Extended Lambda-Maxwell duality and related large class of dyonic and neutral exactly solvable 4D Einstein-Maxwell-dilaton models discovered

We report the discovered class of exact static solutions of several 4D Einstein-Maxwell-dilaton systems: string-induced, Liouville, trigonometric, polynomial, etc., for three basic topologies (spherical, hyperbolical and flat) being uniformly treated. In addition to the usual electric-magnetic duality this class obeys a certain extended duality between Maxwell-dilaton coupling and dilaton mass. Though major solutions we obtain are dyonic, the class also comprises interesting neutral models. As a by-product, we significantly succeded in resolving of the two important problems, one of which has been standing more than a decade (system with the string-inspired exponential Maxwell-dilaton coupling and non-vanishing dilaton mass) and another one - gravity coupled to massive neutral scalar field: generalized Liouville, Sin(h), Cos(h) - is about fifty years old. Finally, we demonstrate the full separability of the static EMD system and publicize the simple procedure of how to generate new integrability classes.