Stationary Dilatons with Arbitrary Electromagnetic Field

TL;DR

This work develops axisymmetric stationary solutions of the 5D Einstein–Maxwell–Dilaton system with coupling $\alpha^2=3$ by employing a potential-space formalism built on two harmonic maps $\lambda$ and $\tau$, enabling an arbitrary electromagnetic field. Through SL$(3,\mathbb{R})$-invariant transformations, the authors generate two main solution classes from seed solutions: one electrically charged by coupling a vacuum seed with a scalar, and another magnetically charged arising from a magnetized seed, both admitting rotating generalizations. Explicit metrics and electromagnetic fields are constructed, including a Kerr-like limit and Belinsky–Ruffini-type configurations, with detailed expressions for mass $M$, angular momentum parameter $a$, and electromagnetic potentials. The results highlight how dilaton coupling and higher-dimensional structure yield rich families of charged and magnetized spacetimes, expanding the landscape of exact solutions in 5D gravity.

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 $q=δ=0$.