Solutions of the spherically symmetric SU(2) Einstein-Yang-Mills equations defined in the far field

TL;DR

This paper analytically demonstrates that all static, spherically symmetric SU(2) Einstein-Yang-Mills solutions in the far field possess finite ADM mass and at most two horizons, classifying solutions based on metric behavior at the origin.

Contribution

It provides a rigorous analytical proof of properties of these solutions and classifies them into three types based on their metric behavior.

Findings

All solutions have finite ADM mass.

Solutions have at most two horizons.

Three solution types are identified based on metric behavior.

Abstract

It is shown analytically that every static, spherically symmetric solution to the Einstein Yang Mills equations with SU(2) gauge group that is defined in the far field has finite ADM mass. Moreover, there can be at most two horizons for such solutions. The three types of solutions possible, Bartnik-McKinnon particle-like solutions, Reissner-Nordstrom-like solutions, and black hole solutions having only one horizon are distinguished by the behavior of the metric coefficients at the origin.