Charged Black Hole with Inverse Electrodynamics

Nonlinear electrodynamics has been frequently employed in the study of black holes. Some of these black holes may be regular, while others are singular. In this work, we consider a nonlinear electrodynamics model known as inverse electrodynamics to obtain black hole solutions. We demonstrate that, in addition to these solutions not being regular, they are also not asymptotically flat. We investigate which energy conditions are violated in the presence of this type of source. Furthermore, we calculate thermodynamic quantities and find that there are two phases, with one of them being thermodynamically stable. Finally, we derive the geodesics for massive and massless particles in this spacetime. For the massive case, we observe that there are no bound orbits.