Curvature Diffusions in General Relativity

TL;DR

This paper introduces a family of curvature-dependent covariant diffusions on Lorentz manifolds, analyzing their behavior especially on Robertson-Walker and Einstein-de Sitter-like spacetimes, linking diffusion effects to spacetime curvature.

Contribution

It defines curvature-driven covariant diffusions on Lorentz manifolds and studies their asymptotic behavior in specific cosmological models, a novel approach in stochastic general relativity.

Findings

Diffusions are influenced by spacetime curvature.

Asymptotic behavior analyzed for Robertson-Walker and Einstein-de Sitter spacetimes.

Provides insights into particle interactions with curved spacetime.

Abstract

We define and study on Lorentz manifolds a family of covariant diffusions in which the quadratic variation is locally determined by the curvature. This allows the interpretation of the diffusion effect on a particle by its interaction with the ambient space-time. We will focus on the case of warped products, especially Robertson-Walker manifolds, and analyse their asymptotic behaviour in the case of Einstein-de Sitter-like manifolds.