Anisotropic Compact Star Model Satisfying Karmarkar Conditions

TL;DR

This paper introduces a new anisotropic compact star model satisfying Karmarkar conditions, providing physically viable solutions that match observed star data and fulfill key physical conditions.

Contribution

The study presents a novel anisotropic star model based on Karmarkar conditions, with solutions that are physically consistent and applicable to observed compact stars.

Findings

Model satisfies regularity, energy, and causality conditions.

Predictions closely match observed data for multiple star candidates.

Provides a mathematically well-behaved solution for anisotropic compact stars.

Abstract

A new class of solutions describing the composition of compact stars has been proposed, assuming that the fluid distribution inside the star is anisotropic. This is achieved by assuming the appropriate metric potential and then solving Einstein's field equations using Karmarkar conditions [Karmarkar K. R., \textit{Proc. Indian Acad. Sci.} \textbf{27} (1948) 56] to derive the expressions for star density, the radial and tangential pressures in terms of the constants A, B, a paramter `a' and the curvature parameter R. The equations thus obtained have been passed through rigorous conditional analysis. It is further shown that the model is physically viable and mathematically well-behaved, fulfilling the requisite conditions viz., regularity condition, strong energy condition, causality condition, etc. Observed star candidates including EXO 1785-248, SMC X-1, SAXJ1808.43658(SS2), HER X-1, 4U 1538-52, Cen X-3 and LMC X-4 were found to conform to a good approximation through the outcome of this model for a=0.5.