Structures of General Relativity in Dilaton-Maxwell Electrodynamics

Abstract

It is shown that electro (magneto) static sector of Maxwell's electrodynamics coupled to the dilaton field in a string theory form possesses the symmetry group of the stationary General Relativity in vacuum. Performing the Ernst formalism, we develope a technique for generation of exact solutions in this modified electrodynamics on the base of the normalized Ehlers symmetry transformation. In the electrostatic case, we construct and study a general class of spherically symmetric solutions that describes a point-like sourse of the Coulomb type. It is shown that this source is characterized by asymptotical freedom of the electrostatic interaction at short distances. Also it is established that the total electrostatic energy of this source is finite and inversely proportional to the dilaton-Maxwell coupling constant.