Instability of Einstein-Yang-Mills Solitons for Arbitrary Gauge Groups

TL;DR

This paper proves that all static, spherically symmetric Einstein-Yang-Mills solitons are unstable across all gauge groups by analyzing their perturbation spectra through a Schrödinger-type equation.

Contribution

It demonstrates the universal instability of Einstein-Yang-Mills solitons for any gauge group using a novel spectral analysis approach.

Findings

All such solutions have exponentially growing unstable modes.

The instability is proven without explicit solutions, relying on spectral properties.

The method applies broadly to arbitrary gauge groups.

Abstract

We prove that static, spherically symmetric, asymptotically flat, regular solutions of the Einstein-Yang-Mills equations are unstable for arbitrary gauge groups. The proof involves the following main steps. First, we show that the frequency spectrum of a class of radial perturbations is determined by a coupled system of radial "Schroedinger equations". Eigenstates with negative eigenvalues correspond to exponentially growing modes. Using the variational principle for the ground state it is then proven that there always exist unstable modes (at least for "generic" solitons). This conclusion is reached without explicit knowledge of the possible equilibrium solutions.