Acceptability Conditions and Relativistic Barotropic Equations of State

TL;DR

This paper presents an algorithm to generate exact anisotropic solutions from barotropic equations of state, illustrating it with generalized polytropic models that satisfy physical acceptability and avoid sound velocity singularities.

Contribution

It introduces a novel algorithm for constructing anisotropic solutions from barotropic EoS and develops generalized polytropic models that are physically meaningful and free from sound velocity issues.

Findings

Developed an algorithm for anisotropic solution generation.

Generalized polytropic models satisfy physical acceptability.

Avoidance of sound velocity singularities in generalized models.

Abstract

We sketch an algorithm to generate exact anisotropic solutions starting from a barotropic EoS and setting an ansatz on the metric functions. To illustrate the method, we use a generalization of the polytropic equation of state consisting of a combination of a polytrope plus a linear term. Based on this generalization, we develop two models which are not deprived of physical meaning as well as fulfilling the stringent criteria of physical acceptability conditions. We also show that some relativistic anisotropic polytropic models may have singular tangential sound velocity for polytropic indexes greater than one. This happens in anisotropic matter configurations when the polytropic equation of state is implemented together with an ansatz on the metric functions. The generalized polytropic equation of state is free from this pathology in the tangential sound velocity.