Statistical mechanics in a conformally static setting. II

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Abstract
This paper examines the statistical mechanics of a collection of N identical, classical point masses, which interact relativistically via a simple scalar field in a conformally static background geometry. The model system considered here should be representative of any system in which the particle and field equations are both linear. Attention focuses first upon the formulation of exact equations for the evolution of appropriately defined reduced distribution functions and the interpretation of these relations. In particular, a projection operator formalism is used to derive exact coupled equations for the evolution of the irreducible one-particle and one-oscillator distributions, which contain no explicit reference to more complicated particle–oscillator correlation functions. Attention focuses also upon the issue of how the analysis would be further complicated by allowing for nonlinear effects, e.g., in the particle equations of motion. The subtleties that arise in this case serve to indicate the limitations of the kinetic theory of self-gravitating systems developed by Israel and Kandrup, which entails the consideration of particle and field equations linearized about some (possibly highly nontrivial!) background solution.