Black holes in $f(R)$ gravity coupled to nonlinear electromagnetic fields

TL;DR

This paper develops a method to find static, spherically symmetric black hole solutions in $f(R)$ gravity coupled with nonlinear electromagnetic fields, introducing new solutions and analyzing their thermodynamic properties.

Contribution

It presents a novel framework for constructing black hole solutions in $f(R)$ gravity with nonlinear electromagnetic coupling, including two new explicit solutions and thermodynamic analysis.

Findings

Two new black hole solutions in $f(R)$ gravity with nonlinear electromagnetic fields.

Analysis of energy conditions for the solutions.

Calculation of entropy, energy, and thermodynamic topology of the black holes.

Abstract

We establish a framework to construct spherically symmetric and static solutions in $f(R)$ gravity coupled with nonlinear electromagnetic fields. We present two new specific solutions and discuss the energy conditions. We calculate some thermodynamic quantities of the obtained black holes like entropy and energy and investigate their thermodynamic topology.