Analytical study of anisotropic compact star models

TL;DR

This paper develops a systematic method for generating and analyzing anisotropic relativistic star models based on energy density and radial pressure, simplifying the process of verifying physical realism.

Contribution

It introduces a new formalism for constructing anisotropic star solutions and demonstrates its application with models having linear equations of state.

Findings

Solutions depend on three free constants.

Reduced the need for multiple inequalities to verify physical conditions.

Applied method to various known models.

Abstract

A simple classification is given of the anisotropic relativistic star models, resembling the one of charged isotropic solutions. On the ground of this database, and taking into account the conditions for physically realistic star models, a method is proposed for generating all such solutions. It is based on the energy density and the radial pressure as seeding functions. Numerous relations between the realistic conditions are found and the need for a graphic proof is reduced just to one pair of inequalities. This general formalism is illustrated with an example of a class of solutions with linear equation of state and simple energy density. It is found that the solutions depend on three free constants and concrete examples are given. Some other popular models are studied with the same method.