Relativistic compact stars in Tolman spacetime via an anisotropic approach

TL;DR

This paper develops a singularity-free, anisotropic stellar model within Einstein's general relativity using Tolman's ansatz, fitting observed data of a specific compact star and verifying physical and stability conditions.

Contribution

It presents a new exact solution for anisotropic compact stars based on Tolman's ansatz, consistent with physical and observational constraints.

Findings

Model satisfies all physical criteria for realistic compact stars.

Energy conditions are verified graphically.

Stability of the model is confirmed through various tests.

Abstract

In this present work, we have obtained a singularity-free spherically symmetric stellar model with anisotropic pressure in the background of Einstein's general theory of relativity. The Einstein's field equations have been solved by exploiting Tolman {\em ansatz} [Richard C Tolman, Phys. Rev. 55:364, 1939] in $(3+1)$-dimensional space-time. Using observed values of mass and radius of the compact star PSR J1903+327, we have calculated the numerical values of all the constants from the boundary conditions. All the physical characteristics of the proposed model have been discussed both analytically and graphically. The new exact solution satisfies all the physical criteria for a realistic compact star. The matter variables are regular and well behaved throughout the stellar structure. Constraints on model parameters have been obtained. All the energy conditions are verified with the help of graphical representation. The stability condition of the present model has been described through different testings.