Analytic Electrically Charged Black Holes in $F(R)$-ModMax Theory

Abstract: Motivated by a new model of nonlinear electrodynamics known as Modified Maxwell (ModMax) theory, an exact analytical solution for black holes is obtained by coupling ModMax nonlinear electrodynamics and $F(R)$ gravity. Then, the effects of the system's parameters ($F(R)$-ModMax gravity parameters) on the event horizons are analyzed. The obtained black holes thermodynamic properties in the $F(R)$-ModMax theory are investigated by extracting their thermodynamic quantities such as Hawking temperature, electric charge, electric potential, entropy, and also total mass. The first law of thermodynamics for the system under study is evaluated. Next, by considering these black holes, the impact of various parameters on both the local stability and global stability are investigated by examining the heat capacity and the Helmholtz free energy, respectively. Finally, the thermodynamic geometry of the black hole in $F(R)$-ModMax gravity is investigated by applying the thermodynamic metric (the HPEM metric).