A diffusion process in curved space-time

Details A diffusion process in curved space-time A diffusion process in curved space-time

Jul 2004

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2004jmp....45.2744d&link_type=abstract

Journal of Mathematical Physics, Volume 45, Issue 7, pp. 2744-2760 (2004).

Mathematics

Mathematical Physics

21

Self-Gravitating Systems, Continuous Media And Classical Fields In Curved Spacetime, Special Relativity, Mathematical And Relativistic Aspects Of Cosmology

Scientific paper

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.

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