Existence of Noncompact Static Spherically Symmetric Solutions of Einstein SU(2) Yang Mills Equations with small Cosmological Constant

TL;DR

This paper proves the existence of certain noncompact, static, spherically symmetric solutions to Einstein's equations coupled with SU(2) Yang-Mills fields when the cosmological constant is small, including their coordinate singularity structure.

Contribution

It demonstrates the existence of smooth, static, spherically symmetric Einstein-Yang-Mills solutions with small cosmological constant and analyzes their singularity properties.

Findings

Solutions possess a coordinate singularity at some radius

Singularity can be removed via a Kruskal-like coordinate transformation

Existence of solutions is established for small cosmological constants

Abstract

We consider static spherically symmetric solutions of Einstein's equations coupled to an SU(2) Yang Mills field that are smooth at the center of spherical symmetry. We prove that with small cosmological constant there exist solutions that possess a coordinate singularity at some r that is not maximum. The singularity can be removed with a Kruskal-like change of coordinates.