Stability of Anisotropic Cylinder with Zero Expansion

TL;DR

This paper investigates the stability of an anisotropic collapsing cylinder with zero expansion, analyzing how pressure anisotropy and energy density inhomogeneity influence its dynamical stability across different gravitational regimes.

Contribution

It introduces a perturbation scheme to study stability in Newtonian and post-Newtonian regimes for anisotropic cylinders with vacuum cavities.

Findings

Stability depends on pressure anisotropy and energy density inhomogeneity.

Stability is independent of fluid stiffness.

Vacuum cavity formation affects collapse dynamics.

Abstract

We study the dynamical instability of anisotropic collapsing cylinder with the expansion-free condition, which generates vacuum cavity within fluid distribution. The perturbation scheme is applied to distinguish Newtonian, post-Newtonian and post-post Newtonian terms, which are used for constructing dynamical equation at Newtonian and post-Newtonian regimes. We analyze the role of pressure anisotropy and energy density inhomogeneity on the stability of collapsing cylinder. It turns out that stability of the cylinder depends upon these physical properties of the fluid, not on the stiffness of the fluid.