Action integrals and partition functions in quantum gravity

Journal Article · Sun May 15 00:00:00 EDT 1977 · Phys. Rev., D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.15.2752· OSTI ID:7258722

Gibbons, G W; Hawking, S W

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.

• Research Organization: Department of Applied Mathematics and Theoretical Physics, University of Cambridge, England
• OSTI ID: 7258722
• Journal Information: Phys. Rev., D; (United States), Vol. 15:10
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
GRAVITATIONAL FIELDS
PARTITION FUNCTIONS
SPACE-TIME
ANGULAR MOMENTUM
BLACK HOLES
DE SITTER GROUP
EINSTEIN FIELD EQUATIONS
ENTROPY
METRICS
STARS
THERMODYNAMICS
VACUUM STATES
EQUATIONS
FIELD EQUATIONS
FUNCTIONS
LIE GROUPS
PHYSICAL PROPERTIES
SYMMETRY GROUPS
THERMODYNAMIC PROPERTIES
657003* - Theoretical & Mathematical Physics- Relativity & Gravitation