Generating solutions for charged compact configurations in f(R) gravity

Abstract

We present a systematic method for generating solutions of charged, spherically symmetric compact objects in modified f ( R ) gravity. The stellar interior is modeled with an anisotropic matter distribution, allowing distinct radial and tangential stresses. The modified field equations initially provide three relations among five unknown functions. To construct a consistent system, we impose a linear equation of state together with two geometric constraints: the conformally flat condition (vanishing Weyl tensor) and the Karmarkar condition associated with class-I embedding. These conditions lead to a closed expression for the energy density, which serves as a generating function for the model. Within this framework, the radial pressure, tangential pressure, and anisotropy factor naturally emerge as key drivers in the generation of solutions. The resulting Riccati equation is transformed into a second-order linear homogeneous form, enabling explicit construction of stellar models. Our analysis demonstrates that once a particular solution is identified, entire families of generating solutions can be obtained in f ( R ) gravity, with the anisotropy factor playing a central role in their formulation.