Dynamical system analysis for the Einstein-Yang-Mills equations

TL;DR

This paper applies dynamical systems techniques to analyze local solutions of the static, spherically symmetric Einstein-Yang-Mills equations with SU(2), classifying solutions, proving existence of oscillating metrics, and discovering new singular solutions.

Contribution

It introduces a dynamical systems framework to classify and analyze local solutions of the Einstein-Yang-Mills equations, including new singular solutions.

Findings

Classified solutions near the origin.

Proved existence of solutions with oscillating metrics.

Discovered two new local singular solutions.

Abstract

Local solutions of the static, spherically symmetric Einstein-Yang-Mills (EYM) equations with SU(2) gauge group are studied on the basis of dynamical systems methods. This approach enables us to classify EYM solutions in the origin neighborhood, to prove the existence of solutions with the oscillating metric as well as the existence of local solutions for all known formal power series expansions, to study the extendibility of solutions, and to find two new local singular solutions.