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Generalized uncertainty relation and Hawking radiation of the black hole. (English) Zbl 1187.83050

Summary: Recently, there has been much attention devoted to the correction to the black hole radiation spectrum and the quantum corrections to Bekenstein-Hawking entropy. In particular, many researchers have expressed a vested interest in the coefficient of the logarithmic term of the black hole entropy correction term. In this paper, we calculate the radiation spectrum of arbitrary dimension Schwarzschild black hole after considering the generalized uncertainty principle. The correction value of Bekenstein-Hawking entropy is derived.

MSC:

83C57 Black holes
83C47 Methods of quantum field theory in general relativity and gravitational theory
80A10 Classical and relativistic thermodynamics
Full Text: DOI

References:

[1] Hawking, S.W.: Particle creation by black holes. Commun. Math. Phys. 43, 199 (1975) · Zbl 1378.83040 · doi:10.1007/BF02345020
[2] Gibbons, G.W., Hawking, S.W.: Action integrals and partition functions in quantum gravity. Phys. Rev. D 15, 2752 (1977) · doi:10.1103/PhysRevD.15.2752
[3] Bardeen, J.M., Carter, B., Hawking, S.W.: The four laws of black hole mechanics. Commun. Math. Phys. 31, 161 (1973) · Zbl 1125.83309 · doi:10.1007/BF01645742
[4] Wald, R.M.: General Relativity. University of Chicago Press, Chicago (1984)
[5] Damour, T., Ruffini, R.: Black-hole evaporation in the Klein-Sauter-Heisenberg-Euler formalism. Phys. Rev. D 14, 332 (1976) · doi:10.1103/PhysRevD.14.332
[6] Unruh, W.G.: Notes on black-hole evaporation. Phys. Rev. D 14, 870 (1976) · Zbl 0322.53013 · doi:10.1103/PhysRevD.14.870
[7] Hartle, J.B., Hawking, S.W.: Path-integral derivation of black-hole radiance. Phys. Rev. D 13, 2188 (1976) · doi:10.1103/PhysRevD.13.2188
[8] Sannan, S.: Heuristic derivation of the probability distributions of particles emitted by a black hole. Gen. Relativ. Gravit. 20, 239 (1988) · doi:10.1007/BF00759183
[9] Gibbons, G.W., Perry, M.J., Pope, C.N.: The first law of thermodynamics for Kerr-anti-de Sitter black holes. Class. Quantum Gravity 22, 1503 (2005) · Zbl 1068.83010 · doi:10.1088/0264-9381/22/9/002
[10] Cai, R.G., Kim, S.P., Wang, B.: Ricci flat black holes and Hawking-Page phase transition in Gauss-Bonnet gravity and dilaton gravity. Phys. Rev. D 76, 024011 (2007) · Zbl 1222.83093 · doi:10.1103/PhysRevD.76.024011
[11] Cai, R.G.: Cardy–Verlinde formula and thermodynamics of black holes in de Sitter spaces. Nucl. Phys. B 628, 375 (2002) · Zbl 0992.83036 · doi:10.1016/S0550-3213(02)00064-0
[12] Cai, R.G., Cao, L.M.: Thermodynamics of apparent horizon in brane world scenario. Nucl. Phys. B 785, 135 (2007) · Zbl 1150.83010 · doi:10.1016/j.nuclphysb.2007.06.016
[13] Dehghani, M.H.: Charged rotating black branes in anti-de Sitter Einstein-Gauss-Bonnet gravity. Phys. Rev. D 67, 064017 (2003) · Zbl 1222.83166 · doi:10.1103/PhysRevD.67.064017
[14] Parikh, M.K., Wilczek, F.: Hawking radiation as tunneling. Phys. Rev. Lett. 85, 5042 (2000) · Zbl 1369.83053 · doi:10.1103/PhysRevLett.85.5042
[15] Vagenas, E.C.: Are extremal 2D black holes really frozen? Phys. Lett. B 503, 399 (2001) · Zbl 0977.83041 · doi:10.1016/S0370-2693(01)00242-8
