Stationary Dilatons with Arbitrary Electromagnetic Field

Abstract

We present two new classes of axisymmetric stationary solutions of the Einstein-Maxwell-Dilaton equations with coupling constant $α^2=3$. Both classes are written in terms of two harmonic maps $λ$ and $τ$. $λ$ determines the gravitational potential and $τ$ 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 ($δ$) parameters, one with electric charge ($q$) another one with magnetic dipole ($Q$) parameter. The first solution contains the Kerr metric for $q=δ=0$.