Microcanonical functional integral for the gravitational field

Journal Article · Mon Feb 15 04:00:00 EST 1993 · Physical Review, D (Particles Fields); (United States)

DOI:https://doi.org/10.1103/PhysRevD.47.1420· OSTI ID:6993692

Brown, J D; York, Jr, J W ^[1]

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1. Institute of Field Physics and Theoretical Astrophysics and Relativity Group, Department of Physics and Astronomy, The University of North Carolina, Chapel Hill, North Carolina 27599-3255 (United States)

The gravitational field in a spatially finite region is described as a microcanonical system. The density of states [nu] is expressed formally as a functional integral over Lorentzian metrics and is a functional of the geometrical boundary data that are fixed in the corresponding action. These boundary data are the thermodynamical extensive variables, including the energy and angular momentum of the system. When the boundary data are chosen such that the system is described semiclassically by [ital any] real stationary axisymmetric black hole, then in this same approximation ln[nu] is shown to equal 1/4 the area of the black-hole event horizon. The canonical and grand canonical partition functions are obtained by integral transforms of [nu] that lead to imaginary-time'' functional integrals. A general form of the first law of thermodynamics for stationary black holes is derived. For the simpler case of nonrelativistic mechanics, the density of states is expressed as a real-time functional integral and then used to deduce Feynman's imaginary-time functional integral for the canonical partition function.

• OSTI ID: 6993692
• Journal Information: Physical Review, D (Particles Fields); (United States), Journal Name: Physical Review, D (Particles Fields); (United States) Vol. 47:4; ISSN 0556-2821; ISSN PRVDAQ
• Country of Publication: United States
• Language: English

Related Subjects

661100 -- Classical & Quantum Mechanics-- (1992-)
662110* -- General Theory of Particles & Fields-- Theory of Fields & Strings-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANGULAR MOMENTUM
BLACK HOLES
BOUNDARY CONDITIONS
ENERGY LEVELS
ENTROPY
FEYNMAN PATH INTEGRAL
FUNCTIONAL ANALYSIS
FUNCTIONS
GRAVITATIONAL FIELDS
INTEGRALS
MATHEMATICS
METRICS
PARTITION FUNCTIONS
PHYSICAL PROPERTIES
SEMICLASSICAL APPROXIMATION
THERMODYNAMIC PROPERTIES