Acceptability Conditions and Relativistic Anisotropic Generalized Polytropes

TL;DR

This study investigates the physical acceptability of anisotropic polytropic models in General Relativity, identifying parameter conditions for stable, realistic compact objects with specific anisotropic features.

Contribution

It introduces a generalized polytropic equation of state with anisotropy, analyzing stability and acceptability conditions through extensive modeling and simulations.

Findings

Polytropes based on total energy density are more stable.

Small positive anisotropies yield acceptable models.

Tangential pressure dominance enhances acceptability.

Abstract

This paper explored the physical acceptability conditions for anisotropic matter configurations in General Relativity. The study considered a generalized polytropic equation of state $P=\kappa {\rho}^{\gamma}+\alpha \rho -\beta$ for a heuristic anisotropy. We integrated the corresponding Lane-Emden equation for several hundred models and found the parameter-space portion ensuring the configurations' acceptability. Polytrope based on the total energy density are more stable than those with baryonic density, and small positive local anisotropies produce acceptable models. We also found that polytropic configurations where tangential pressures are greater than radial ones are also more acceptable. Finally, convective disturbances do not generate cracking instabilities. Several models emerging from our simulations could represent candidate of astrophysical compact objects.