Linear superposition of regular black hole solutions of Einstein nonlinear electrodynamics

In this paper we focus on certain properties of the Schwarzschild metrics that, to the best of our knowledge, have gone unnoticed. These properties include (i) the existence of a generalized Birkhoff theorem for general nonlinear electrodynamics, (ii) the existence of two double eigenvalues of the Einstein tensor G(nu)(mu) coincident in number with the two pairs of eigenvalues of the electrodynamics energy-momentum tensors, (iii) the partial fitting of the dominant energy conditions, (iv) linear superpositions of solutions of the Einstein electrodynamics equations through the inverse integration method, and (v) the generating technique of solutions with a Reissner-Nordstrom limit at spatial infinity. Each of these aspects are treated in detail, and a class of regular black hole solutions is reported and studied to some extent.