Anisotropic extensions of isotropic Finch–Skea metric in the charged modified gravity

Abstract In this study, we explore the Finch–Skea perfect fluid solution and extend its domain to three distinct anisotropic interior models within the framework of the f ( R , T ) theory, incorporating the influence of an electromagnetic field. We assume a static spherical spacetime initially coupled with an isotropic matter distribution. We then introduce a Lagrangian corresponding to an additional gravitating source, taking into account its role in inducing pressure anisotropy within the original fluid source. By deriving the field equations for the combined matter setup, we applied a radial component transformation, which yielded two distinct systems of equations. In addition, we consider a charged exterior spacetime to determine the three constants associated with the Finch–Skea solution at the boundary. Our findings suggest that under certain parametric choices, all three resulting models exhibited physical relevance within this modified theory.