THE NUMBER OF SPHALERON INSTABILITIES OF THE BARTNIK-McKINNON SOLITONS AND NON-ABELIAN BLACK HOLES

TL;DR

This paper rigorously proves the exact number of sphaleron-like unstable modes for specific non-abelian solutions in Einstein-Yang-Mills theory, enhancing understanding of their stability properties.

Contribution

It provides a precise mathematical proof of the number of unstable modes for the nth Bartnik-McKinnon soliton and black hole solutions in SU(2) Einstein-Yang-Mills theory.

Findings

Exactly n odd-parity sphaleron-like unstable modes identified

Number of unstable modes matches the solution index n

Clarifies stability characteristics of non-abelian black holes

Abstract

It is proven that there are precisely $n$ odd-parity sphaleron-like unstable modes of the $n$-th Bartnik-McKinnon soliton and the $n$-th non-abelian black hole solution of the Einstein-Yang-Mills theory for the gauge group $SU(2)$.