Sound Speeds, Cracking and Stability of Self-Gravitating Anisotropic Compact Objects

TL;DR

This paper investigates how density fluctuations and local anisotropy affect the stability of self-gravitating compact objects in general relativity, using the concept of cracking to identify potentially unstable regions based on sound speed differences.

Contribution

It introduces an approach using sound speed anisotropy and cracking to analyze the stability of anisotropic compact objects in general relativity.

Findings

Unstable regions can be identified by differences in tangential and radial sound speeds.

Potential instability occurs when tangential sound speed exceeds radial sound speed.

Cracking provides an effective method to assess local stability in anisotropic matter configurations.

Abstract

Using the the concept of cracking we explore the influence of density fluctuations and local anisotropy have on the stability of local and non-local anisotropic matter configurations in general relativity. This concept, conceived to describe the behaviour of a fluid distribution just after its departure from equilibrium, provides an alternative approach to consider the stability of selfgravitating compact objects. We show that potentially unstable regions within a configuration can be identify as a function of the difference of propagations of sound along tangential and radial directions. In fact, it is found that these regions could occur when, at particular point within the distribution, the tangential speed of sound is greater than radial one.