Regular black holes from analytic

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