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.

Singularity-free interaction in dilaton-Maxwell electrodynamics

“…Following [7], let us consider the dilaton-Maxwell electrodynamics with negative kinetic term for dilaton field:…”

“…In [7] we studied the system with the dilatation symmetry that is realized on the dilaton-Maxwell background only: this symmetry was not supported by the dynamics of test charging particles. In this paper, we 'extend' dilatation symmetry approach to the total scheme under consideration.…”

“…In this paper, we 'extend' dilatation symmetry approach to the total scheme under consideration. We use the duality between the static dilaton-Maxwell background and stationary General Relativity, which was found in [7], to work with essentially nonlinear DME system. Namely, we perform the so-called 'charging Ehlers transformation' (see [8]- [13]) to create the most general spherically symmetric dilaton-Maxwell background, which describes the fundamental electrical/magnetic sources in DME.…”

Least Action Principle for Lorentz Force in Dilaton-Maxwell Electrodynamics

“…Then, in [9] it was studied a static background of DME with σ = +1 (it has been shown that this choice of the sign leads to a remarkable duality between static DME and stationary General Relativity in vacuum). Let's fix this type of DME; in [9] it was shown that a general spherically symmetric solution of the DME equations with trivial spatial asymptotics reads:…”

“…where we put b = αβ (this result immediately follows from Eqs. (26), (15), (9), (17) and (29)). Thus, the most general form of the potential for the radial dynamics of a test particle on the background of DME with a given value of the dilaton-Maxwell coupling α contains the free parameter β which can not be fixed by the underlying dilatation symmetry (2) (for example, β = −2/3 in the Kaluza-Klein theory case).…”