Stationary perturbations and infinitesimal rotations of static Einstein-Yang-Mills configurations with bosonic matter

TL;DR

This paper develops a framework using Kaluza-Klein structure to analyze stationary perturbations of static Einstein-Yang-Mills configurations with bosonic matter, revealing conditions for non-zero angular momentum and rotating solutions.

Contribution

It introduces a gauge-invariant, self-adjoint system for analyzing perturbations leading to angular momentum in Einstein-Yang-Mills configurations with bosonic matter.

Findings

Perturbations with non-zero ADM angular momentum are governed by a self-adjoint scalar system.

Slowly rotating black holes are generic in non-Abelian gauge theories with bosonic matter.

Soliton solutions generally do not have rotating counterparts.

Abstract

Using the Kaluza-Klein structure of stationary spacetimes, a framework for analyzing stationary perturbations of static Einstein-Yang-Mills configurations with bosonic matter fields is presented. It is shown that the perturbations giving rise to non-vanishing ADM angular momentum are governed by a self-adjoint system of equations for a set of gauge invariant scalar amplitudes. The method is illustrated for SU(2) gauge fields, coupled to a Higgs doublet or a Higgs triplet. It is argued that slowly rotating black holes arise generically in self-gravitating non-Abelian gauge theories with bosonic matter, whereas, in general, soliton solutions do not have rotating counterparts.