Effect of $f(R)$-gravity models on compact stars

We study the possibility of forming anisotropic compact stars in the framework of $f(R)$-modified gravity in a static spherically symmetric space–time. We find the unknown coefficients involved in the metric using masses and radii of the compact stars 4U 1820-30, Cen X-3, EXO 1785-248, and LMC X-4. We obtain the hydrostatic equilibrium equation for different forces and use the generalized Tolman–Oppenheimer–Volkoff equation to analyze the behavior of stars. Moreover, we verify the regularity conditions, anisotropic behavior, energy conditions, and stability of the compact stars. We use the effective energy–momentum tensor in $f(R)$ gravity for the analysis. We show that in the framework of $f(R)$ gravity theory, these compact stars have physically acceptable patterns. Our results here also agree with those in general relativity, which is a special case of $f(R)$ gravity.