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Cited by 3,449Black Holes and Theoretical PhysicsNoncommutative and Quantum Gravity TheoriesRelativity and Gravitational Theory

Action integrals and partition functions in quantum gravity

Gibbons, G. W., Hawking, S. W.·1977·Physical Review D
DOI 10.1103/physrevd.15.2752
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Abstract

One can evaluate the action for a gravitational field on a section of the complexified spacetime which avoids the singularities. In this manner we obtain finite, purely imaginary values for the actions of the Kerr-Newman solutions and de Sitter space. One interpretation of these values is that they give the probabilities for finding such metrics in the vacuum state. Another interpretation is that they give the contribution of that metric to the partition function for a grand canonical ensemble at a certain temperature, angular momentum, and charge. We use this approach to evaluate the entropy of these metrics and find that it is always equal to one quarter the area of the event horizon in fundamental units. This agrees with previous derivations by completely different methods. In the case of a stationary system such as a star with no event horizon, the gravitational field has no entropy.

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Crossref · 10.1103/physrevd.15.2752

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4 of 4 references verified0 citation errors · 0 not checkable

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  • For manifolds with boundary, the GHY boundary term and a holographic counterterm are needed to make sense of the model at an asymptotically AdS boundary.

    “For manifolds that have a boundary , we wrote explicitly the Gibbons–Hawking–York (GHY) boundary term (Gibbons and Hawking 1977; York 1972), and a holographic counterterm (the “”) which is needed a posteriori to make sense of the model at an asymptotically AdS boundary as will become clear later on.”

    From Solvable models of quantum black holes: a review on Jackiw–Teitelboim gravity (2023) · cites this paper as Gibbons and Hawking 1977

  • The gravitational path integral computes the black hole partition function by integrating over smooth geometries with boundary conditions corresponding to fixed inverse temperature, fixing the size of the thermal circle.

    “The gravitational path integral pioneered by Gibbons and Hawking (Gibbons and Hawking 1977) that computes the black hole partition function instructs us to integrate over smooth geometries with boundary conditions corresponding to fixed inverse temperature , fixing the size of the thermal circle.”

    From Solvable models of quantum black holes: a review on Jackiw–Teitelboim gravity (2023) · cites this paper as Gibbons and Hawking 1977

  • The continuous-spectrum disease has been linked to divergences in black hole entropy and their renormalization.

    “The “disease” of the continuous spectrum has been tied to the phenomenon of divergences in the calculation of black hole entropy [15] and the question of their renormalization [19].”

    From Very long time scales and black hole thermal equilibrium (2003) · cites this paper as [19]

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Authors
Gibbons, G. W., & Hawking, S. W.
Affiliations
University of Cambridge (GB)
ORCID
Venue
Physical Review D
Publisher
American Physical Society (APS)
Published
1977-05-15
Volume
15
Issue
10
Pages
2752-2756
ISSN
0556-2821 (ISSN-L)
DOI
10.1103/physrevd.15.2752
OpenAlex
W2144012213
Cited by
3,449
References
4
Citations by year
2026: 144 · 2025: 236 · 2024: 199 · 2023: 202 · 2022: 151 · 2021: 159 · 2020: 141 · 2019: 121 · 2018: 115 · 2017: 94 · 2016: 106 · 2015: 106 · 2014: 94 · 2013: 99 · 2012: 97
FWCI
8.00
Type
journal article
Language
en
Open access
closed
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields (publishedVersion)
Topics
  • Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
  • Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
Keywords
quantum gravity, action integral, partition function, Kerr-Newman solution, de Sitter space, gravitational entropy, event horizon area, grand canonical ensemble, black hole thermodynamics, stationary spacetimes

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