Action integrals and partition functions in quantum gravity

G. W. Gibbons and S. W. Hawking
Phys. Rev. D 15, 2752 – Published 15 May 1977
An article within the collection: The Work of Stephen Hawking in Physical Review
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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.

  • Received 4 October 1976

DOI:https://doi.org/10.1103/PhysRevD.15.2752

©1977 American Physical Society

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This article appears in the following collection:

The Work of Stephen Hawking in Physical Review

To mark the passing of Stephen Hawking, we gathered together his 55 papers in Physical Review D and Physical Review Letters. They probe the edges of space and time, from "Black holes and thermodynamics” to "Wave function of the Universe."

Authors & Affiliations

G. W. Gibbons* and S. W. Hawking

  • Department of Applied Mathematics and Theoretical Physics, University of Cambridge, England

  • *Present address: Max-Planck-Institute für Physik und Astrophysik, 8 München 40, Postfach 401212, West Germany. Telephone: 327001.

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Issue

Vol. 15, Iss. 10 — 15 May 1977

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