Odd-Parity Negative Modes of Einstein-Yang-Mills Black Holes and Sphalerons

TL;DR

This paper analytically proves the existence of negative modes in the odd-parity sector of Einstein-Yang-Mills black holes, highlighting their importance in stability analysis and sphaleron interpretations.

Contribution

It provides a general analytical proof of negative modes in the odd-parity sector for all known non-abelian Einstein-Yang-Mills black holes.

Findings

Negative modes exist in the odd-parity sector of these black holes.

Normalizability is crucial for stability analysis.

Odd-parity negative modes relate to sphaleron solutions.

Abstract

An analytical proof of the existence of negative modes in the odd--parity perturbation sector is given for all known non-abelian Einstein--Yang--Mills black holes. The significance of the normalizability condition in the functional stability analysis is emphasized. The role of the odd--parity negative modes in the sphaleron interpretation of the Bartnik--McKinnon solutions is discussed.