Statistical Mechanical Origin of the Entropy of a Rotating, Charged Black Hole

W. H. Zurek; Kip S. Thorne

doi:10.1103/PhysRevLett.54.2171

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Statistical Mechanical Origin of the Entropy of a Rotating, Charged Black Hole

W. H. Zurek

Kip S. Thorne

Theoretical Astrophysics, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, and California Institute of Technology, Pasadena, California 91125

California Institute of Technology, Pasadena, California 91125, and Institute of Theoretical Physics, University of California at Santa Barbara, Santa Barbara, California 93106

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Phys. Rev. Lett. 54, 2171 – Published 20 May, 1985

DOI: https://doi.org/10.1103/PhysRevLett.54.2171

Abstract

It is shown that the entropy of a rotating, charged black hole is, in senses made precise in the paper, (i) the logarithm of the number of quantum mechanically distinct ways that the hole could have been made, and (ii) the logarithm of the number of configurations that the hole's "atmosphere," as measured by stationary observers, could assume in the presence of its background noise of acceleration radiation. In addition, a proof is given of the generalized second law of thermodynamics.

References (21)

S. W. Hawking, Commun. Math. Phys. 43, 199 (1975)
J. M. Bardeen, B. Carter, and S. W. Hawking, Commun. Math. Phys. 31, 181 (1973)
S. W. Hawking, Phys. Rev. 13, 191 (1976)
J. D. Bekenstein, Phys. Rev. D 7, 2333 (1973)
J. D. Bekenstein, Phys. Today 33, No. 1, 24 (1980)
J. D. Bekenstein, in To Fulfill a Vision—Jerusalem Einstein Centennial Symposium, edited by Y. Ne'eman (Addison Wesley, Reading, Mass., 1979)
P. C. W. Davies and R. M. Wald in Quantum Gravity 2, edited by C. J. Isham, R. Penrose, and D. W. Sciama (Clarendon, Oxford, 1981)
U. H. Gerlach, Phys. Rev. D 14, 1479 (1976)
J. W. York, Phys. Rev. D 28, 2929 (1983)
Omitted endnote
D. N. Page, Phys. Rev. D 13, 198 (1976)
W. H. Zurke, Phys. Rev. Lett. 49, 1683, (1982) D. N. Page, 50, 1013 (1983)
W. G. Unruh, Phys. Rev. D 14, 870 (1976)
W. G. Unruh and R. M. Wald, Phys. Rev. D 25, 942 (1982)
K. S. Thorne, in "Highlights of Modern Astrophysics," edited by S. L. Shapiro and S. A. Teukolsky (Wiley, New York, to be published)
J. M. Bardeen, in Black Holes, edited by C. DeWitt and B. S. DeWitt (Gordon and Breach, New York, 1973), p. 215
Sec. 5.3 of K. S. Thorne and D. M. Macdonald, Mon. Not. Roy. Astron. Soc. 198, 339 (1982)
Sec. 3.3 of D. W. Sciama, P. Candelas, and D. Deutsch, Adv. Phys. 30, 327 (1981) B. Carter, in General Relativity, an Einstein Centenary Survey, edited by S. W. Hawking and W. Israel (Cambridge Univ. Press, Cambridge, 1979), p. 294
Sciama et al., [18]
D. M. Macdonald and W.-M. Suen, to be published
J. D. Bekenstein, Phys. Rev. D 12, 3017 (1975)

[c1] S. W. Hawking, Commun. Math. Phys. 43, 199 (1975)

[c2] J. M. Bardeen, B. Carter, and S. W. Hawking, Commun. Math. Phys. 31, 181 (1973)

[c3] S. W. Hawking, Phys. Rev. 13, 191 (1976)

[c4] J. D. Bekenstein, Phys. Rev. D 7, 2333 (1973)

[c5] J. D. Bekenstein, Phys. Today 33, No. 1, 24 (1980)

[c6] J. D. Bekenstein, in To Fulfill a Vision—Jerusalem Einstein Centennial Symposium, edited by Y. Ne'eman (Addison Wesley, Reading, Mass., 1979)

[c7] P. C. W. Davies and R. M. Wald in Quantum Gravity 2, edited by C. J. Isham, R. Penrose, and D. W. Sciama (Clarendon, Oxford, 1981)

[c8] U. H. Gerlach, Phys. Rev. D 14, 1479 (1976)

[c9] J. W. York, Phys. Rev. D 28, 2929 (1983)

[c10] Omitted endnote

[c11] D. N. Page, Phys. Rev. D 13, 198 (1976)

[c12] W. H. Zurke, Phys. Rev. Lett. 49, 1683, (1982) D. N. Page, 50, 1013 (1983)

[c13] W. G. Unruh, Phys. Rev. D 14, 870 (1976)

[c14] W. G. Unruh and R. M. Wald, Phys. Rev. D 25, 942 (1982)

[c15] K. S. Thorne, in "Highlights of Modern Astrophysics," edited by S. L. Shapiro and S. A. Teukolsky (Wiley, New York, to be published)

[c16] J. M. Bardeen, in Black Holes, edited by C. DeWitt and B. S. DeWitt (Gordon and Breach, New York, 1973), p. 215

[c17] Sec. 5.3 of K. S. Thorne and D. M. Macdonald, Mon. Not. Roy. Astron. Soc. 198, 339 (1982)

[c18] Sec. 3.3 of D. W. Sciama, P. Candelas, and D. Deutsch, Adv. Phys. 30, 327 (1981) B. Carter, in General Relativity, an Einstein Centenary Survey, edited by S. W. Hawking and W. Israel (Cambridge Univ. Press, Cambridge, 1979), p. 294

[c19] Sciama et al., [18]

[c20] D. M. Macdonald and W.-M. Suen, to be published

[c21] J. D. Bekenstein, Phys. Rev. D 12, 3017 (1975)

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Statistical Mechanical Origin of the Entropy of a Rotating, Charged Black Hole

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