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采用两种新的乌龟坐标变换,用改进的Damour-Ruffini方法研究了动态Kinnersley黑洞的Hawking辐射.在新乌龟坐标变换下,将Klein-Gordon方程在视界附近变换成平直时空的标准波动方程形式,得到了黑洞的表面引力及Hawking温度,该温度在黑洞表面不同点有不同的值.值得注意的是,旧的乌龟坐标变换存在量纲错误,新乌龟坐标变换没有量纲问题,选不同的旧乌龟坐标变换计算同一黑洞所得结果不同,但是采用不同的新乌龟坐标变换所得结果仍然不同.
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关键词:
- 黑洞 /
- 乌龟坐标变换 /
- Hawking辐射 /
- Klein-Gorden方程
With two new tortoise coordinate transformations, Hawking effect from a dynamical Kinnersley black hole is investigated by using the improved Damour-Ruffini method. After the tortoise coordinate transformation, the Klein-Gordon equation can be written in the standard form at the event horizon. Then extending the outgoing wave from outside to inside of the horizon analytically, the surface gravity and the Hawking temperature can be obtained automatically. It is found that Hawking temperature of different points on the surface are different. There is a problem of dimension in the usual tortoise coordinate and the results are different from those of the same black hole by using two different tortoise coordinate transformations. The results obtained by using two new tortoise coordinate transformations are still different.-
Keywords:
- black hole /
- tortoise coordinate transformation /
- Hawking radiation /
- Klein-Gordon equation
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[2] Gibbons G W, Hawking S W 1977 Phys. Rev. D 15 2752
[3] Damour T, Ruffini R 1976 Phys. Rev. D 14 332
[4] Sannan S 1988 Gen. Rel. Grav. 20 239
[5] Zhao Z 1999 Thermal Property of Black Hole and Singularity of Spacetime(Beijing: Beijing Normal University Press) p236 (in Chinese)[赵 峥 1999黑洞的热性质与时空奇异性(北京:北京师范大学出版社)第236页]
[6] Zhao Z, Dai X X 1991 Chin. Phys. Lett. 8 548
[7] Sun M C, Zhao R, Zhao Z 1995 IL Nuovo Cimento B 110 829
[8] Zhao Z, Huang W H 1993 J. Beijing Normal University (Natural Science) 29 87(in Chinese) [赵 峥、 黄维华 1993, 北京师范大学学报(自然科学版) 29 87]
[9] Zhao Z, Luo Z Q, Dai X X 1994 IL Nuovo Cimento B 109 483
[10] Zhao R, Zhang L C, Li H F 2010 Acta Phys. Sin. 59 2982(in Chinese)[赵 仁、 张丽春、 李怀繁 2010 59 2982]
[11] Niu Z F, Liu W B 2005 Acta Phys. Sin. 54 475(in Chinese)[牛振风、 刘文彪 2005 54 475]
[12] Pan W Z, Yang X J, Xie Z K 2011 Chin.Phys. B 20 049701
[13] Meng Q M, Jiang J J, Li C A 2010 Acta Phys. Sin. 59 778(in Chinese)[孟庆苗、 蒋继建、 李传安 2010 59 778]
[14] Parikh M Kand Wilczek F 2000 Phys. Rev. Lett. 85 5042
[15] Zhao Z, Yang J, Liu W B 2010 J. Beijing Normal University (Natural Science) 46 32(in Chinese) [赵 峥、 杨 健、 刘文 彪 2010 北京师范大学学报(自然科学版)46 32] 〖16] Wu S Q, Cai X 2002 Gen. Rel. Grav. 34 1207
[16] Yang X J 2003 Ph. D. Dissertation (Beijing: Beijing Normal University) (in Chinese) [杨学军 2003 博士学位论文 北京: 北京师范大学]
[17] Niu Z F, Cao J L, Liu W B 2004 J. Beijing Normal University (Natural Science) 40 481(in Chinese)[牛振风、 曹江陵、 刘文彪 2004 北京师范大学学报(自然科学版) 40 481]
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[1] Hawking S W 1974 Nature 248 30
[2] Gibbons G W, Hawking S W 1977 Phys. Rev. D 15 2752
[3] Damour T, Ruffini R 1976 Phys. Rev. D 14 332
[4] Sannan S 1988 Gen. Rel. Grav. 20 239
[5] Zhao Z 1999 Thermal Property of Black Hole and Singularity of Spacetime(Beijing: Beijing Normal University Press) p236 (in Chinese)[赵 峥 1999黑洞的热性质与时空奇异性(北京:北京师范大学出版社)第236页]
[6] Zhao Z, Dai X X 1991 Chin. Phys. Lett. 8 548
[7] Sun M C, Zhao R, Zhao Z 1995 IL Nuovo Cimento B 110 829
[8] Zhao Z, Huang W H 1993 J. Beijing Normal University (Natural Science) 29 87(in Chinese) [赵 峥、 黄维华 1993, 北京师范大学学报(自然科学版) 29 87]
[9] Zhao Z, Luo Z Q, Dai X X 1994 IL Nuovo Cimento B 109 483
[10] Zhao R, Zhang L C, Li H F 2010 Acta Phys. Sin. 59 2982(in Chinese)[赵 仁、 张丽春、 李怀繁 2010 59 2982]
[11] Niu Z F, Liu W B 2005 Acta Phys. Sin. 54 475(in Chinese)[牛振风、 刘文彪 2005 54 475]
[12] Pan W Z, Yang X J, Xie Z K 2011 Chin.Phys. B 20 049701
[13] Meng Q M, Jiang J J, Li C A 2010 Acta Phys. Sin. 59 778(in Chinese)[孟庆苗、 蒋继建、 李传安 2010 59 778]
[14] Parikh M Kand Wilczek F 2000 Phys. Rev. Lett. 85 5042
[15] Zhao Z, Yang J, Liu W B 2010 J. Beijing Normal University (Natural Science) 46 32(in Chinese) [赵 峥、 杨 健、 刘文 彪 2010 北京师范大学学报(自然科学版)46 32] 〖16] Wu S Q, Cai X 2002 Gen. Rel. Grav. 34 1207
[16] Yang X J 2003 Ph. D. Dissertation (Beijing: Beijing Normal University) (in Chinese) [杨学军 2003 博士学位论文 北京: 北京师范大学]
[17] Niu Z F, Cao J L, Liu W B 2004 J. Beijing Normal University (Natural Science) 40 481(in Chinese)[牛振风、 曹江陵、 刘文彪 2004 北京师范大学学报(自然科学版) 40 481]
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