Diffusion in Curved Spacetimes

Abstract

Using simple kinematical arguments, we derive the Fokker-Planck equation for diffusion processes in curved spacetimes. In the case of Brownian motion, it coincides with Eckart's relativistic heat equation (albeit in a simpler form), and therefore provides a microscopic justification for his phenomenological heat-flux ansatz. Furthermore, we obtain the small-time asymptotic expansion of the mean square displacement of Brownian motion in static spacetimes. Beyond general relativity itself, this result has potential applications in analogue gravitational systems.

14 pages, substantially revised version

References in corpus (2)

• Relativistic Brownian Motion
• Experimental demonstration of the supersonic-subsonic bifurcation in the circular jump: A hydrodynamic white hole

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