On the Limiting Solution of the Bartnik-McKinnon Family

TL;DR

This paper investigates the limiting behavior of the Bartnik-McKinnon solutions, demonstrating that its exterior corresponds to an extremal Reissner-Nordström black hole rather than a novel non-abelian black hole as previously claimed.

Contribution

It clarifies the nature of the limiting solution of the Bartnik-McKinnon family, correcting a recent misconception about its structure.

Findings

The limiting solution is an extremal Reissner-Nordström black hole.

Contradicts previous claims of a new non-abelian black hole.

Provides a rigorous analysis of the solution's exterior geometry.

Abstract

We analyze the limiting solution of the Bartnik-McKinnon family and show that its exterior is an extremal Reissner-Nordstr{\o}m black hole and not a new type of non-abelian black hole as claimed in a recent article by Smoller and Wasserman.