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 $α$ and $β$, respectively. For $α\geq 3$, $β\geq 4$, and $|q| \leq 2 s_c m$ the corresponding solutions are regular charged black holes. For $α=3$, they also satisfy the weak energy condition. For $α=β=0$ we recover the Reissner-Nordström singular solution and for $α=3$, $β=4$ the family includes a previous regular black hole reported by the authors.