Random Walks in Curved Spacetimes
Résumé
We introduce the master equation describing random walks in curved spacetimes, and derive the corresponding Fokker-Planck equation. By a combination of redshift and spatial curvature effects, the latter brings about corrections to Einstein's square-root law for the RMS displacement. We compute the first correction explicitely, and evaluate it for the cases of the Schwarzschild constant-density star, the Kerr black hole and the Friedmann-Robertson-Walker universe: in the first two cases, gravity turns out to enhance diffusion at small times, while in the third case the sign of the correction depends on the curvature of space and grows quadratically with the cosmological redshift.