Structures of General Relativity in Dilaton-Maxwell Electrodynamics

TL;DR

This paper reveals that the electrostatic sector of dilaton-Maxwell electrodynamics exhibits a symmetry akin to stationary General Relativity, enabling the generation of exact solutions and revealing finite energy Coulomb-like sources with short-distance asymptotic freedom.

Contribution

It develops a solution-generating technique based on Ehlers symmetry for dilaton-Maxwell electrodynamics and constructs a class of finite-energy Coulomb-like solutions.

Findings

Electrostatic solutions exhibit asymptotic freedom at short distances.

Total electrostatic energy is finite and inversely proportional to the coupling constant.

The symmetry group matches that of stationary vacuum General Relativity.

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.