Stationary axisymmetric SU(2) Einstein-Yang-Mills fields with restricted circularity conditions are Abelian

TL;DR

This paper proves that under certain circularity conditions, stationary axisymmetric SU(2) Einstein-Yang-Mills fields must be Abelian or the spacetime cannot be asymptotically flat, revealing a fundamental restriction on such fields.

Contribution

It demonstrates that specific circularity conditions in SU(2) Einstein-Yang-Mills theory enforce the fields to be Abelian, clarifying the structure of solutions under these conditions.

Findings

SU(2) fields are Abelian under circularity conditions

Non-Abelian solutions are not asymptotically flat

Circularity conditions restrict the field's algebraic type

Abstract

In this paper we prove that in a stationary axisymmetric SU(2) Einstein-Yang-Mills theory the most reasonable circularity conditions that can be considered for the Yang-Mills fields imply in fact that the field is of embedded Abelian type, or else that the metric is not asymptotically flat.