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First, we effectively reduce the higher-dimensional rotation metric to a 2-dimensional metric near the event horizon which contains only the (t-r) sector. Then, we study the Unruh/Hawking temperature for (1+1)-dimensional space-time with the new global embedding method. It is shown that the viewpoint of Banerjee and Majhi is correct. We also extend the study to the case of higher-dimensional rotation black hole.
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Keywords:
- black hole /
- higher-dimensional rotation /
- Hawking effect /
- Unruh effect
[1] Hawking S W 1974 Nature 248 30
[2] Hawking S W 1975 Commun. Math. Phys. 43 199
[3] [4] Unruh W G 1976 Phys. Rev. D 14 870
[5] [6] Fulling S A 1973 Phys. Rev. D 7 2850
[7] [8] [9] Davies P C W 1975 J. Phys. A 8 609
[10] [11] Deser S, Levin O 1997 Class. Quantum Grav. 14 L163
[12] [13] Deser S, Levin O 1998 Class. Quantum Grav. 15 L85
[14] [15] Deser S, Levin O 1999 Phys. Rev. D 59 064004
[16] Hong S T, Kim W T, Oh J J, Park Y J 2001 Phys. Rev. D 63 127502
[17] [18] Santos N L, Dias O J C, Lemos J P S 2004 Phys. Rev. D 70 124033
[19] [20] [21] Chen H Z, Tian Y 2005 Phys. Rev. D 71 104008
[22] [23] Chen H Z, Tian Y, Gao Y H, Song X C 2004 J. High Energy Phys. (10) 011
[24] [25] Tian Y 2005 J. High Energy Phys. (06) 045
[26] [27] Brynjolfsson E J, Thorlactus L 2008 J. High Energy Phys. (09) 066
[28] Hirayama T, Kao P W, Kawamoto S, Lin F L 2011 Nucl. Phys. B 844 1
[29] [30] [31] Caceres E, Chernicoff M, Guijosa A, Pedraza J F 2010 J. High Energy Phys. (06) 078
[32] [33] Crispino L C B, Higuchi A, Matsas G E A 2008 Rev. Mod. Phys. 80 787
[34] [35] Banerjee R, Majhi B R 2010 Phys. Lett. B 690 83
[36] Robinson S P, Wilczek F 2005 Phys. Rev. Lett. 95 011303
[37] [38] [39] Iso S, Umetsu H, Wilczek F 2006 Phys. Rev. D 74 044017
[40] [41] Umetsu K 2010 Int. J. Mod. Phys. A 25 4123
[42] Porfyriadis A P 2009 Phys. Rev. D 79 084039
[43] [44] Vasudevan M, Stevens K A, Page D N 2005 Class. Quantum Grav. 22 1469
[45] [46] [47] Gibbons G W, Lu H, Page D N, Pope C N 2004 Phys. Rev. Lett. 93 171102
[48] [49] Xu Z, Chen B 2007 Phys. Rev. D 75 024041
[50] Myers R C, Perry M J 1986 Ann. Phys. 172 304
[51] [52] [53] Gibbons G W, Perry M J, Pope C N 2005 Class. Quantum Grav. 22 1503
[54] [55] Vasudevan M, Stevens K A, Page D N 2005 Class. Quantum Grav. 22 339
[56] [57] Gibbons G W, Lu H, Page D N, Pope C N 2005 J. Geom. Phys. 53 49
[58] [59] Zhao R, Zhang L C, Li H F, Wu Y Q 2010 Eur. Phys. J. C 65 289
[60] [61] Tolman R C 1987 Relativity, Thermodynamics and Cosmology (New York: Dover Pulication) p318
[62] [63] Yang S Z, Lin K 2010 Acta Phys. Sin. 59 5266 (in Chinese)[杨树政、 林 恺 2010 59 5266]
[64] [65] Zhang J Y, Zhao Z 2006 Acta Phys. Sin. 55 3796 (in Chinese)[张静仪、 赵 峥 2006 55 3796]
