Static Axially Symmetric Einstein-Yang-Mills-Dilaton Solutions: I.Regular Solutions

TL;DR

This paper explores static axially symmetric solutions in Einstein-Yang-Mills-dilaton theory, revealing their structure, properties, and how they form sequences approaching known extremal solutions as parameters vary.

Contribution

It provides a detailed analysis of new axially symmetric solutions with higher winding numbers and node numbers, extending understanding beyond spherically symmetric cases.

Findings

Solutions exhibit torus-like energy density distributions.

Sequences of solutions approach extremal Einstein-Maxwell-dilaton and Reissner-Nordström solutions.

Winding number and node number influence the solution properties and limiting behaviors.

Abstract

We discuss the static axially symmetric regular solutions, obtained recently in Einstein-Yang-Mills and Einstein-Yang-Mills-dilaton theory [1]. These asymptotically flat solutions are characterized by the winding number $n>1$ and the node number $k$ of the purely magnetic gauge field. The well-known spherically symmetric solutions have winding number $n=1$. The axially symmetric solutions satisfy the same relations between the metric and the dilaton field as their spherically symmetric counterparts. Exhibiting a strong peak along the $\rho$-axis, the energy density of the matter fields of the axially symmetric solutions has a torus-like shape. For fixed winding number $n$ with increasing node number $k$ the solutions form sequences. The sequences of magnetically neutral non-abelian axially symmetric regular solutions with winding number $n$ tend to magnetically charged abelian spherically symmetric limiting solutions, corresponding to ``extremal'' Einstein-Maxwell-dilaton solutions for finite values of $\gamma$ and to extremal Reissner-Nordstr\o m solutions for $\gamma=0$, with $n$ units of magnetic charge.