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Cited by 1,307

The DOI matches its Crossref record; 4 of the 4 references it cites were found in a registry or an index.

Black holes and thermodynamics

Hawking, S. W.·1976·Physical Review D
DOI 10.1103/physrevd.13.191
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Abstract

A black hole of given mass, angular momentum, and charge can have a large number of different unobservable internal configurations which reflect the possible different initial configurations of the matter which collapsed to produce the hole. The logarithm of this number can be regarded as the entropy of the black hole and is a measure of the amount of information about the initial state which was lost in the formation of the black hole. If one makes the hypothesis that the entropy is finite, one can deduce that the black holes must emit thermal radiation at some nonzero temperature. Conversely, the recently derived quantum-mechanical result that black holes do emit thermal radiation at temperature $\frac{\ensuremath{\kappa}\ensuremath{\hbar}}{2\ensuremath{\pi}kc}$, where $\ensuremath{\kappa}$ is the surface gravity, enables one to prove that the entropy is finite and is equal to $\frac{{c}^{3}A}{4G\ensuremath{\hbar}}$, where $A$ is the surface area of the event horizon or boundary of the black hole. Because black holes have negative specific heat, they cannot be in stable thermal equilibrium except when the additional energy available is less than 1/4 the mass of the black hole. This means that the standard statistical-mechanical canonical ensemble cannot be applied when gravitational interactions are important. Black holes behave in a completely random and time-symmetric way and are indistinguishable, for an external observer, from white holes. The irreversibility that appea…

Overview

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Crossref · 10.1103/physrevd.13.191

Cites

4 of 4 references verified0 citation errors · 0 not checkable

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  • The Bekenstein-Hawking entropy-area relation is S = k_B c3 A[H]/(4ħG).

    “This is encapsulated by the Bekenstein-Hawking entropy-area relation,”

    From Three-Dimensional Quantum Black Holes: A Primer (2024) · cites this paper as [114]

Citations

Cites

Flagged first, then by citations

Research works printed but not linked: 15

  1. C. W. Misner, 1973, Gravitation
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  3. U. H. Gerlach, Phys. Rev. D
  4. L. Parker, 1975, Phys. Rev. D, 12, 1519, 10.1103/PhysRevD.12.1519 · DOI
  5. J. D. Bekenstein, 1973, Phys. Rev. D, 7, 2333, 10.1103/PhysRevD.7.2333 · DOI · Paper page
  6. J. D. Bekenstein, 1974, Phys. Rev. D, 9, 3292, 10.1103/PhysRevD.9.3292 · DOI · Paper page
  7. S. W. Hawking, 1972, Commun. Math. Phys., 25, 152, 10.1007/BF01877517 · DOI · Paper page
  8. W. Israel, 1967, Phys. Rev., 164, 1776, 10.1103/PhysRev.164.1776 · DOI
  9. B. Carter, 1970, Phys. Rev. Lett., 26, 331, 10.1103/PhysRevLett.26.331 · DOI
  10. H. Muller zum Hagen, 1973, Gen. Relativ. Gravit., 4, 53, 10.1007/BF00769760 · DOI
  11. D. C. Robinson, 1974, Phys. Rev. D, 10, 458, 10.1103/PhysRevD.10.458 · DOI
  12. D. C. Robinson, 1975, Phys. Rev. Lett., 34, 905, 10.1103/PhysRevLett.34.905 · DOI
  13. R. Hagedorn, 1973, Cargèse Lectures in Physics
  14. S. C. Frautschi, 1971, Phys. Rev. D., 3, 2821, 10.1103/PhysRevD.3.2821 · DOI
  15. H. Everett, 1957, Rev. Mod. Phys., 29, 454, 10.1103/RevModPhys.29.454 · DOI · Paper page

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Metadata

Authors
Hawking, S. W.
Venue
Physical Review D
Publisher
American Physical Society (APS)
Published
1976-01-15
Volume
13
Issue
2
Pages
191-197
ISSN
0556-2821
DOI
10.1103/physrevd.13.191
Cited by
1,307
References
4
Language
en
Licence
link.aps.org/licenses/aps-default-license (vor)

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