Induced Perturbations and Stochastic effects in Collapsing Relativistic Stars

TL;DR

This paper introduces a modified model for relativistic stars incorporating stress tensor fluctuations as stochastic sources in Einstein's equations, exploring their impact on star dynamics and potential links to fluctuation-dissipation principles in curved spacetime.

Contribution

It presents a novel stochastic framework for relativistic star modeling by integrating stress tensor fluctuations into Einstein's equations.

Findings

Stress tensor fluctuations act as stochastic sources in Einstein's equations.

Fluctuations influence the statistical properties of the star's fluid and metric.

Discussion of potential fluctuation-dissipation relations in curved spacetime.

Abstract

We present a modified model for relativistic stars which are usually represented by perfect fluids. Fluctuations of the stress tensor act as source in the modified Einstein's equation, giving it a Langevin equation form. The occurrence of these fluctuations is attributed to the microphysics of the interior of the star and their contribution to statistical properties of the fluid and the induced metric perturbations are argued to be of significance. We also discuss the response of fluctuations of the stress tensor in the interior of the star and possible developments towards fluctuation-dissipation theorem issues in curved spacetime. The aim and further directions of research envisioned are discussed intermittently throughout the manuscript and towards the end.