Study of Anisotropic Compact Stars in Starobinsky Model

Abstract

The aim of this paper is to study the formation of anisotropic compact stars in modified $f(R)$ theory of gravity, which is the generalization of the Einstein's gravity. To this end, we have used the solution of Krori and Barua to the anisotropic distribution of matter in $f(R)$ gravity. Further, we have matched the interior solution with the exterior solution to determine the constants of Krori and Barua solution. Finally the constant have been determined by using the data of compact compact stars like 4$U1820-30, Her X-1, SAX J 1808-3658$. Using the evaluated form of the solutions, we have discussed the regularity of matter components at the center as well as on the boundary, energy conditions, anisotropy, stability analysis and mass-radius relation of the compact stars 4$U1820-30$, $Her X-1$, $SAX J 1808-3658.$