[66] [67] Wu S Q, Zeng Y, Cai X, Yan M L 2003 Acta Phys. Sin. 52 1340 (in Chinese)[吴双清、 曾 喻、 蔡 勖、 阎沐霖 2003 52 1340]
[68] Liu W B 2007 Acta Phys. Sin. 56 6164 (in Chinese )[刘文彪 2007 56 6164]
[69] [70] Li H L, Jiang Q Q, Yang S Z 2006 Acta Phys. Sin. 55 539 (in Chinese ) [李慧玲、 蒋青权、 杨树政 2006 55 539]
[71] -
[1] Hawking S W 1974 Nature 248 30
[2] Hawking S W 1975 Commun. Math. Phys. 43 199
[3] [4] Unruh W G 1976 Phys. Rev. D 14 870
[5] [6] Fulling S A 1973 Phys. Rev. D 7 2850
[7] [8] [9] Davies P C W 1975 J. Phys. A 8 609
[10] [11] Deser S, Levin O 1997 Class. Quantum Grav. 14 L163
[12] [13] Deser S, Levin O 1998 Class. Quantum Grav. 15 L85
[14] [15] Deser S, Levin O 1999 Phys. Rev. D 59 064004
[16] Hong S T, Kim W T, Oh J J, Park Y J 2001 Phys. Rev. D 63 127502
[17] [18] Santos N L, Dias O J C, Lemos J P S 2004 Phys. Rev. D 70 124033
[19] [20] [21] Chen H Z, Tian Y 2005 Phys. Rev. D 71 104008
[22] [23] Chen H Z, Tian Y, Gao Y H, Song X C 2004 J. High Energy Phys. (10) 011
[24] [25] Tian Y 2005 J. High Energy Phys. (06) 045
[26] [27] Brynjolfsson E J, Thorlactus L 2008 J. High Energy Phys. (09) 066
[28] Hirayama T, Kao P W, Kawamoto S, Lin F L 2011 Nucl. Phys. B 844 1
[29] [30] [31] Caceres E, Chernicoff M, Guijosa A, Pedraza J F 2010 J. High Energy Phys. (06) 078
[32] [33] Crispino L C B, Higuchi A, Matsas G E A 2008 Rev. Mod. Phys. 80 787
[34] [35] Banerjee R, Majhi B R 2010 Phys. Lett. B 690 83
[36] Robinson S P, Wilczek F 2005 Phys. Rev. Lett. 95 011303
[37] [38] [39] Iso S, Umetsu H, Wilczek F 2006 Phys. Rev. D 74 044017
[40] [41] Umetsu K 2010 Int. J. Mod. Phys. A 25 4123
[42] Porfyriadis A P 2009 Phys. Rev. D 79 084039
[43] [44] Vasudevan M, Stevens K A, Page D N 2005 Class. Quantum Grav. 22 1469
[45] [46] [47] Gibbons G W, Lu H, Page D N, Pope C N 2004 Phys. Rev. Lett. 93 171102
[48] [49] Xu Z, Chen B 2007 Phys. Rev. D 75 024041
[50] Myers R C, Perry M J 1986 Ann. Phys. 172 304
[51] [52] [53] Gibbons G W, Perry M J, Pope C N 2005 Class. Quantum Grav. 22 1503
[54] [55] Vasudevan M, Stevens K A, Page D N 2005 Class. Quantum Grav. 22 339
[56] [57] Gibbons G W, Lu H, Page D N, Pope C N 2005 J. Geom. Phys. 53 49
[58] [59] Zhao R, Zhang L C, Li H F, Wu Y Q 2010 Eur. Phys. J. C 65 289
[60] [61] Tolman R C 1987 Relativity, Thermodynamics and Cosmology (New York: Dover Pulication) p318
[62] [63] Yang S Z, Lin K 2010 Acta Phys. Sin. 59 5266 (in Chinese)[杨树政、 林 恺 2010 59 5266]
[64] [65] Zhang J Y, Zhao Z 2006 Acta Phys. Sin. 55 3796 (in Chinese)[张静仪、 赵 峥 2006 55 3796]
[66] [67] Wu S Q, Zeng Y, Cai X, Yan M L 2003 Acta Phys. Sin. 52 1340 (in Chinese)[吴双清、 曾 喻、 蔡 勖、 阎沐霖 2003 52 1340]
[68] Liu W B 2007 Acta Phys. Sin. 56 6164 (in Chinese )[刘文彪 2007 56 6164]
[69] [70] Li H L, Jiang Q Q, Yang S Z 2006 Acta Phys. Sin. 55 539 (in Chinese ) [李慧玲、 蒋青权、 杨树政 2006 55 539]
[71]
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