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

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.