Far Field Behavior of Noncompact Static Spherically Symmetric Solutions of Einstein SU(2) Yang Mills Equations

TL;DR

This paper proves that certain Einstein-Yang Mills solutions with a positive cosmological constant are globally smooth outside a singularity and asymptotically resemble Schwarzschild deSitter space with no Yang Mills field.

Contribution

It demonstrates the global regularity and asymptotic behavior of noncompact static spherically symmetric Einstein-Yang Mills solutions with a positive cosmological constant.

Findings

Solutions are globally smooth except at a coordinate singularity.

Solutions asymptotically approach Schwarzschild deSitter space.

Yang Mills field vanishes at infinity.

Abstract

The Einstein equations with small positive cosmological constant coupled to an SU(2) Yang Mills field admits solutions that possess a coordinate singularity at a noncritical radius. Here, we prove that these solutions are otherwise globally smooth and that they asymptotically approach Schwarzschild deSitter space with a vanishing Yang Mills field.