On the stability of the shear-free condition

TL;DR

This paper investigates the stability of the shear-free condition in spherically symmetric anisotropic, viscous fluids, revealing conditions under which shear-free states can become unstable, especially in geodesic fluids.

Contribution

It derives the evolution equation for shear in anisotropic viscous fluids and analyzes the stability of shear-free conditions, including specific cases like geodesic fluids.

Findings

Shear-free condition may be unstable in geodesic fluids.

Departure from shear-free state is influenced by expansion scalar and pressure anisotropy.

Stability depends on scalar functions related to anisotropy, viscosity, and inhomogeneity.

Abstract

The evolution equation for the shear is reobtained for a spherically symmetric anisotropic, viscous dissipative fluid distribution, which allows us to investigate conditions for the stability of the shear-free condition. The specific case of geodesic fluids is considered in detail, showing that the shear-free condition, in this particular case, may be unstable, the departure from the shear-free condition being controlled by the expansion scalar and a single scalar function defined in terms of the anisotropy of the pressure, the shear viscosity and the Weyl tensor or, alternatively, in terms of the anisotropy of the pressure, the dissipative variables and the energy density inhomogeneity.