无截断薄膜模型与Dirac场的黑洞熵

杨学军; 赵峥

doi:10.7498/aps.60.060401

摘要

计算黑洞熵的砖墙模型被改进为薄膜模型后其物理思想更直接而明了,且突出了事件视界作为静态或稳态黑洞特征面的重要性.但为避免发散,薄膜模型同样需要引入紫外截断因子.截断因子的引入非常人为,至今没有给以合理的解释.有文献将广义不确定关系引入黑洞熵的计算而不需要任何截断便可避免发散.本文以静态球对称黑洞Dirac场的熵的计算为例,阐述了无截断薄膜模型及其与有截断薄膜模型的本质区别.

关键词:

The physical idea of thin film model improved from brick-wall model is more direct and clearer than brick-wall model and gives prominence to the significance of the event horizon serving as the characteristic surface of a static or stationary black hole. To remove the divergence of the density of states, an ultraviolet cutoff factor is also introduced into the thin film model. The cutoff is introduced artificially and it has not been understood clearly up to now. There is an indication in a reference that the divergence can be removed without any cutoff when the generalized uncertainty relation is used to calculate black hole entropy. In this paper, thin film model without cutoff and the essential difference between the thin film model without cutoff and the thin film model with cutoff are expounded by the example of calculating the entropy of spherically symmetric static black hole Dirac field.

Keywords:

作者及机构信息

杨学军²,
赵峥¹

(1)北京师范大学物理系,北京 100875; (2)绍兴文理学院物理与电子信息系,绍兴 312000

基金项目: 国家自然科学基金(批准号:10873003,11045005)和浙江省自然科学基金(批准号:Y6090739)资助的课题.

Authors and contacts

Zhao Zheng²,
Yang Xue-Jun¹

(1)Department of Physics and Electronic Information, Shaoxing University, Shaoxing 312000, China; (2)Department of Physics, Beijing Normal University, Beijing 100875, China

参考文献

[1]	't Hooft G 1985 Nucl. Phys. B 256 727
[2]	Li X, Zhao Z 2000 Phys. Rev. D 62 104001
[3]	Liu W B, Zhao Z 2001 Chin. Phys. Lett. 18 345
[4]	Gao C J, Shen Y G 2001 Chin. Phys. Lett. 18 1167
[5]	Zhao R, Zhang L C, Hu S Q 2006 Acta Phys. Sin. 55 3902(in Chinese)[赵仁、张丽春、胡双启 2006 55 3902]
[6]	Liu C Z 2005 Acta Phys. Sin. 54 1977 (in Chinese)[刘成周 2005 54 1977]
[7]	Hu S Q, Zhao R 2005 Chin. Phys. 14 1977
[8]	Wang G Z, Wang J L 2004 Acta Phys. Sin. 53 1669 (in Chinese)[王钢柱、王纪龙 2004 53 1669]
[9]	Li X 2002 Phys. Lett. B 540 9
[10]	Ashtekar A, Rovelli C, Smolin L 1992 Phys. Rev. Lett. 69 237
[11]	Gross D J, Mende P F 1988 Nucl. Phys. B 303 407
[12]	Amati D, Ciafaloni M, Veneziano G 1987 Phys. Lett. B 197 81
[13]	Maggiore M 1994 Phys. Rev. D 49 5182
[14]	Witten E 1997 Phys. Today 49 24
[15]	Kempf A, Mangano A, Mann R B 1995 Phys. Rev. D 52 1180
[16]	Benczik S, Chang L N, Minic D, Dkamura N, Rayyan S, Takeuchi T 2002 Phys. Rev. D 66 026003
[17]	Chang L N, Minic D, Okamura N, Takeuchi T 2002 Phys. Rev. D 65 125028
[18]	Zhao R, Zhang L C, Li H F 2009 Acta Phys. Sin. 58 2193 (in Chinese)[赵仁、张丽春、李怀繁 2009 58 2193]
[19]	Xie Z K, Yu G X, Liu C Z 2010 Acta Phys. Sin. 59 4390 (in Chinese)[谢志堃、余国祥、刘成周 2010 59 4390]
[20]	Zhao Z 1999 Thermal Properties of Black Holes and Singularities of Space-Time (Beijing: Beijing Normal University Press) p36, p29 (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36页、第29页]
[21]	Newman E, Penrose R 1962 J. Math. 3 566
[22]	Page D N 1976 Phys. Rev. D 14 1509
[23]	Susskind L 1995 J. Math. Phys. 36 6377
[24]	't Hooft G 1993 gr-qc/9310026

施引文献

[1]	't Hooft G 1985 Nucl. Phys. B 256 727
[2]	Li X, Zhao Z 2000 Phys. Rev. D 62 104001
[3]	Liu W B, Zhao Z 2001 Chin. Phys. Lett. 18 345
[4]	Gao C J, Shen Y G 2001 Chin. Phys. Lett. 18 1167
[5]	Zhao R, Zhang L C, Hu S Q 2006 Acta Phys. Sin. 55 3902(in Chinese)[赵仁、张丽春、胡双启 2006 55 3902]
[6]	Liu C Z 2005 Acta Phys. Sin. 54 1977 (in Chinese)[刘成周 2005 54 1977]
[7]	Hu S Q, Zhao R 2005 Chin. Phys. 14 1977
[8]	Wang G Z, Wang J L 2004 Acta Phys. Sin. 53 1669 (in Chinese)[王钢柱、王纪龙 2004 53 1669]
[9]	Li X 2002 Phys. Lett. B 540 9
[10]	Ashtekar A, Rovelli C, Smolin L 1992 Phys. Rev. Lett. 69 237
[11]	Gross D J, Mende P F 1988 Nucl. Phys. B 303 407
[12]	Amati D, Ciafaloni M, Veneziano G 1987 Phys. Lett. B 197 81
[13]	Maggiore M 1994 Phys. Rev. D 49 5182
[14]	Witten E 1997 Phys. Today 49 24
[15]	Kempf A, Mangano A, Mann R B 1995 Phys. Rev. D 52 1180
[16]	Benczik S, Chang L N, Minic D, Dkamura N, Rayyan S, Takeuchi T 2002 Phys. Rev. D 66 026003
[17]	Chang L N, Minic D, Okamura N, Takeuchi T 2002 Phys. Rev. D 65 125028
[18]	Zhao R, Zhang L C, Li H F 2009 Acta Phys. Sin. 58 2193 (in Chinese)[赵仁、张丽春、李怀繁 2009 58 2193]
[19]	Xie Z K, Yu G X, Liu C Z 2010 Acta Phys. Sin. 59 4390 (in Chinese)[谢志堃、余国祥、刘成周 2010 59 4390]
[20]	Zhao Z 1999 Thermal Properties of Black Holes and Singularities of Space-Time (Beijing: Beijing Normal University Press) p36, p29 (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36页、第29页]
[21]	Newman E, Penrose R 1962 J. Math. 3 566
[22]	Page D N 1976 Phys. Rev. D 14 1509
[23]	Susskind L 1995 J. Math. Phys. 36 6377
[24]	't Hooft G 1993 gr-qc/9310026

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