Radial pulsations and stability of anisotropic stars with quasi-local equation of state

TL;DR

This paper investigates the stability and pulsation modes of anisotropic stars using a quasi-local equation of state, revealing how anisotropy influences stability thresholds and providing examples of stable configurations.

Contribution

It introduces a novel approach to modeling anisotropic stars with a quasi-local EoS and analyzes their stability and pulsation modes using standard methods.

Findings

Stable configurations with increasing core energy density are found.

Anisotropy raises the surface compactness threshold for stability.

Radial pulsation modes confirm the predicted stability limits.

Abstract

Quasi-local variables, i.e. quantities whose values can be derived from physics accessible within an arbitrarily small neighborhood of a spacetime point, are used to construct the equation of state (EoS) for the anisotropic fluid in the spherical symmetry. One parameter families of equilibrium solutions are obtained making it possible to assess stability properties by means of the standard M(R) method. Normal modes of radial pulsation are computed as well and are found to confirm the onset of instability as predicted by the M(R) method. As an example, a stable configuration with outwardly increasing energy density in the core is obtained with a simple quasi-local extension of the polytropic EoS. It is also found that the loss of stability occurs at higher surface compactness when the anisotropy of pressures is present.