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A diffusion process in curved space-time. (English) Zbl 1071.82031

Summary: We construct a curved space–time generalization of the special relativistic Ornstein–Uhlenbeck Process. This is done by deriving a manifestly covariant Kolmogorov equation that describes diffusion in curved space–times. The simple case of diffusion in a spatially flat Friedmann–Robertson–Walker universe is then considered. It is proven that, at least in these space–times, Kolmogorov equation admits as possible solution a natural generalization of the flat space–time Jüttner equilibrium solution. The first correction to Jüttner’s distribution in a slowly expanding universe is also obtained explicitly.

MSC:

82B41 Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics
83C47 Methods of quantum field theory in general relativity and gravitational theory
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