A new model for spherically symmetric anisotropic compact star

TL;DR

This paper introduces a new anisotropic solution to Einstein's field equations for modeling realistic compact stars like Her X-1 and RXJ 1856-37, analyzing their physical properties and stability.

Contribution

The paper presents a novel anisotropic model for compact stars based on embedding class one metric, with detailed numerical analysis and comparison to observed objects.

Findings

Density and pressure depend on anisotropic factor

Model matches observed properties of specific compact stars

Stability conditions are discussed in the context of anisotropy

Abstract

In this article we obtain a new anisotropic solution for Einstein's field equation of embedding class one metric. The solution is representing the realistic objects such as $Her~X-1$ and $RXJ~1856-37$. We perform detailed investigation of both objects by solving numerically the Einstein field equations under with anisotropic pressure. The physical features of the parameters depend on the anisotropic factor i.e. if anisotropy is zero everywhere inside the star then the density and pressures will become zero and metric turns out to be flat. We report our results and compare with the above mentioned two compact objects on a number of key aspects: the central density, the surface density onset and the critical scaling behavior, the effective mass and radius ratio, the anisotropization with isotropic initial conditions, adiabatic index and red shift. Along with this we have also made a comparison between the classical limit and theoretical model treatment of the compact objects. Finally we discuss the implications of our findings for the stability condition in relativistic compact star.