Anisotropic static solutions in modelling highly compact bodies

TL;DR

This paper derives exact solutions to Einstein's field equations for anisotropic spheres, broadening the scope of models for highly compact astrophysical bodies with diverse energy density profiles.

Contribution

It introduces new classes of anisotropic solutions that include physically realistic energy density distributions, extending previous models to more general cases.

Findings

Two classes of solutions with different energy density behaviors.

Models include the limiting case of  energy density.

Solutions accommodate both increasing and decreasing energy density profiles.

Abstract

Einstein field equations for anisotropic spheres are solved and exact interior solutions obtained. This paper extends earlier treatments to include anisotropic models which accommodate a wider variety of physically viable energy densities. Two classes of solutions are possible. The first class contains the limiting case $\mu\propto r^{-2}$ for the energy density which arises in many astrophysical applications. In the second class the singularity at the center of the star is not present in the energy density. The models presented in this paper allow for increasing and decreasing profiles in the behavior of the energy density.