Stochastic Gravity: Theory and Applications

TL;DR

This paper introduces stochastic gravity, extending semiclassical gravity with noise-driven sources, and explores its theoretical foundations and three applications including metric perturbations, structure formation, and black hole backreaction.

Contribution

It presents the first comprehensive overview of stochastic gravity theory, including axiomatic and functional approaches, and demonstrates its applications in various gravitational phenomena.

Findings

Computed two-point correlation functions for metric perturbations.

Provided insights into structure formation via stochastic gravity.

Analyzed backreaction effects of Hawking radiation on black holes.

Abstract

Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein-Langevin equation, which has in addition sources due to the noise kernel.In the first part, we describe the fundamentals of this new theory via two approaches: the axiomatic and the functional. In the second part, we describe three applications of stochastic gravity theory. First, we consider metric perturbations in a Minkowski spacetime: we compute the two-point correlation functions for the linearized Einstein tensor and for the metric perturbations. Second, we discuss structure formation from the stochastic gravity viewpoint. Third, we discuss the backreaction of Hawking radiation in the gravitational background of a quasi-static black hole.