Solutions with negative mass for the SU(2) Einstein-Yang-Mills equations

TL;DR

This paper investigates static, spherically symmetric solutions to the SU(2) Einstein-Yang-Mills equations with nonpositive ADM mass, revealing unique solutions with zero nodes in the gauge field, distinct from known particlelike or black hole solutions.

Contribution

It clarifies the structure of solutions with nonpositive mass and demonstrates the existence of solutions with zero gauge field nodes, a novel feature in this context.

Findings

Solutions with nonpositive ADM mass have zero gauge field nodes.

Numerical results show these solutions differ from particlelike and black hole solutions.

The solutions' structure is clarified for the first time in this setting.

Abstract

The aim of this note is to clarify the structure of nontrivial global solutions with nonpositive ADM mass for the static, spherically symmetric Einstein-Yang-Mills equations with SU(2) gauge group. The presented numerical results demonstrate that these solutions have zero number of nodes of the gauge field function. This is a feature that is present neither for particlelike nor for black hole solutions.