On the general theory for construction the static solutions for two charges in General Relativity

In this talk we present a general family of static asymptotically flat solutions for the superposed gravitational and electromagnetic fields of two Reissner-Nordstrom sources with arbitrary parameters: masses, charges and separating distance. The Inverse Scattering Method for Einstein-Maxwell equations for stationary axisymmetric fields is outlined. The family of equilibrium configurations of two Reissner-Nordstrom sources (one of which should be a black hole and another one $\vert $a naked singularity) described in our first talk arises after a restriction of the parameters of the general solution presented here by the equilibrium condition which provides the absence in the solution of conical singularities on the symmetry axis between the sources.