Two-sided NED black-hole, naked-singularity, and soliton solutions

We consider non-linear electrodynamics (NED) minimally coupled to general relativity. We derive novel electrically charged, spherically symmetric, black-hole solutions having, for some set of parameters, all their NED fields (the electric field and the square of the electromagnetic field) regular for all values of the radial coordinate. For another set of parameters, the NED fields and the Kretschmann scalar are regular as the radial coordinate runs from one spatial infinity to another spatial infinity without the metric being a wormhole. We obtain solutions that have two distinct or the same asymptotic behaviors (two spatial infinities) with equal or unequal ADM masses and solutions with always one horizon whatever the ratio of the electric charge to mass. We comment on some regularity theorems and generalize them to multi-valued NED Lagrangians. The derived regular solutions do not violate the weak energy condition.