Anisotropic compact star models in Karmarkar space time continuum

Abstract

In the present article, we have explored some new anisotropic compact star models by using embedded class one space time metric. We proceed our calculations by assuming a particular form of $g_{rr}$ metric potential and solved for the other metric $g_{tt}$ using Karmarkar condition. The matter density, radial pressure, tangential pressure, mass function, surface red-shift, anisotropy are all well behaved inside the fluid sphere. The solution satisfies all energy conditions i.e. strong energy condition, null energy condition, dominant energy condition and weak energy condition. The solution also satisfies the causality condition and can represent stable stellar fluid system as the adiabatic index $\varGamma > 4/3$ and the stability factor $-1\leq v_{t}^{2}-v_{r}^{2}\leq 0$ holds good inside the fluid sphere. We have framed our solution for two compact stars PSR J1614-2230 and SAX J1808.4-3658, which are well-behaved in all respects. The mass and radius of the compact stars PSR J1614-2230 and SAXJ1808.4-3658, obtained from the models are very close to the observational data proposed by Gangopadhyay et al. (Mon. Not. R. Astron. Soc. 431:3216, 2013) and Bhattacharya (2001) respectively.