant. Grav. 21, 1725–1736 (2004)ADSMathSciNetCrossRefGoogle Scholar
  31. 31.
    Feng, Z.W., Yang, S.Z.: Thermodynamic phase transition of a black hole in rainbow gravity. Phys. Lett. B 772, 737–742 (2017)ADSCrossRefGoogle Scholar
  32. 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)ADSCrossRefGoogle Scholar
  33. 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)ADSCrossRefGoogle Scholar
  34. 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)ADSCrossRefGoogle Scholar
  35. 35.
    Zhao, Z., Huang, W.H.: Temperature of non-stationary Kerr-Newman black hole. Chin. Phys. Lett. 9, 333 (1992)ADSMathSciNetCrossRefGoogle Scholar
  36. 36.
    Jing, J.L., Pan, Q.Y.: Quasinormal modes of a stationary axisymmetric EMDA black hole. Chin. Phys. 15, 77 (2006)ADSCrossRefGoogle Scholar
  37. 37.
    William, A.H., Lance, D.W.: Evolution of charged evaporating black holes. Phys. Rev. D 41, 1142 (1990)Google Scholar

Copyright information

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

Authors and Affiliations

  1. 1.Physics and Space Science CollegeChina West Normal UniversityNanchongChina

Personalised recommendations