On a regular charged black hole with a nonlinear electric source

Abstract

A modified version of the Reissner-Nordstrom metric is proposed on the grounds of the nonlinear electrodynamics model. The source of curvature is an anisotropic fluid with $p_{r} = -\rho$ which resembles the Maxwell stress tensor at $r >> q^{2}/2m$, where $q$ and $m$ are the mass and charge of the particle, respectively. We found the black hole horizon entropy obeys the relation $S = |W|/2T = A_{H}/4$, with $W$ the Komar energy and $A_{H}$ the horizon area. The electric field around the source depends not only on its charge but also on its mass. The corresponding electrostatic potential $\Phi(r)$ is finite everywhere, vanishes at the origin and at $r = q^{2}/6m$ and is nonzero asymptotically, with $\Phi_{\infty} = 3m/2q$.