Cracking isotropic and anisotropic relativistic spheres

TL;DR

This paper investigates how density fluctuations affect the stability of relativistic fluid spheres, extending the concept of cracking to both isotropic and anisotropic models, and analyzing their potential for instability.

Contribution

It refines the concept of cracking by considering local density fluctuations and their impact on relativistic fluid spheres with barotropic equations of state.

Findings

Both isotropic and anisotropic models can exhibit cracking.

Some anisotropic models previously prone to cracking become stable.

The approach provides insights into potential instabilities and evolution of relativistic fluids.

Abstract

We explore the influence of density fluctuations on isotropic and anisotropic configurations, extending the concept of cracking for general relativistic fluid spheres. This concept, conceived to describe the behaviour of anisotropic matter distributions just after its departure from equilibrium, could provide some insight on potential instabilities and future evolution of relativistic fluids. We have refined the idea of cracking, considering local fluctuations --represented by any function of compact support defined in a closed interval-- and their effect on the state variables and their gradients through "barotropic" equations of state, $P = P(\rho)$ and $P_{\perp}= P_{\perp}(\rho)$. Under this approach it is found that both isotropic and anisotropic models could exhibit cracking (or overturning), and that previously crackable anisotropic models become uncrackable.