非热平衡Schwarzschildde Sitter黑洞的熵

数学物理学报 ›› 2003, Vol. 23 ›› Issue (2): 169-174.

非热平衡Schwarzschildde Sitter黑洞的熵

刘文彪, 赵峥

北京师范大学物理学系|北京师范大学理论物理研究所

出版日期:2003-04-25 发布日期:2003-04-25
基金资助:
国家自然科学基金（19773003）和教育部博士点基金

The Entropy of Thermal Nonequilibrium |Schwarzschildde Sitter Spacetime

LIU Wen-Biao, DIAO Zheng-

Online:2003-04-25 Published:2003-04-25
Supported by:
国家自然科学基金（19773003）和教育部博士点基金

摘要/Abstract

摘要：

从Schwarzschildde Sitter时空背景下的KleinGordon方程出发，利用brickwall方法计算了黑洞的自由能和熵。这种黑洞由于存在两个视界面，而且它们的温度不相同，因此用一般方法计算熵存在着一定的困难。采用改进的brickwall模型，认为自由能和熵主要来自于视界附近薄层的贡献，很好地解决了这一困难，并得到了满意的结果。结果表明，这种黑洞的熵为它的两个视界面积之和的1/4，与人们预期的结果相符。由此可见，渐近de Sitter时空中的黑洞熵除了黑洞视界面的贡献之外，还应包括宇宙视界面的贡献。这从一定程度上揭示了黑洞熵与视界面积之间的内在联系，也更进一步地揭示了brickwall模型的本质。

关键词: de Sitter时空； Schwarzschild黑洞；黑洞熵； Brickwall方法；视界.

Abstract:

Thinking of KleinGordon equation in Schwarzschildde Sitter spacetime, the authors calculate the free energy and entropy of this kind of black hole via brickwall method. It is difficult to calculate the free energy because there are twohorizons whose temperature is different from one another. Taking improved brickwall model, which means that the free energy and entropy are mainly from a thinlayer close to the horizon, the authors overcame the problem successfully and got a goodresult. It is found that the entropy of this system is 1/4 of the sum of the areas of the two event horizons. This is coincided to the result expected. The entropy of this system not only includes the contribution of the black hole horizon,but also includes the contribution of the cosmological horizon. It is found that there is an internal relation between the event horizon and the entropy. The authors also understand more about what is the brickwall model.

Key words: de Sitter spacetime, Schwarzschild black hole, Entropy of black hole;Brickwall method, Horizon.

中图分类号:

刘文彪, 赵峥. 非热平衡Schwarzschildde Sitter黑洞的熵[J]. 数学物理学报, 2003, 23(2): 169-174.

LIU Wen-Biao, DIAO Zheng-. The Entropy of Thermal Nonequilibrium |Schwarzschildde Sitter Spacetime[J]. Acta mathematica scientia,Series A, 2003, 23(2): 169-174.

参考文献

［1］Bekenstein J D. Black hole and entropy. Phys Rev, 1973, D7: 2333
［2］ Hawking S W. Particle creation by black holes. Commun Math Phys, 1975, 43: 199
［3］ Bardeen J M, Carter B, Hawking S W. The four laws of black hole mechanic

s. Math Phys, 1973, 31: 161
［4］ G 't Hooft. On the quantum structure of a black hole. Nuclear Physics, 1985, B256: 727
［5］Ghosh A, Mitra P. Entropy in Dilatonic black hole background. Phys Rev Lett, 1994, 73: 2521
［6］ Cai R G, Zhu L B. Entropy of scalar fields and its duality invariance inthreedimensional spacetimes. Phys Lett, 1996, A291: 191
［7］ Lee H, Kim S W, Kim W T. Nonvanishing entropy of extremal charged blackholes. Phys Rev, 1996, D54: 6559
［8］ Lee M H, Kim J K. Entropy of a quantum field in rotating black hole. Phys Rev, 1996, D54: 3904
［9］ Ho J, Kim W T, Park Y J, Shin H. Entropy in the KerrNewman black hole. Class Quantum Grav, 1997, 14: 2617
［10］Jing Jiliang. Entropy of the quantum scalar field in static black holes. International Journal of Theoretical Physics, 1998, 37(5): 1441
［11］罗智坚，朱建阳。Schwarzschild黑洞背景下Dirac场的熵。物理学报，1999, 48（3）: 395
［12］刘文彪，朱建阳，赵峥。Nernst定理与RN黑洞Dirac场的熵。物理学报，2000，49（3）： 581
［13］Liu Wenbiao, Zhao Zheng. Entropy of the Dirac field in a KerrNewman bl

ack hole. Phys Rev, 2000, D61(6)： 063003
［14］ Gibbons G W, Hawking S W. Cosmological event horizons, thermodynamics, and particle creation. Phys Rev, 1977, D15: 2738
［15］ Gibbons G W, Hawking S W. Action integrals and partition functions in quantum gravity. Phys Rev, 1977,D15: 2752
［16］刘文彪，高长军，赵峥。de Sitter时空背景下的熵。北京师范大学学报（自然科学版）, 2000, 36(1): 62
［17］ Cai R G, Ji J Y, Soh K S. Action and entropy of black holes in spacetimes with a cosmological constant. Class Quantum Grav, 1998, 15: 2783
［18］李翔，赵峥。黑洞熵公式的简单推导。北京师范大学学报（自然科学版）, 2000, 36(2): 193
［19］赵峥，刘辽。一般稳态时空视界的确定。物理学报，1991, 40: 154
［20］赵峥. 黑洞温度、熵变化率和时间尺度的压缩。北京师范大学学报（自然科学版），1995, 31(4): 476