Shearing Expansion-free Spherical Anisotropic Fluid Evolution

TL;DR

This paper systematically studies the evolution of spherically symmetric, expansion-free, dissipative anisotropic fluids, deriving field equations, junction conditions, and analyzing physical implications such as cavity formation.

Contribution

It provides a comprehensive set of equations and conditions for expansion-free anisotropic fluids, including the integration of the expansionfree condition and analysis of physical meanings.

Findings

Cavity formation is inevitable in expansionfree evolution.

The Skripkin model is recovered in the nondissipative case.

Two definitions of radial velocity are discussed for physical interpretation.

Abstract

Spherically symmetric expansionfree distributions are systematically studied. The whole set of field equations and junction conditions are presented for a general distribution of dissipative anisotropic fluid (principal stresses unequal), and the expansionfree condition is integrated. In order to understand the physical meaning of expansionfree motion, two different definitions for the radial velocity of a fluid element are discussed. It is shown that the appearance of a cavity is inevitable in the expansionfree evolution. The nondissipative case is considered in detail and the Skripkin model is recovered.