Nonequilibrium statistical mechanics in the general theory of relativity. I. A general formalism

Journal Article · Sun Jan 01 04:00:00 EST 1984 · Ann. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1016/0003-4916(84)90080-0· OSTI ID:5144664

Israel, W; Kandrup, H E

This is the first in a series of papers, the overall objective of which is the formulation of a new covariant approach to nonequilibrium statistical mechanics in classical general relativity. The objecct here is the development of a tractable theory for self-gravitating systems. It is argued that the ''state'' of an N-particle system may be characterized by an N-particle distribution function, defined in an 8N-dimensional phase space, which satisfies a collection of N conservation equations. By mapping the true physics onto a fictitious ''background'' spacetime, which may be chosen to satisfy some ''average'' field equations, one then obtains a useful covariant notion of ''evolution'' in response to a fluctuating ''gravitational force.'' For many cases of practical interest, one may suppose (i) that these fluctuating forces satisfy linear field equations and (ii) that they may be modeled by a direct interaction. In this case, one can use a relativistic projection operator formalism to derive exact closed equations for the evolution of such objects as an appropriately defined reduced one-particle distribution function. By capturing, in a natural way, the notion of a dilute gas, or impulse, approximation, one is then led to a comparatively simple equation for the one-particle distribution. If, furthermore, one treats the effects of the fluctuating forces as ''localized'' in space and time, one obtains a tractable kinetic equation which reduces, in the Newtonian limit, to the stardard Landau equation.

• Research Organization: Department of Physics and Theoretical Physics Institute University of Alberta, Edmonton, Alberta, Canada T6G 2J1
• OSTI ID: 5144664
• Journal Information: Ann. Phys. (N.Y.); (United States), Journal Name: Ann. Phys. (N.Y.); (United States) Vol. 152:1; ISSN APNYA
• Country of Publication: United States
• Language: English

Related Subjects

657003* -- Theoretical & Mathematical Physics-- Relativity & Gravitation
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BOLTZMANN-VLASOV EQUATION
DIFFERENTIAL EQUATIONS
DISTRIBUTION FUNCTIONS
EQUATIONS
FIELD EQUATIONS
FIELD THEORIES
FUNCTIONS
GENERAL RELATIVITY THEORY
GRAVITATION
HAMILTONIANS
KINETIC EQUATIONS
MANY-BODY PROBLEM
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS
PHASE SPACE
PROJECTION OPERATORS
QUANTUM OPERATORS
SPACE
SPACE-TIME
STATISTICAL MECHANICS