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In this paper, using the Hamilton-Jacobi method beyond semiclassical approximation in black hole physics which was developed by Banerjee and Majhi, we compute the temperature and entropy of the black hole surrounded by quintessence and obtain the corrected temperature and entropy. In the corrected entropy, the area law involves logarithmic area correction together with the standard inverse power of area term.
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Keywords:
- Hawking radiation /
- quintessence /
- black hole
[1] Hawking S W 1975 Commun. Math. Phys. 43 199
[2] Hartle J B, Hawking S W 1976 Phys. Rev. D 13 2188
[3] Gibbons G W, Hawking S W 1977 Phys. Rev. D 15 2732
[4] Christensen S M, Fulling S A 1977 Phys. Rev. D 15 2088
[5] Zhao Z 1981 Acta Phys. Sin. 30 158 (in Chinese) [赵 峥 1981 物理学报 30 158]
[6] Yang B, Zhao Z 1994 Acta Phys. Sin. 43 858 (in Chinese) [杨 波、 赵 峥 1994 物理学报 43 858]
[7] Parikh M K, Wilczek F 2000 Phys. Rev. Lett. 85 5042
[8] Vagenas E C 2003 Phys. Lett. B 559 65
[9] Setare M R, Vagenas E C 2004 Phys. Lett. B 584 127
[10] Medved A J 2002 Class. Quant. Grav. 19 589
[11] Medved A J 2002 Phys. Rev. D 66 124009
[12] Parikh M K 2004 Gen. Rel. Grav. 36 2419
[13] Parikh M K 2004 Int. J. Mod. Phys. D 13 2351
[14] Medved A J, Vagenas E C 2005 Mod. Phys. Lett. A 20 2449
[15] Arzano M, Medved A J, Vagenas E C 2005 J. High Energ. Phys. 09 037
[16] Setare M R, Vagenas E C 2005 Mod. Phys. Lett. A 20 1723
[17] Kerner R, Mann R B 2006 Phys. Rev. D 73 104010
[18] Zhang J Y, Zhao Z 2005 Phys. Lett. B 618 14
[19] Han Y W 2005 Acta Phys. Sin. 54 5018 (in Chinese) [韩亦文 2005 物理学报 54 5018]
[20] Hu Y P, Zhang J Y, Zhao Z 2007 Acta Phys. Sin. 56 0683 (in Chinese) [胡亚鹏、 张靖仪、 赵 峥 2007 物理学报 56 0683]
[21] Jing Q Q, Wu S Q, Cai X 2007 Phys. Rev. D 75 064029
[22] Kerner R, Mann R B 2007 Phys. Rev. D 75 084022
[23] Li R, Ren J R 2008 Phys. Lett. B 661 370
[24] Peng J J, Wu S Q 2008 Phys. Lett. B 661 300
[25] Kerner R, Mann R B 2008 Phys. Lett. B 665 277
[26] Das S, Majumdar P, Bhaduri R K 2002 Class. Quantum Grav. 20 2355
[27] Jing Q Q 2008 Phys. Lett. B 666 517
[28] Ma Z Z 2008 Phys. Lett. B 666 376
[29] Zhang B, Cai Q Y, Zhan M S 2008 Phys. Lett. B 665 260
[30] He X K, Liu W B 2007 Phys. Lett. B 653 330
[31] Zhou S W, Liu W B 2008 Phys. Rev. D 77 104021
[32] Zhang J Y 2008 Phys. Lett. B 668 353
[33] Zhang J Y, Fan J H 2007 Chin. Phys. 16 3879
[34] Zhang J Y, Zhao Z 2003 Acta Phys. Sin. 52 2096 (in Chinese) [张靖仪、 赵 峥 2003 物理学报 52 2096]
[35] Liu W B 2007 Acta Phys. Sin. 56 6164 (in Chinese) [刘文彪 2007 物理学报 56 6164]
[36] Gong T X, Wang Y J 2009 Commun. Theor. Phys. 52 974
[37] Fursaev D V 1995 Phys. Rev. D 51 R5352
[38] Mann R B, Solodukhin S N 1998 Nucl. Phys. B 523 293
[39] Kaul R K, Majumdar P 2000 Phys. Rev. Lett. 84 5255
[40] Govindarajan T R, Kaul R K, Suneeta V 2001 Class. Quantum Grav. 18 2877
[41] More S S 2005 Class. Quantum Grav. 22 4129
[42] Mukherji S, Pal S S 2002 J. High Energ. Phys. 0205 026
[43] Ghosh A, Mitra P 2005 Phys. Lett. B 616 114
[44] Page D N 2005 New J. Phys. 7 203
[45] Banerjee R, Majhi B R 2008 J.High Energ. Phys. 0806 095
[46] Wang Y J 2008 Classical Black Hole and Quantum Black Hole (Beijing: Science Press) pp256 (in Chinese) [王永久 2008 经典黑洞和量子黑洞 (北京: 科学出版社) 第256页]
[47] Chen J H, Wang Y J 2008 Commun. Theor. Phys. 50 101
[48] Srinivasan K, Padmanabhan T 1999 Phys. Rev. D 60 024007
