Black hole solution in the framework of $\arctan$-electrodynamics

Abstract

An $arctan$-electrodynamics coupled with the gravitational field is investigated. We obtain the regular black hole solution that at $r\rightarrow \infty$ gives corrections to the Reissner-Nordstr\"om solution. The corrections to Coulomb's law at $r\rightarrow\infty$ are found. We evaluate the mass of the black hole that is a function of the dimensional parameter $\beta$ introduced in the model. The magnetically charged black hole was investigated and we have obtained the magnetic mass of the black hole and the metric function at $r\rightarrow \infty$. The regular black hole solution is obtained at $r\rightarrow 0$ with the de Sitter core. We show that there is no singularity of the Ricci scalar for electrically and magnetically charged black holes. Restrictions on the electric and magnetic fields are found that follow from the requirement of the absence of superluminal sound speed and the requirement of a classical stability.