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

TL;DR

This paper derives exact static, spherically symmetric solutions in f(R) gravity coupled with nonlinear electrodynamics, including new solutions with regular electric fields and constant curvature scenarios.

Contribution

It provides new exact solutions in f(R) gravity with nonlinear electrodynamics, expanding understanding of regular electric fields and specific curvature cases.

Findings

New exact solutions with regular electric fields at the center.

Confirmation of previous solutions and discovery of new pure electric solutions.

Analysis of constant curvature and specific f(R) forms.

Abstract

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. Firstly, 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. Secondly, motivated by the existence of regular electric fields at the center, and allowing for the case of g_tt\g_rr \= -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).