[16] Vagenas, E.C.: Two-dimensional dilatonic black holes and Hawking irradiation. Mod. Phys. Lett. A 17, 609 (2002) · Zbl 1083.83532 · doi:10.1142/S0217732302006862
[17] Vagenas, E.C.: Semiclassical corrections to the Bekenstein-Hawking entropy of the BTZ black hole via self-gravitation. Phys. Lett. B 533, 302 (2002) · Zbl 0994.83031 · doi:10.1016/S0370-2693(02)01695-7
[18] Vagenas, E.C.: Generalization of the KKW analysis for black hole radiation. Phys. Lett. B 559, 65 (2003) · Zbl 1011.83016 · doi:10.1016/S0370-2693(03)00302-2
[19] Setare, M.R., Vagenas, E.C.: Self-gravitational corrections to the Cardy-Verlinde formula of the Achücarro-Ortiz black hole. Phys. Lett. B 584, 127 (2004) · Zbl 1246.83145 · doi:10.1016/j.physletb.2004.01.039
[20] Kerner, R., Mann, R.B.: Tunnelling, temperature, and Taub-NUT black holes. Phys. Rev. D 73, 104010 (2006) · doi:10.1103/PhysRevD.73.104010
[21] Kerner, R., Mann, R.B.: Tunnelling from Gödel black holes. Phys. Rev. D 75, 084022 (2007) · Zbl 1140.83377 · doi:10.1103/PhysRevD.75.084022
[22] Kerner, R., Mann, R.B.: Charged fermions tunnelling from Kerr-Newman black holes. Phys. Lett. B 665, 277 (2008) · Zbl 1140.83377 · doi:10.1016/j.physletb.2008.06.012
[23] Cai, R.G., Cao, L.M., Hu, Y.P.: Hawking radiation of apparent horizon in a FRW universe. Class. Quantum Gravity 26, 155018 (2009) · Zbl 1172.83347 · doi:10.1088/0264-9381/26/15/155018
[24] Zhang, J.Y., Fan, J.H.: Tunnelling effect of charged and magnetized particles from the Kerr-Newman-Kasuya black hole. Phys. Lett. B 648, 133 (2007) · Zbl 1248.83090 · doi:10.1016/j.physletb.2007.03.006
[25] Wu, X., Gao, S.: Tunneling effect near a weakly isolated horizon. Phys. Rev. D 75, 044027 (2007) · doi:10.1103/PhysRevD.75.044027
[26] Arzano, M., Medved, A.J.M., Vagenas, E.C.: Hawking radiation as tunneling through the quantum horizon. J. High Energy Phys. 09, 037 (2005) · Zbl 1081.83019 · doi:10.1088/1126-6708/2005/09/037
[27] Jiang, Q.Q., Wu, S.Q., Cai, X.: Hawking radiation from dilatonic black holes via anomalies. Phys. Rev. D 75, 064029 (2007) · doi:10.1103/PhysRevD.75.064029
[28] Li, R., Ren, J.R.: Dirac particles tunneling from BTZ black hole. Phys. Lett. B 661, 370 (2008) · Zbl 1282.83035 · doi:10.1016/j.physletb.2008.01.077
[29] Peng, J.J., Wu, S.Q.: Covariant anomalies and Hawking radiation from charged rotating black strings in anti-de Sitter spacetimes. Phys. Lett. B 661, 300 (2008) · Zbl 1282.83037
[30] He, X.K., B Liu, W.: Modified Hawking radiation in a BTZ black hole using Damour-Ruffini method. Phys. Lett. B 653, 330 (2007) · Zbl 1246.83118 · doi:10.1016/j.physletb.2007.08.010
[31] Zhou, S.W., Liu, W.B.: Hawking radiation of charged Dirac particles from a Kerr-Newman black hole. Phys. Rev. D 77, 104021 (2008) · doi:10.1103/PhysRevD.77.104021
[32] Medved, A.J.M., Vagenas, E.C.: When conceptual worlds collide: The generalized uncertainty principle and the Bekenstein-Hawking entropy. Phys. Rev. D 70, 124021 (2004) · doi:10.1103/PhysRevD.70.124021
[33] Chatterjee, A., Majumdar, P.: Universal canonical black hole entropy. Phys. Rev. Lett. 92, 141301 (2004) · Zbl 1267.83053 · doi:10.1103/PhysRevLett.92.141301
