Stochastic Gravity: Theory and Applications

TL;DR

This paper introduces stochastic gravity, extending semiclassical gravity with noise-induced metric fluctuations, and explores its applications in spacetime stability, structure formation, and black hole backreaction.

Contribution

It develops the foundational theory of stochastic gravity and demonstrates its use in analyzing metric perturbations, structure formation, and black hole evaporation effects.

Findings

Minkowski spacetime is stable under stochastic gravity.

Metric perturbations exhibit specific two-point correlation functions.

Black hole horizon fluctuations are characterized by stochastic effects.

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, compute the two-point correlation functions of these perturbations and prove that Minkowski spacetime is a stable solution of semiclassical gravity. Second, we discuss structure formation from the stochastic gravity viewpoint. Third, we discuss the backreaction of Hawking radiation in the gravitational background of a black hole and describe the metric fluctuations near the event horizon of an evaporating black hole