Instability Proof for Einstein-Yang-Mills Solitons and Black Holes with Arbitrary Gauge Groups

TL;DR

This paper proves that all static, spherically symmetric Einstein-Yang-Mills solitons and black holes are unstable for any gauge group, using a method that does not require explicit solutions.

Contribution

It provides a general instability proof for Einstein-Yang-Mills solutions across arbitrary gauge groups without needing explicit solution forms.

Findings

All such solutions are unstable.

The proof applies to arbitrary gauge groups.

Instability holds for the generic case.

Abstract

We prove that static, spherically symmetric, asymptotically flat soliton and black hole solutions of the Einstein-Yang-Mills equations are unstable for arbitrary gauge groups, at least for the ``generic" case. This conclusion is derived without explicit knowledge of the possible equilibrium solutions.