Stellar model for anisotropic compact stars in Schwarzchild’s coordinates

Abstract

In this article, we have presented a completely new, well-behaved, physically acceptable and stable anisotropic fluid sphere model. For this purpose we have used a well-known Vaidya-Tikekar [J. Astrophys. Astron. 3, 325 (1982)] ansatz for metric potential ${g}_{rr}$ to generate the model. We have investigated the various physical aspects for our model such as energy density, pressure (radial as well as transverse), anisotropy factor, mass, compactness parameter, surface, and gravitational redshifts. Energy conditions, equilibrium, and stability analysis has been done using graphs. This ensured that our proposed solutions are well-behaved and hence represent physically acceptable models for anisotropic fluid spheres. For comparison with observational data we have considered the compact stars: Her X-1, $4\mathrm{U}1538\penalty1000-\hskip0pt52$, SAX $\mathrm{J}1808.4\penalty1000-\hskip0pt3658$, LMC X-4, SMC X-1, EXO $1785\penalty1000-\hskip0pt248$, Cen X-3, 4U $1820\penalty1000-\hskip0pt30$, PSR $\mathrm{J}1903+327$, 4U $1608\penalty1000-\hskip0pt52$, Vela X-1, PSR $\mathrm{J}1614\penalty1000-\hskip0pt2230$, Cyg X-2 and PSR $\mathrm{B}1913+16$. The calculated value of central density of each of these compact stars, using this model, is of order ${10}^{14}$ or ${10}^{15}$, which is considerably high and consistent with ultracompact stars. We have also estimated the approximate moment of inertia for each of the considered compact stars.