Black Hole Fluctuations and Backreaction in Stochastic Gravity

TL;DR

This paper develops a framework using influence functional formalism to analyze black hole backreaction and Hawking radiation as a stochastic process, connecting quantum field theory with gravitational dynamics.

Contribution

It introduces a novel approach to model black hole backreaction via the Einstein-Langevin equation, incorporating stochastic noise and dissipation from quantum effects.

Findings

Derivation of the Einstein-Langevin equation for black holes

Connection between noise and particle production differences

Framework applicable once accurate Green's functions are available

Abstract

We present a framework for analyzing black hole backreaction from the point of view of quantum open systems using influence functional formalism. We focus on the model of a black hole described by a radially perturbed quasi-static metric and Hawking radiation by a conformally coupled massless quantum scalar field. It is shown that the closed-time-path (CTP) effective action yields a non-local dissipation term as well as a stochastic noise term in the equation of motion, the Einstein-Langevin equation. Once the thermal Green's function in a Schwarzschild background becomes available to the required accuracy the strategy described here can be applied to obtain concrete results on backreaction. We also present an alternative derivation of the CTP effective action in terms of the Bogolyubov coefficients, thus making a connection with the interpretation of the noise term as measuring the difference in particle production in alternative histories.