Realistic anisotropic Karmarkar stars in Rastall gravitational framework

Abstract

In this study, we discuss the anisotropic matter distribution of compact stars in the context of Rastall modified theory of gravity by applying Karmarkar condition of embedding technique. For this purpose, we consider the spherical symmetric geometry and solve the resulting Rastall field equations by taking different values of Rastall parameter, i.e., ξ=0.05,ξ=−0.05, and ξ=−0.15 into account. Since the Karmarkar condition links both metric potentials through a differential equation and allows one to pick one of the metric potential, so we pick a well-known interesting form of grr component of metric as eλ(r)=1+cr21+ar2n(1+br2)2. We elaborate the properties of compact stars Vela X-1, 4U 1820-30 and SAX J 1808.4-3658 for different positive values of n, i.e., 1.8≤n<7, where n≠2,4,6. It is interesting to mention here that results are not justified for n≥7. Also, we find no solution for even integral values of n, but for odd integers, we obtain physically admissible solutions representing the compact stars. For greater values of n, we obtain stiff fluid equations of state in which adiabatic index shows the increasing behavior and speed of sound approximates to speed of light. It is seen that the causality condition is violated for all values of n≥7 and the values of n between 0 and 1.8 generate complex values of transverse sound speed vt.