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

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.

12 pages, no figures. Presented at IARD 2010 Conference, Hualien, Taiwan (May 2010). Proceedings to appear in Journal of Physics: Conference Series

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