A Fluctuation Dissipation Relation for Relativistic stars

Abstract

A fluctuation-dissipation relation for perturbed configuration of a relativistic star is obtained. The stochastic fluctuations of the classical stress tensor comprising the matter content ( a perfect fluid) of the relativistic star, act as the source in a classical Einstien-Langevin equation describing the system. We discuss the linear response of these fluctuations of the stress tensor and develop a fluctuation-dissipation relation from the first principles. Thus a system-bath separation in terms of spacetime metric and matter content is proposed, to study equilibrium and non equilibrium statistical properties for a relativistic star. This is not derived from or related to the scalar fields or quantum stress tensors and their fluctuations, as is usually the case for semiclassical stochastic gravity.