Expansion-Free Cavity Evolution: Some exact Analytical Models

TL;DR

This paper presents new exact analytical models of spherically symmetric anisotropic fluid distributions with vacuum cavities, evolving under zero expansion, including solutions with and without thin shells, to describe post-explosion cavity evolution.

Contribution

It introduces novel exact solutions for cavity evolution under zero expansion, expanding previous models by considering different boundary conditions and shell configurations.

Findings

Derived solutions satisfying Darmois junction conditions

Models include configurations with thin shells at boundaries

Solutions describe evolution after a central explosion

Abstract

We consider spherically symmetric distributions of anisotropic fluids with a central vacuum cavity, evolving under the condition of vanishing expansion scalar. Some analytical solutions are found satisfying Darmois junction conditions on both delimiting boundary surfaces, while some others require the presence of thin shells on either (or both) boundary surfaces. The solutions here obtained model the evolution of the vacuum cavity and the surrounding fluid distribution, emerging after a central explosion. This study complements a previously published work where modeling of the evolution of such kind of systems was achieved through a different kinematical condition.