Regular black holes from analytic f(F2)

We construct regular black holes and horizonless spacetimes that are geodesically complete and satisfy the dominant energy condition from Einstein-f(F-2) gravities with several classes of analytic f(F-2) functions that can be viewed as perturbations to Maxwell's theory in weak field limit. We establish that regular black holes with special static metric (g(tt)g(rr) = -1) violate the strong energy condition and such a regular black hole with Minkowski core violates the null energy condition. We develop a formalism to perform electromagnetic duality transformations in f(F-2). We obtain two new explicit examples where the duality is a symmetry. We study the properties of the corresponding dyonic black holes. We study the geodesic motions of a particular class of solutions that we call horizonless or black hole repulsons.