Plausible families of compact objects with a Non Local Equation of State

TL;DR

This paper explores a family of anisotropic compact object models with non-local equations of state, analyzing their physical properties, stability, and how they evolve with a parameter, revealing tendencies towards increased stiffness and stability.

Contribution

It introduces a new algorithm to generate one-parameter families of interior solutions with non-local equations of state, analyzing their physical and stability properties.

Findings

Models tend to have stiffer equations of state as the parameter increases.

Total mass approaches half of the external radius with increasing parameter.

Models become more stable as the family parameter increases.

Abstract

We investigate the plausibility of some models emerging from an algorithm devised to generate a one-parameter family of interior solutions for the Einstein equations. It is explored how their physical variables change as the family-parameter varies. The models studied correspond to anisotropic spherical matter configurations having a non local equation of state. This particular type of equation of state with no causality problems provides, at a given point, the radial pressure not only as a function of the density but as a functional of the enclosed matter distribution. We have found that there are several model-independent tendencies as the parameter increases: the equation of state tends to be stiffer and the total mass becomes half of its external radius. Profiting from the concept of cracking of materials in General Relativity, we obtain that those models become more stable as the family parameter increases.