Anisotropic compact star model satisfying Karmarkar conditions

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 in Proc. Indian Acad. Sci. 27:56, 1948) to derive the expressions for star density, the radial and tangential pressures in terms of the constants $A$, $B$, a parameter ‘$a$’ 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 $a=0.5$.