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-Nordstrom 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 >= 3, beta >= 4, and vertical bar q vertical bar <= 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-Nordstrom singular solution and for alpha=3, beta=4 the family includes a previous regular black hole reported by the authors.