Cracking and Stability of Non-Rotating Relativistic Spheres with Anisotropic Internal Stresses

TL;DR

This paper investigates how anisotropic internal stresses affect the stability of static, uncharged relativistic spheres, highlighting the importance of pressure anisotropy profiles in determining stable and unstable regions.

Contribution

It introduces a method to analyze stability based on radial anisotropy profiles and examines stability regions in known relativistic star models.

Findings

Pressure anisotropy influences stellar stability.

Radial anisotropy profiles can identify stable and unstable regions.

Application to known models shows specific stability patterns.

Abstract

The stability of static uncharged spheres with anisotropic internal stresses is studied in general relativity. It has been noticed that pressure anisotropy plays an important role for stability of stellar structure. It is shown that radial profile of the stress anisotropy can be considered to decide potentially stable/unstable regions. Finally, pontentially stable/unstable regions of two known models of relativistic star have been examined.