Charged anisotropic Finch–Skea–Bardeen spheres in f(R) gravity with Karmarkar condition

Abstract

The main motivation of this study was to probe the compact stars solution with the help of Karmarkar condition in the background of f(R) theory of gravity. To do so, we assume a viable and realistic f(R) gravity model in the presence of a charged anisotropic fluid sphere along with static spherically symmetric spacetime. Moreover, we consider a specific model of Adler approach for metric potential $$g_{tt}$$ , which shows a new family of solutions and then by using the Karmarkar condition, we obtain the other component of the metric tensor $$g_{rr}$$ . The key feature of our study is to assume the Bardeen model as an exterior geometry. To ensure the viability of f(R) gravity model, we conduct various physical tests like energy density, pressure components, energy bonds, equilibrium condition, Herrera cracking concept, and mass–radius relation. It is observed that all physical attributes follow the physically accepted fact, which confirm the viability and consistency of our model. Our study also shows that the f(R) theory of gravity seems to be an appropriate theory to describe the existence of embedded class-one solutions of compact stars.