Exact solutions of f(R) gravity coupled to nonlinear electrodynamics

In this work, exact solutions of static and spherically symmetric space-times are analyzed in f(R) modified theories of gravity coupled to nonlinear electrodynamics. First, we restrict the metric fields to one degree of freedom, considering the specific case of g(tt)g(rr)=-1. Using the dual P formalism of nonlinear electrodynamics, an exact general solution is deduced in terms of the structural function H-P. In particular, specific exact solutions to the gravitational field equations are found, confirming previous results and new pure electric field solutions are found. Second, motivated by the existence of regular electric fields at the center, and allowing for the case of g(tt)g(rr)not equal-1, new specific solutions are found. Finally, we outline alternative approaches by considering the specific case of constant curvature, followed by the analysis of a specific form for f(R).