Statistical mechanics of the gravitational field in a conformally static setting

Abstract

This paper formulates a statistical description of a collection of N identical classical particles that interact relativistically via linear fields in a fixed background space-time that admits a conformal timelike Killing field. Attention focuses upon the special cases of a simple scalar interaction and a linearized gravitation interaction which should suffice to model many systems of astrophysical interest. The fundamental object of the theory is a complicated distribution function that depends upon appropriate variables for both the particles and the fields. By assuming that, in a first approximation, this distribution factorizes into an infinite product of reduced distribution functions, one recovers the type of mean-field theory developed by such authors as Ipser and Thorne. Alternatively, one may derive various exact and approximate relations which contain information about the interparticle correlations.