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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.
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Keywords:
- black hole entropy /
- thin film model without cutoff /
- generalized uncertainty relation /
- Dirac field
[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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[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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