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The Entropy of Spherically Symmetric Black Holes Due to Arbitrary Spin Fields

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Abstract

Using the membrane model which is based on brick-wall model, we calculated the free energy and entropy of spherically symmetric black holes due to arbitrary spin. The result shows that the entropy of a scalar field and the entropy of a Fermionic field have similar formulas. There is only a coefficient between them.

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REFERENCES

  1. Bekenstein, J. D. (1972). Nuovo Cimento Lett. 4, 737.

    Google Scholar 

  2. Bekenstein, J. D. (1973). Phys. Rev. D 7, 2333.

    Google Scholar 

  3. Bekenstein, J. D. (1974). Phys. Rev. D 9, 3292.

    Google Scholar 

  4. Hawking, S. W. (1975). Commun. Math. Phys. 43, 199.

    Google Scholar 

  5. Kallosh, R., Ortin, T., and Peet, A. (1993). Phys. Rev. D 47, 5400.

    Google Scholar 

  6. 'tHooft, G. (1985). Nucl. Phys. B 256, 727.

    Google Scholar 

  7. Callan, C. and Wilczek, F. (1994). Nucl. Phys. B 333, 55.

    Google Scholar 

  8. Kabat, D. and Strassler, M. J. (1994). Phys. Lett. B 329, 46.

    Google Scholar 

  9. Bombelli, L., Kowl, R. K., Lee, J., and Sourkin, R. (1986). Phys. Rev. D 34, 373.

    Google Scholar 

  10. Srednicki, M. (1993). Phys. Rev. Lett. 71, 666.

    Google Scholar 

  11. Gibbons, G. W. and Hawking, S. W. (1977). Phys. Rev. D 15, 2752.

    Google Scholar 

  12. Solodukhin, S. N. (1995). Phys. Rev. D 51, 609.

    Google Scholar 

  13. Solodukhin, S. N. (1995). Phys. Rev. D 51, 618.

    Google Scholar 

  14. Susskind, L. and Uglum, J. (1994). Phys. Rev. D 50, 2700.

    Google Scholar 

  15. Ghosh, A. and Mitra, P. (1994). Phys. Rev. Lett. 73, 2521.

    Google Scholar 

  16. Ghosh, A. and Mitra, P. (1995). Phys. Lett. B 357, 295.

    Google Scholar 

  17. Russo, J. G. (1995). Phys. Lett. B 359, 69.

    Google Scholar 

  18. Fila, T. M., Preskill, J., Strominger, A., and Trivede, S. P. (1994). Phys. Rev. D 50, 3987.

    Google Scholar 

  19. de Alwis, S. P. and Ohta, N. (1995). Phys. Rev. D 52, 3529.

