Entropy of the Dirac field in a Kerr-Newman black hole

Liu Wenbiao; Zhao Zheng

doi:10.1103/PhysRevD.61.063003

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Entropy of the Dirac field in a Kerr-Newman black hole

Liu Wenbiao and Zhao Zheng

Department of Physics, Insitute of Theoretical Physics, Beijing Normal University, Beijing 100875, China

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Phys. Rev. D 61, 063003 – Published 25 February, 2000

DOI: https://doi.org/10.1103/PhysRevD.61.063003

Abstract

Thinking of the Dirac equations in Newman-Penrose formalism, there are four components of the wave function $ψ_{11}, ψ_{12}, ψ_{21}, ψ_{22} .$ We consider that the total free energy is summed up from the free energies of the four components. Then the entropy of the Dirac field in a Kerr-Newman black hole is calculated via the brick-wall method. We find that the calculation of the Dirac field is similar to that of a scalar field. It also requires a radial and an angular cutoff ε and δ. Moreover, if the cutoff values $\bar{ε}$ and δ satisfy the same proper relation in the scalar field between them, the resulting entropy is 7/2 times the Klein-Gordon field.

References (16)

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[c1] J. D. Bekenstein, Phys. Rev. D 7, 2333 (1973); ibid.9, 3292 (1974).

[c2] S. W. Hawking, Nature (London) 248, 30 (1974); Commun. Math. Phys. 43, 199 (1975).

[c3] V Frolov and I Novikov, Phys. Rev. D 48, 4545 (1993).

[c4] C. G. Callan and F. Wilczek, Phys. Lett. B 333, 55 (1994).

[c5] G ’t Hooft, Nucl. Phys. B256, 727 (1985).

[c6] Jeongwon Ho, Won T. Kim, Young-Jai Park, and Hyeonjoon Shin, Class. Quantum Grav. 14, 2617 (1997).

[c7] Amit Ghosh and P. Mitra, Phys. Lett. B 357, 295 (1995).

[c8] Jiliang Jing, Int. J. Theor. Phys. 37, 1441 (1998).

[c9] Min-Ho Lee and Jae Kwan Kim, Phys. Lett. A 212, 323 (1996).

[c10] Luo Zhijian and Zhu Jianyang, Acta Phys. Sin. 48, 395 (1999).

[c11] R. M. Wald, General Relativity (The University of Chicago Press, Chicago, 1984).

[c12] S. P. de Alwis and N. Ohta, Phys. Rev. D 52, 3529 (1995).

[c13] G. W. Gibbons and S. W. Hawking, Phys. Rev. D 15, 2752 (1977).

[c14] Y. G. Shen, D. M. Chen, and T. J. Zhang, Phys. Rev. D 56, 6698 (1997).

[c15] S. Chandrasekhar, The Mathematical Theory of Black Holes (Oxford University Press, New York, 1983).

[c16] R. H. Price, I. H. Redmount, W. M. Suen, K. S. Thorne, D. A. Macdonald, and R. J. Crowley, in Black Holes: The Membrane Paradigm, edited by K. S. Thorne, R. H. Price, and D. A. Macdonald (Yale University Press, New Haven, Connecticut, 1986).

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Entropy of the Dirac field in a Kerr-Newman black hole

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