Anisotropic generalization of well-known solutions describing relativistic self-gravitating fluid systems: An algorithm

TL;DR

This paper introduces an algorithm to extend well-known isotropic fluid sphere solutions in Einstein's equations to anisotropic cases, enabling more realistic modeling of relativistic stars with anisotropic pressures.

Contribution

The paper presents a novel algorithm that generalizes existing solutions to Einstein's equations for relativistic fluid spheres by incorporating anisotropic pressures.

Findings

Generated new anisotropic solutions from known isotropic ones.

Demonstrated physical viability of a specific anisotropic solution.

Analyzed the impact of anisotropy on pulsar properties.

Abstract

We present an algorithm to generalize a plethora of well-known solutions to Einstein field equations describing spherically symmetric relativistic fluid spheres by relaxing the pressure isotropy condition on the system. By suitably fixing the model parameters in our formulation, we generate closed-form solutions which may be treated as anisotropic generalization of a large class of solutions describing isotropic fluid spheres. From the resultant solutions, a particular solution is taken up to show its physical acceptability. Making use of the current estimate of mass and radius of a known pulsar, the effects of anisotropic stress on the gross physical behaviour of a relativistic compact star is also highlighted.