New Regular Solutions with Axial Symmetry in Einstein-Yang-Mills Theory

TL;DR

This paper constructs new static, axially symmetric, asymptotically flat solutions in Einstein-Yang-Mills theory characterized by two integers, revealing novel solutions for higher polar angle modes and their relation to Einstein-Yang-Mills-Higgs solutions.

Contribution

It introduces a new class of regular Einstein-Yang-Mills solutions with axial symmetry for k>1, expanding the known solution space beyond spherical symmetry.

Findings

New solutions exist for k>1 and n above a minimal value.

Solutions form two branches with different properties.

Lower mass branch solutions relate to Einstein-Yang-Mills-Higgs solutions with ring-like Higgs field nodes.

Abstract

We construct new regular solutions in Einstein-Yang-Mills theory. They are static, axially symmetric and asymptotically flat. They are characterized by a pair of integers (k,n), where k is related to the polar angle and $n$ to the azimuthal angle. The known spherically and axially symmetric EYM solutions have k=1. For k>1 new solutions arise, which form two branches. They exist above a minimal value of n, that increases with k. The solutions on the lower mass branch are related to certain solutions of Einstein-Yang-Mills-Higgs theory, where the nodes of the Higgs field form rings.