Class of Eistein-Maxwell Dilatons

TL;DR

This paper develops a formalism using harmonic maps to analyze Einstein-Maxwell-Dilaton spaces, deriving new classes of solutions including known charged and dilatonic black holes.

Contribution

It introduces a Hamiltonian approach with harmonic parameters to generate and generalize solutions in Einstein-Maxwell-Dilaton theory.

Findings

Derived equations in harmonic parameters for real and complex cases

Presented new classes of solutions including known black holes as special cases

Generalized charged and dilatonic black hole solutions

Abstract

The functional potential formalism is used to analyze stationary axisymmetric spaces in the Einstein-Maxwell-Dilaton theory. Performing a Legendre transformation, a ``Hamiltonian''is obtained, which allows to rewrite the dynamical equations in terms of three complex functions only. Using an ansatz resembling the one used by the harmonic maps ansatz, we express these three functions in terms of the harmonic parameters, studying the cases where these parameters are real, and when they are complex. For each case, the set of equations in terms of these harmonic parameters is derived, and several classes of solutions to the Einstein-Maxwell with arbitrary coupling constant to a dilaton field are presented. Most of the known solutions of charged and dilatonic black holes are contained as special cases and can be non-trivially generalized in different ways.