A linear response relation for perturbed Einstein's equations with a Langevin source: applications to perturbations in compact stars

Abstract

A new linear response relation for the perturbed Einstein's equation is introduced. We give the idea of considering the metric perturbations as a linear response to the fluid (matter) perturbations in strong gravity regions. This can be meaningful when the perturbations in the system are driven by sources internal to the fluid (matter) in the relativistic star. The aim is to study the strong regions embedding the compact matter like that of the internal structure of relativistic stars, with this new framework. The formulations are specifically done to address the generalized stochastic perturbations which can arise in the dense matter at intermediate scales. These internally sourced perturbations lead to the possibility of equilibrium and non-equilibrium (dynamical or thermal) statistical analysis for the properties of compact matter at the sub-hydro mesoscopic scales, which are yet unexplored. A general relativistic Langevin formalism, defining a random driving source and its analytical solutions for a simple example are given. With a first principles approach, this new framework and its potential towards building up a theme of research in asteroseismology is discussed.