Stationary Dilatons with Arbitrary Electromagnetic Field

TL;DR

This paper introduces two new classes of axisymmetric stationary solutions to Einstein-Maxwell-Dilaton equations with arbitrary electromagnetic fields, expressed via harmonic maps, generalizing known solutions like Kerr.

Contribution

It develops a method to generate solutions with arbitrary electromagnetic fields using harmonic maps, expanding the set of known Einstein-Maxwell-Dilaton solutions.

Findings

Derived two classes of solutions with arbitrary electromagnetic fields.

Generated explicit solutions with parameters for mass, rotation, scalar charge, electric charge, and magnetic dipole.

Included a solution that generalizes the Kerr metric.

Abstract

We present two new classes of axisymmetric stationary solutions of the Einstein-Maxwell-Dilaton equations with coupling constant $\alpha^2=3$. Both classes are written in terms of two harmonic maps $\lambda$ and $\tau$. $\lambda$ determines the gravitational potential and $\tau$ the electromagnetic one in such a form that we can have an arbitrary electromagnetic field. As examples we generate two solutions with mass ($M$), rotation ($s$) and scalar ($\delta$) parameters, one with electric charge ($q$) another one with magnetic dipole ($Q$) parameter. The first solution contains the Kerr metric for $q=\delta=0$.