Four-parametric regular black hole solution

We present a regular class of exact black hole solutions of the 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≥3, β≥4, and |q|≤2scm 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.