Separating expansion from contraction: generalized TOV condition, LTB models with pressure and $\Lambda$CDM

TL;DR

This paper develops a generalized TOV condition and gauge-invariant criteria for the existence of a dividing shell in spherically symmetric spacetimes with pressure, including LTB models with a cosmological constant, distinguishing expanding from collapsing regions.

Contribution

It introduces a pressure-dependent generalization of the TOV equilibrium condition and gauge-invariant criteria for separating expanding and collapsing regions in spherically symmetric models.

Findings

Derived gauge-invariant conditions relating curvature, mass, and pressure.

Applied the framework to mbda-CDM LTB models as an example.

Extended the understanding of shell dynamics in pressure-supported spacetimes.

Abstract

We discuss the existence of a dividing shell separating expanding and collapsing regions in spherically symmetric solutions with pressure. We 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, in the framework of a 3+1 spacetime splitting. We consider the particular case of a Lema\^itre-Tolman-Bondi dust models with a cosmological constant (a $\Lambda$-CDM model) as an example of our results.