Separating expansion from contraction and generalizing TOV condition in spherically symmetric models with pressure

TL;DR

This paper develops a gauge-invariant framework to distinguish expanding and collapsing regions in spherically symmetric models with pressure, generalizing the TOV condition and applying it to Lambda-CDM models.

Contribution

It introduces a new gauge-invariant condition that separates expansion from contraction and generalizes the TOV equilibrium condition in pressure-supported spherical models.

Findings

Derived gauge-invariant conditions for dividing shells.

Generalized TOV condition incorporating pressure effects.

Applied framework to Lambda-CDM models.

Abstract

We investigate spherically symmetric solutions with pressure and discuss the existence of a dividing shell separating expanding and collapsing regions. We perform a 3+1 splitting and obtain gauge invariant conditions relating not only the intrinsic spatial curvature of the shells to the ADM mass, but also a function of the pressure which we introduce that generalises the Tolman-Oppenheimer-Volkoff equilibrium condition. We consider the particular case of a Lema\^itre-Tolman dust models with a cosmological constant (a $\Lambda$-CDM model) as an example of our results.