Spherically symmetric models: separating expansion from contraction in models with anisotropic pressures

TL;DR

This paper explores conditions for a dividing shell in spherically symmetric spacetimes with anisotropic fluids, balancing expansion and contraction through pressure gradients and mass distribution, generalizing equilibrium conditions.

Contribution

It introduces a generalized equilibrium condition for separating expanding and collapsing regions in anisotropic fluid models, incorporating both local and non-local effects.

Findings

Derived a relation involving pressure gradients and mass for the dividing shell.

Identified a generalization of the Tolman-Oppenheimer-Volkoff equilibrium.

Presented a dust and radiation solution illustrating the theoretical results.

Abstract

We investigate spherically symmetric spacetimes with an anisotropic fluid and discuss the existence and stability of a dividing shell separating expanding and collapsing regions. We find that the dividing shell is defined by a relation between the pressure gradients, both isotropic and anisotropic, and the strength of the fields induced by the Misner-Sharpe mass inside the separating shell and by the pressure fluxes. This balance is a generalization of the Tolman-Oppenheimer- Volkoff equilibrium condition which defines a local equilibrium condition, but conveys also a non- local character given the definition of the Misner-Sharpe mass. We present a particular solution with dust and radiation that provides an illustration of our results.