Formalism for stochastic perturbations and analysis in relativistic stars

TL;DR

This paper develops a formalism for analyzing stochastic perturbations in relativistic stars, deriving fluctuation-dissipation relations and extending to perturbed TOV equations, offering new insights into dense matter equations of state.

Contribution

It introduces a novel stochastic perturbation framework for relativistic stars, including fluctuation-dissipation relations and extensions to TOV equations, advancing non-equilibrium statistical analysis in astrophysics.

Findings

Derived fluctuation-dissipation relation for spherical stars

Obtained a constant dissipation coefficient without delta-correlated noise

Extended formalism to stochastic TOV equations with pressure perturbations

Abstract

Perturbed Einstein's equations with a linear response relation and a stochastic source, applicable to a relativistic star model are worked out . These perturbations which are stochastic in nature, are of significance for building a non-equilibrium statistical theory in connections with relativistic astrophysics. A fluctuation dissipation relation for a spherically symmetric star in its simplest form is obtained. The FD relation shows how the random velocity fluctuations in the background of the unperturbed star can dissipate into Lagrangian displacement of fluid trajectories of the dense matter. Interestingly in a simple way, a constant (in time) coefficient of dissipation is obtained without a delta correlated noise. This formalism is also extended for perturbed TOV equations which have a stochastic contribution, and show up in terms of the effective or root mean square pressure perturbations. Such contributions can shed light on new ways of analysing the equation of state for dense matter. One may obtain contributions of first and second order in the equation of state using this stochastic approach.