Cavity evolution in relativistic self-gravitating fluids

TL;DR

This paper investigates the evolution of cavities in relativistic fluids under a specific areal evolution condition, providing formal solutions and discussing boundary conditions relevant to astrophysical applications.

Contribution

It introduces a formalism for cavity evolution in relativistic fluids with solutions satisfying different boundary conditions, expanding understanding of such systems in astrophysics.

Findings

Solutions satisfying Darmois conditions are presented.

Some solutions involve shells requiring Israel conditions.

Potential applications to astrophysical scenarios are discussed.

Abstract

We consider the evolution of cavities within spherically symmetric relativistic fluids, under the assumption that proper radial distance between neighboring fluid elements remains constant during their evolution (purely areal evolution condition). The general formalism is deployed and solutions are presented. Some of them satisfy Darmois conditions whereas others present shells and must satisfy Israel conditions, on either one or both boundary surfaces. Prospective applications of these results to some astrophysical scenarios is suggested.