Instability of Gravitating Sphalerons

TL;DR

This paper proves that gravitating sphaleron solutions in the Einstein-Yang-Mills-Higgs system are inherently unstable by analyzing their radial perturbations, using a variational approach that does not need detailed solution data.

Contribution

It introduces a variational method to demonstrate the instability of gravitating sphalerons without requiring detailed knowledge of the solutions.

Findings

Existence of always unstable modes in gravitating sphalerons.

Method applicable to regular solutions, not directly to black holes.

Provides a general proof of instability for these configurations.

Abstract

We prove the instability of the gravitating regular sphaleron solutions of the $SU(2)$ Einstein-Yang-Mills-Higgs system with a Higgs doublet, by studying the frequency spectrum of a class of radial perturbations. With the help of a variational principle we show that there exist always unstable modes. Our method has the advantage that no detailed knowledge of the equilibrium solution is required. It does, however, not directly apply to black holes.