Separating expansion from contraction in spherically symmetric models with a perfect-fluid: Generalization of the Tolman-Oppenheimer-Volkoff condition and application to models with a cosmological constant

TL;DR

This paper develops gauge-invariant conditions to identify a dividing shell in spherically symmetric perfect-fluid spacetimes, generalizing the TOV condition, and applies it to models with a cosmological constant, enhancing understanding of cosmic structure boundaries.

Contribution

It introduces a generalized TOV-like condition for separating expanding and collapsing regions in spherically symmetric perfect-fluid models, with applications to b5-CDM and core models.

Findings

Conditions successfully identify dividing shells in models

Application to b5-CDM with cosmological constant demonstrates practical relevance

Models show local fitting of dividing shells to theoretical criteria

Abstract

We investigate spherically symmetric perfect-fluid spacetimes and discuss the existence and stability of a dividing shell separating expanding and collapsing regions. We perform a 3+1 splitting and obtain gauge invariant conditions relating the intrinsic spatial curvature of the shells to the Misner-Sharp mass and to a function of the pressure that we introduce and that generalizes the Tolman-Oppenheimer-Volkoff equilibrium condition. We find that surfaces fulfilling those two conditions fit, locally, the requirements of a dividing shell and we argue that cosmological initial conditions should allow its global validity. We analyze the particular cases of the Lema\^itre-Tolman-Bondi dust models with a cosmological constant as an example of a cold dark matter model with a cosmological constant (\Lambda-CDM) and its generalization to contain a central perfect-fluid core. These models provide simple, but physically interesting illustrations of our results.