An analytical anisotropic compact stellar model of embedding class I

TL;DR

This paper develops an analytical model of anisotropic compact stars satisfying Einstein's field equations with Karmarkar embedding, matching Schwarzschild exterior, and analyzing physical and stability properties for observed pulsars.

Contribution

It presents a new anisotropic stellar model satisfying embedding class I conditions with detailed physical and stability analysis, matching observed pulsar data.

Findings

Model satisfies physical and stability conditions.

Mass-radius relationship aligns with observed pulsars.

Moment of inertia profile agrees with theoretical expectations.

Abstract

A class of solutions of Einstein field equations satisfying Karmarkar embedding condition is presented which could describe static, spherical fluid configurations, and could serve as models for compact stars. The fluid under consideration has unequal principal stresses i.e. fluid is locally anisotropic. A certain physically motivated geometry of metric potential has been chosen and codependency of the metric potentials outlines the formation of the model. The exterior spacetime is assumed as described by the exterior Schwarzschild solution. The smooth matching of the interior to the exterior Schwarzschild spacetime metric across the boundary and the condition that radial pressure is zero across the boundary lead us to determine the model parameters. Physical requirements and stability analysis of the model demanded for a physically realistic star are satisfied. The developed model has been investigated graphically by exploring data from some of the known compact objects. The mass-radius (M-R) relationship that shows the maximum mass admissible for observed pulsars for a given surface density has also been investigated. Moreover, the physical profile of the moment of inertia (I) thus obtained from the solutions is confirmed by the Bejger-Haensel concept.