[49] Modak S K 2009 Phys. Lett. B 671 167
[50] Mitra P 2007 Phys. Lett. B 648 240
[51] York Jr J W 1985 Phys. Rev. D 31 775
[52] Lousto C O, Sanchez N 1988 Phys. Lett. B 212 411
[53] Bardeen J M, Carter B, Hawking S W 1973 Commun. Theor. Phys. 31 161
-
[1] Hawking S W 1975 Commun. Math. Phys. 43 199
[2] Hartle J B, Hawking S W 1976 Phys. Rev. D 13 2188
[3] Gibbons G W, Hawking S W 1977 Phys. Rev. D 15 2732
[4] Christensen S M, Fulling S A 1977 Phys. Rev. D 15 2088
[5] Zhao Z 1981 Acta Phys. Sin. 30 158 (in Chinese) [赵 峥 1981 物理学报 30 158]
[6] Yang B, Zhao Z 1994 Acta Phys. Sin. 43 858 (in Chinese) [杨 波、 赵 峥 1994 物理学报 43 858]
[7] Parikh M K, Wilczek F 2000 Phys. Rev. Lett. 85 5042
[8] Vagenas E C 2003 Phys. Lett. B 559 65
[9] Setare M R, Vagenas E C 2004 Phys. Lett. B 584 127
[10] Medved A J 2002 Class. Quant. Grav. 19 589
[11] Medved A J 2002 Phys. Rev. D 66 124009
[12] Parikh M K 2004 Gen. Rel. Grav. 36 2419
[13] Parikh M K 2004 Int. J. Mod. Phys. D 13 2351
[14] Medved A J, Vagenas E C 2005 Mod. Phys. Lett. A 20 2449
[15] Arzano M, Medved A J, Vagenas E C 2005 J. High Energ. Phys. 09 037
[16] Setare M R, Vagenas E C 2005 Mod. Phys. Lett. A 20 1723
[17] Kerner R, Mann R B 2006 Phys. Rev. D 73 104010
[18] Zhang J Y, Zhao Z 2005 Phys. Lett. B 618 14
[19] Han Y W 2005 Acta Phys. Sin. 54 5018 (in Chinese) [韩亦文 2005 物理学报 54 5018]
[20] Hu Y P, Zhang J Y, Zhao Z 2007 Acta Phys. Sin. 56 0683 (in Chinese) [胡亚鹏、 张靖仪、 赵 峥 2007 物理学报 56 0683]
[21] Jing Q Q, Wu S Q, Cai X 2007 Phys. Rev. D 75 064029
[22] Kerner R, Mann R B 2007 Phys. Rev. D 75 084022
[23] Li R, Ren J R 2008 Phys. Lett. B 661 370
[24] Peng J J, Wu S Q 2008 Phys. Lett. B 661 300
[25] Kerner R, Mann R B 2008 Phys. Lett. B 665 277
[26] Das S, Majumdar P, Bhaduri R K 2002 Class. Quantum Grav. 20 2355
[27] Jing Q Q 2008 Phys. Lett. B 666 517
[28] Ma Z Z 2008 Phys. Lett. B 666 376
[29] Zhang B, Cai Q Y, Zhan M S 2008 Phys. Lett. B 665 260
[30] He X K, Liu W B 2007 Phys. Lett. B 653 330
[31] Zhou S W, Liu W B 2008 Phys. Rev. D 77 104021
[32] Zhang J Y 2008 Phys. Lett. B 668 353
[33] Zhang J Y, Fan J H 2007 Chin. Phys. 16 3879
[34] Zhang J Y, Zhao Z 2003 Acta Phys. Sin. 52 2096 (in Chinese) [张靖仪、 赵 峥 2003 物理学报 52 2096]
[35] Liu W B 2007 Acta Phys. Sin. 56 6164 (in Chinese) [刘文彪 2007 物理学报 56 6164]
[36] Gong T X, Wang Y J 2009 Commun. Theor. Phys. 52 974
[37] Fursaev D V 1995 Phys. Rev. D 51 R5352
[38] Mann R B, Solodukhin S N 1998 Nucl. Phys. B 523 293
[39] Kaul R K, Majumdar P 2000 Phys. Rev. Lett. 84 5255
[40] Govindarajan T R, Kaul R K, Suneeta V 2001 Class. Quantum Grav. 18 2877
[41] More S S 2005 Class. Quantum Grav. 22 4129
[42] Mukherji S, Pal S S 2002 J. High Energ. Phys. 0205 026
[43] Ghosh A, Mitra P 2005 Phys. Lett. B 616 114
[44] Page D N 2005 New J. Phys. 7 203
[45] Banerjee R, Majhi B R 2008 J.High Energ. Phys. 0806 095
[46] Wang Y J 2008 Classical Black Hole and Quantum Black Hole (Beijing: Science Press) pp256 (in Chinese) [王永久 2008 经典黑洞和量子黑洞 (北京: 科学出版社) 第256页]
[47] Chen J H, Wang Y J 2008 Commun. Theor. Phys. 50 101
[48] Srinivasan K, Padmanabhan T 1999 Phys. Rev. D 60 024007
[49] Modak S K 2009 Phys. Lett. B 671 167
[50] Mitra P 2007 Phys. Lett. B 648 240
[51] York Jr J W 1985 Phys. Rev. D 31 775
[52] Lousto C O, Sanchez N 1988 Phys. Lett. B 212 411
[53] Bardeen J M, Carter B, Hawking S W 1973 Commun. Theor. Phys. 31 161
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