Correlations of the stress-energy tensor in AdS spaces via the generalized zeta-function method

TL;DR

This paper computes the vacuum expectation values of stress-energy tensor correlations in AdS spaces using a generalized zeta-function method, providing insights into quantum fluctuations relevant for stochastic gravity.

Contribution

It introduces a novel application of the generalized zeta-function approach to calculate stress-energy correlators in AdS spaces, including analytic expressions for eigenmodes.

Findings

Derived explicit expressions for stress-energy tensor correlators.

Analyzed short and long distance behaviors of the correlators.

Facilitated stochastic gravity studies in AdS backgrounds.

Abstract

We calculate the vacuum expectation values of the stress-energy bitensor of a minimally coupled massless scalar field in anti-de Sitter (AdS) spaces. These correlators, also known as the noise kernel, act as sources in the Einstein-Langevin equations of stochastic gravity [1,2] which govern the induced metric fluctuations beyond the mean-field dynamics described by the semiclassical Einstein equations of semiclassical gravity. Because the AdS spaces are maximally symmetric the eigenmodes have analytic expressions which facilitate the computation of the zeta-function [3,4]. Upon taking the second functional variation of the generalized zeta function introduced in [5] we obtain the correlators of the stress tensor. Both the short and the long geodesic distance limits of the correlators are presented.