Stochastic semiclassical gravity

TL;DR

This paper develops a stochastic extension of semiclassical gravity, deriving the Einstein-Langevin equation from influence functionals and exploring fluctuation-dissipation relations and particle creation in stationary spacetimes.

Contribution

It formally derives the Einstein-Langevin equation using influence functional methods and analyzes fluctuation effects in stationary and conformally stationary backgrounds.

Findings

Fluctuation-dissipation relations are established for specific spacetimes.

Particle creation is linked to vacuum stress-energy fluctuations.

Stochastic metric fluctuations enhance particle creation.

Abstract

In the first part of this paper, we show that the semiclassical Einstein-Langevin equation, introduced in the framework of a stochastic generalization of semiclassical gravity to describe the back reaction of matter stress-energy fluctuations, can be formally derived from a functional method based on the influence functional of Feynman and Vernon. In the second part, we derive a number of results for background solutions of semiclassical gravity consisting of stationary and conformally stationary spacetimes and scalar fields in thermal equilibrium states. For these cases, fluctuation-dissipation relations are derived. We also show that particle creation is related to the vacuum stress-energy fluctuations and that it is enhanced by the presence of stochastic metric fluctuations.