Abstract
Using the quantum statistical method, the difficulty of solving the wave equation on the background of the black hole is avoided. We directly solve the partition functions of Bose and Fermi field on the background of an axisymmetric Kerr-Newman black hole using the new equation of state density motivated by the generalized uncertainty principle in the quantum gravity. Then near the black hole horizon, we calculate entropies of Bose and Fermi field between the black hole horizon surface and the hypersurface with the same inherent radiation temperature measured by an observer at an infinite distance. In our results there are not cutoffs and little mass approximation introduced in the conventional brick-wall method. The series expansion of the black hole entropy is obtained. And this series is convergent. It provides a way for studying the quantum statistical entropy of a black hole in a non-spherical symmetric spacetime.
Similar content being viewed by others
References
Bekenstein, J.D.: Phys. Rev. D 7, 2333 (1973)
Hawking, S.W.: Commun. Math. Phys. 43, 199 (1975)
Bardeen, J.M., Carter, B., Hawking, S.W.: Math. Phys. 31, 161 (1973)
Hochberg, D., Kephart, T.W., York, J.W.: Phys. Rev. D 48, 479 (1993)
Padmanaban, T.: Phys. Lett. A 136, 203 (1989)
Lee, H., Kim, S.W., Kim, W.T.: Phys. Rev. D 54, 6559 (1996)
’t Hooft, G.: Nucl. Phys. B 256, 727 (1985)
Cognola, G., Lecca, P.: Phys. Rev. D 57, 1108 (1998)
Cai, R.G., Ji, J.Y., Soh, K.S.: Class. Quantum Gravity 15, 2783 (1998)
Lee, H., Kim, J.W.: Phys. Rev. D 54, 3904 (1996)
Ghosh, A., Mitra, P.: Phys. Rev. Lett. 73, 2521 (1994)
Jing, J., Yan, M.L.: Phys. Rev. D 60, 084015 (1999)
Kenmoku, M., Ishimoto, K., Nandi, K.K., Shigemoto, K.: Phys. Rev. D 73, 064004 (2006)
Zhao, R., Zhang, J.F., Zhang, L.C.: Nucl. Phys. B 609, 247 (2001)
Li, X., Zhao, Z.: Phys. Rev. D 62, 104001 (2000)
He, F., Zhao, Z., Kim, S.W.: Phys. Rev. D 64, 044025 (2001)
Gao, C.J., Shen, Y.G.: Phys. Rev. D 65, 084043 (2002)
Kempt, A., Mangano, G., Mann, R.B.: Phys. Rev. D 52, 1108 (1995)
Cheng, N., Minic, D., Okamura, N., Takeuchi, T.: Phys. Rev. D 65, 125028 (2002)
Hossenfelder, S.: Phys. Rev. D 73, 105013 (2006)
Hossenfelder, S.: Class. Quantum Gravity 25, 038003 (2008)
Nouicer, K.: Phys. Lett. B 646, 63 (2007)
Setare, M.R.: Phys. Rev. D 70, 087501 (2004)
Medved, A.J.M., Vagenas, E.C.: Phys. Rev. D 70, 124021 (2004)
Setare, M.R.: Int. J. Mod. Phys. A 21, 1325 (2006)
Li, X.: Phys. Lett. B 540, 9 (2002)
Zhao, R., Wu, Y.Q., Zhang, L.C.: Class. Quantum Gravity 20, 4885 (2003)
Zhao, R., Zhang, S.L.: Gen. Relativ. Gravit. 36, 2123 (2004)
Zhao, R., Zhang, S.L.: Gen. Relativ. Gravit. 36, 2539 (2004)
Kim, W., Kim, Y.W., Park, Y.J.: Phys. Rev. D 74, 104001 (2006)
Kim, W., Kim, Y.W., Park, Y.J.: Phys. Rev. D 75, 127501 (2007)
Yoon, M., Ha, J., Kim, W.: Phys. Rev. D 76, 047501 (2007)
Tolman, R.C.: Relativity, Thermodynamics and Cosmology. Oxford University Press, London (1934)
Kim, Y.W., Park, Y.J.: Phys. Lett. B 655, 172 (2007)
Chatterjee, A., Majumdar, P.: Phys. Rev. D 71, 024003 (2005)
Myung, Y.S.: Phys. Lett. B 579, 205 (2004)
Zhao, R., Zhang, S.L.: Phys. Lett. B 641, 208 (2006)
Zhao, R., Zhang, S.L.: Phys. Lett. B 641, 318 (2006)
Zhao, R., Zhao, H.X., Hu, S.Q.: Mod. Phys. Lett. A 22, 1737 (2007)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Zhao, R., Zhang, LC., Li, HF. et al. Entropy of Kerr-Newman Black Hole to All Orders in the Planck Length. Int J Theor Phys 47, 3083–3090 (2008). https://doi.org/10.1007/s10773-008-9740-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10773-008-9740-z