Four Parametric Regular Black Hole Solution

Abstract

We present a regular class of exact black hole solutions of Einstein equations coupled with a nonlinear electrodynamics source. For weak fields the nonlinear electrodynamics becomes the Maxwell theory, and asymptotically the solutions behave as the Reissner-Nordström one. The class is endowed with four parameters, which can be thought of as the mass $m$, charge $q$, and a sort of dipole and quadrupole moments $\alpha$ and $\beta$, respectively. For $\alpha \ge 3$, $\beta \ge 4$, and $|q|\le 2s_{c}m$ the corresponding solutions are regular charged black holes. For $\alpha =3$, they also satisfy the weak energy condition. For $\alpha =\beta =0$ we recover the Reissner-Nordström singular solution and for $\alpha =3$, $\beta =4$ the family includes a previous regular black hole reported by the authors.

RevTeX, 6 pages, minor changes