Stability of spherically symmetric timelike thin-shells in general relativity with a variable equation of state

TL;DR

This paper investigates the stability of spherically symmetric timelike thin-shells in general relativity, considering a variable equation of state where pressure depends on surface density and radius, with applications to different spacetime configurations.

Contribution

It introduces a model with a variable equation of state for thin-shells and analyzes their stability in various spacetime scenarios, including non-identical clouds of strings and Minkowski-Schwarzschild connections.

Findings

Stability conditions depend on the variable equation of state.

Explicit stability analysis for shells connecting different spacetimes.

Application to specific spacetime configurations like clouds of strings and Schwarzschild.

Abstract

We study spherically symmetric timelike thin-shells in $3+1-$dimensional bulk spacetime with a variable equation of state for the fluid presented on the shell. In such a fluid the angular pressure $p$ is a function of both surface energy density $\sigma $ and the radius $R$ of the thin-shell. Explicit cases of the thin shells connecting two non-identical cloud of strings spacetimes and a flat Minkowski spacetime to the Schwarzschild metric are investigated.