Authors: Matteo Smerlak
Date: 17 Apr 2011
Abstract: 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 generates subleading 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 diverges at the Big Bang - unless space is flat.
© M. Vallisneri 2012 — last modified on 2010/01/29
Tantum in modicis, quantum in maximis