[34] Kaul, R.K., Majumdar, P.: Logarithmic correction to the Bekenstein-Hawking entropy. Phys. Rev. Lett. 84, 5255 (2000) · doi:10.1103/PhysRevLett.84.5255
[35] Camellia, G.A., Arzano, M., Procaccini, A.: Severe constraints on the loop-quantum-gravity energy-momentum dispersion relation from the black-hole area-entropy law. Phys. Rev. D 70, 107501 (2004) · doi:10.1103/PhysRevD.70.107501
[36] Chatterjee, A., Majumdar, P.: Mass and charge fluctuations and black hole entropy. Phys. Rev. D 71, 024003 (2005) · doi:10.1103/PhysRevD.71.024003
[37] Myung, Y.S.: Logarithmic corrections to three-dimensional black holes and de Sitter spaces. Phys. Lett. B 579, 205 (2004) · Zbl 1246.83136 · doi:10.1016/j.physletb.2003.11.002
[38] Akbar, M.M., Das, S.: Entropy corrections for Schwarzschild and Reissner-Nordström black holes. Class. Quantum Gravity 21, 1383 (2004) · Zbl 1194.83051 · doi:10.1088/0264-9381/21/6/007
[39] Das, S., Majumdar, P., Bhaduri, R.K.: General logarithmic corrections to black-hole entropy. Class. Quantum Gravity 19, 2355 (2002) · Zbl 1003.83025 · doi:10.1088/0264-9381/19/9/302
[40] Zhao, R., Zhang, S.L.: Canonical entropy of three-dimensional BTZ black hole. Phys. Lett. B 641, 318 (2006) · Zbl 1248.83092 · doi:10.1016/j.physletb.2006.08.068
[41] Zhao, R., Zhang, S.L.: Generalized uncertainty principle and black hole entropy. Phys. Lett. B 641, 208 (2006) · Zbl 1248.83083 · doi:10.1016/j.physletb.2006.08.056
[42] Medved, A.J.M., Vagenas, E.C.: On Hawking radiation as tunneling with logarithmic corrections. Mod. Phys. Lett. A 20, 1723 (2005) · Zbl 1081.83019 · doi:10.1142/S0217732305018025
[43] Setare, M.R.: Corrections to the Cardy-Verlinde formula from the generalized uncertainty principle. Phys. Rev. D 70, 087501 (2004) · Zbl 1191.83029 · doi:10.1103/PhysRevD.70.087501
[44] Banerjee, R., Majhi, B.R.: Quantum tunneling beyond semiclassical approximation. J. High Energy Phys. 06, 095 (2008) · Zbl 1282.83025 · doi:10.1088/1126-6708/2008/06/095
[45] Banerjee, R., Majhi, B.R.: Quantum tunneling and back reaction. Phys. Lett. B 662, 62 (2008) · Zbl 1282.83025 · doi:10.1016/j.physletb.2008.02.044
[46] Ghosh, A., Mitra, P.: Log correction to the black hole area law. Phys. Rev. D 71, 027502 (2005) · doi:10.1103/PhysRevD.71.027502
[47] Domagala, M., Lewandowski, J.: Black-hole entropy from quantum geometry. Class. Quantum Gravity 21, 5233 (2004) · Zbl 1062.83053 · doi:10.1088/0264-9381/21/22/014
[48] Meissner, K.A.: Black-hole entropy in loop quantum gravity. Class. Quantum Gravity 21, 5245 (2004) · Zbl 1062.83056 · doi:10.1088/0264-9381/21/22/015
[49] Hod, S.: High-order corrections to the entropy and area of quantum black holes. Class. Quantum Gravity 21, L97 (2004) · Zbl 1061.83521 · doi:10.1088/0264-9381/21/14/L01
[50] Medved, A.J.M.: A comment on black hole entropy or does nature abhor a logarithm? Class. Quantum Gravity 22, 133 (2005) · Zbl 1060.83522 · doi:10.1088/0264-9381/22/1/009
[51] Painlevé, P.: La mecanique classique el la theorie de la relativite. C. R. Acad. Sci. (Paris) 173, 677 (1921) · JFM 48.0997.03
[52] Parikh, M.K., Wilczek, F.: Self-interaction correction to black hole radiance. Nucl. Phys. B 433, 403 (1995) · doi:10.1016/0550-3213(94)00411-7
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