    Google Scholar 

  20. Zhou, J. G., Zimmerschied, F., Liang, J. Q., and Müller-Kirsten, H. J. W. (1995). Phys. Lett. B 359, 62.

    Google Scholar 

  21. Hawking, S. W., Hoyowitz, G. T. and Ross, S. F. (1995). Phys. Rev. D 51, 4302.

    Google Scholar 

  22. Ichinose, I. and Satoh, Y. (1995). Nucl. Phys. B 447, 340.

    Google Scholar 

  23. Teitelbiom, C. (1995). Phys. Rev. D 51, 4315.

    Google Scholar 

  24. Larsen, F. and Wilczek, F. (1996). Nucl. Phys. B 458, 249.

    Google Scholar 

  25. Carlip, S. and Teitelbiom, C. (1995). Phys. Rev. D 51, 622.

    Google Scholar 

  26. Carlip, S. (1995). Phys. Rev. D 51, 632.

    Google Scholar 

  27. Larssen, F. and Wilczek, F. (1995). Ann. Phys. (N.Y.) 243, 280.

    Google Scholar 

  28. Brown, J. D. (1995). Phys. Rev. D 52, 7011.

    Google Scholar 

  29. Kabat, D. Shenker, S. h. and Strassler, M. J. (1995). Phys. Rev. D 52, 7027.

    Google Scholar 

  30. Solodukhin, S. N. (1995). Phys. Rev. D 52, 7046.

    Google Scholar 

  31. Pinto-Neto, N. and Soares, I. D. (1995). Phys. Rev. D 52, 5665.

    Google Scholar 

  32. Jacobson, T. Kang, G. and Myers, R. C. (1995). Phys. Rev. D 52, 3518.

    Google Scholar 

  33. Demers, J. G. Lafrance, R. and Myers, R. C. (1995). Phys. Rev. D 52, 2245.

    Google Scholar 

  34. Lee, H. Kim, S. W. and Kim, W. T. (1996). Phys. Rev. D 54, 6559.

    Google Scholar 

  35. Solodukhin, S. N. (1996). Phys. Rev. D 54, 3900.

    Google Scholar 

  36. Mann, R. B. and Solodukhin, S. N. (1996). Phys. Rev. D 54, 3932.

    Google Scholar 

  37. Gubser, S. S. Klebanov, I. R. and Peet, A. W. (1996). Phys. Rev. D 54, 3915.

    Google Scholar 

  38. Cvetic, M. and Youm, D. (1996). Phys. Rev. D 54, 2612.

    Google Scholar 

  39. Lee, M. H. and Kim, J. K. (1996). Phys. Lett. A 212, 323.

    Google Scholar 

  40. Lee, M. H. and Kim, J. K. (1996). Phys. Rev. D 54, 3904.

    Google Scholar 

  41. Lee, M. H. Kim, H. C. and Kim, J. K. (1996). Phys. Lett. B 388, 487.

    Google Scholar 

  42. Kim, S. W. Kim, W. T. Park, Y. J. and Shin, H. (1997). Phys. Lett. B 392, 311.

    Google Scholar 

  43. Shen, Y. G. Chen, D. M. and Zhang, T. J. (1997). Phys. Rev. D56, 6698.

    Google Scholar 

  44. Cognola, G. and Lecca, P. (1998). Phys. Rev. D 57, 1108.

    Google Scholar 

  45. Shen, Y. G. and Chen, D. M. (1998). Inter. J. Theor. Phys. 37, 3041.

    Google Scholar 

  46. Shen, Y. G. Chen, D. M., (1998) Nuovo Cimento. B, 113.

    Google Scholar 

  47. Shen, Y. G. Chen, D. M. (1998). Gen. Rel. Grav. 31, 315.

    Google Scholar 

  48. Shen, Y. G. Chen, D. M. (1999). Mod. Phys. Lett. A14, 239.

    Google Scholar 

  49. Shen, Y. G. Chen, D. M. (1999). Science. In. China. A42, 438.

    Google Scholar 

  50. Shen, Y. G. (2000). Phys. Lett. A266, 234.

    Google Scholar 

  51. Shen, Y. G. Chen, D. M. (2000). Gen. Rel. Grav. 32, 2269.

    Google Scholar 

  52. Shen, Y.G. (2000). Gen. Rel. Grav. 32, 1647.

    Google Scholar 

  53. Shen, Y. G. (2000). Mod. Phys. Lett. A15, 1901.

    Google Scholar 

  54. Shen, Y. G. Chen, D. M. (2001). Inter. J. Mod. Phys. D 10, 539.

    Google Scholar 

  55. Shen, Y. G. Cheng, Z, Y. (2001). Inter. J. Theor. Phys. 40, 1009.

    Google Scholar 

  56. Gao, C.J. and Liu, W.B. Int. J. Theor. Phys. 39, 2221 (2000).

    Google Scholar 

  57. Li, X. and Zhao, Z. (2000). Phys. Rev. D 62, 10400–1.

    Google Scholar 

  58. Gibbons, G.W. and Kallosh, R.E. (1995). Phys.Rev. D51,2839.

    Google Scholar 

  59. Liberati, S. (1997). Phys.Rev. D 56,6548.

    Google Scholar 

  60. Newman, E. and Penrose, R. (1962). J. Math. Phys. 3, 556.

    Google Scholar 

  61. Teukolsky, S. A. (1973). Astrophys. J. 185, 635.

    Google Scholar 

  62. Teukolsky, S. A.and Press. W.H. (1974). Astrophys. J. 193, 443.

    Google Scholar 

  63. Goldberg, J.W. Macfarlane, A.J. Newman, E.T. Rohrlich, F. and Sudarshan, E.C.G. (1967). J.Math. Phys. 8, 2155.

    Google Scholar 

  64. Jenson, B.P. Maclaughlin, J.G.and Ottewill, A.C. (1995). Phys.Rev. D 51, 5676.

    Google Scholar 

  65. Garfinkle, D., Horowitz, G.T. and Strominger, A. (1991) Phys. Rev. D 43, 3140.

    Google Scholar 

  66. Gibbons, G.W.and Maeda. K. (1998). Nucl.Phys. B 298,741.

    Google Scholar 

  67. Horne. J. and Horowitz. G.T. (1992). Phys.Rev. D 46,1340.

    Google Scholar 

  68. Horowitz, G.T. and Strominger, A. (1991). Nucl.Phys. B 360, 197.

    Google Scholar 

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Authors and Affiliations

  1. Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai, 200030, China

    You-Gen Shen & Chang-Jun Gao

  2. National Astronomical Observatories, Beijing, 100012, China

    You-Gen Shen & Chang-Jun Gao

  3. Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing, 100080, China

    You-Gen Shen

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  1. You-Gen Shen
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  2. Chang-Jun Gao
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Shen, YG., Gao, CJ. The Entropy of Spherically Symmetric Black Holes Due to Arbitrary Spin Fields. General Relativity and Gravitation 34, 1193–1205 (2002). https://doi.org/10.1023/A:1019722400436

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