New approach to the classification and solving of Einstein-Maxwell-dilaton gravity and its application for a particular set of exactly solvable models

We prove the full separability of the static dyonic Einstein-Maxwell-dilaton system for three basic geometries that in turn yields the simple procedure of getting what we call the classes of integrability. It reveals the sector structure of EMD theory — in particular, it demonstrates that each graviton-dilaton scale relation determines a unique coupling-potential pair. Illustrating these concepts, we study the so-called linear class, which has a number of remarkable features: it comprises numerous EMD models including string-inspired, Liouville, trigonometric, polynomial, etc., and the majority of them remain nontrivial even if both charges are zeros; in addition to the usual electric-magnetic duality it obeys a certain duality between Maxwell-dilaton coupling and the dilaton potential. We single out some models inside this class and obtain the families of exact dyonic solutions. In a certain limit they can be interpreted as the Reissner–Nordström–de Sitter (with “renormalized” dyonic charge) plus small logarithmic corrections. The latter change the global structure of the nonperturbed solution by shifting and splitting of horizons, breaking down extremality and “dressing” the naked singularity. Finally, a certain cosmological-type model brings some insight concerning the appearance of a cosmological electrostatic field in the low-energy limit of string theory.