Anisotropic Stars II : Stability

TL;DR

This paper analyzes the stability of anisotropic stars under radial perturbations, extending Chandrasekhar's formalism to include anisotropy, and finds that tangential pressure enhances stability, allowing for smaller adiabatic indices.

Contribution

It extends the stability analysis of self-gravitating spheres to anisotropic cases using a generalized Chandrasekhar formalism in general relativity.

Findings

Anisotropic spheres are more stable when tangential pressure exceeds radial pressure.

Stability is achieved at smaller adiabatic indices compared to isotropic models.

Both Newtonian and relativistic perturbation treatments are considered.

Abstract

We investigate the stability of self-gravitating spherically symmetric anisotropic spheres under radial perturbations. We consider both the Newtonian and the full general-relativistic perturbation treatment. In the general-relativistic case, we extend the variational formalism for spheres with isotropic pressure developed by Chandrasekhar. We find that, in general, when the tangential pressure is greater than the radial pressure, the stability of the anisotropic sphere is enhanced when compared to isotropic configurations. In particular, anisotropic spheres are found to be stable for smaller values of the adiabatic index $\gamma$.