Corrections to Reissner-Nordstr\"om black hole solution due to exponential nonlinear electrodynamics

An exponential model of nonlinear electrodynamics coupled with the gravitational field is analyzed. It was shown that weak, dominant, and strong energy conditions are satisfied. We obtain corrections to Coulomb's law at $r\rightarrow\infty$. It was demonstrated that electric-magnetic duality between ${\cal F}$ and ${\cal P}$ frames is violated. The asymptotic black hole solution at $r\rightarrow \infty$ is found that contains corrections to the Reissner-Nordstr\"om solution. The electromagnetic mass of the black hole is calculated, expressed through the parameter $\beta$ of the model.