Models of anisotropic compact stars in the Rastall theory of gravity

Abstract

In the present work, we have studied the anisotropic compact stars in the regime of Rastall theory using Karori and Barua $(\mathit{KB})$ type metric. For this investigation, we have considered three different known compact stars with anisotropic configuration namely, 4U 1820-30, Her X-1 and SAX J 1808.4-3658(SSI) with radii 10 km, 7.7 km and 7.07 km respectively. Formulation of field equations in this modified theory have also been presented. The unknown constants in KB metric have been obtained by using the matching of interior solution with the exterior vacuum solution. We investigate the various physical aspects of the presented model such as variation of energy density, energy conditions, hydrostatic equilibrium, stability, compactness and surface redshift. Graphical analysis of the variables involved in the obtained solution is also presented to observe their behavior more clearly. We also demonstrate the numerical values of some physical parameters in the tabular form by using the observational values of mass and radius. We also compute the numerical values of $\frac{2M}{R}$ using the presented model to check the Buchdahl limit for our system. The detailed analysis of matter variables revealed the regularity and stability of our proposed model.