Perturbation theory for self-gravitating gauge fields I: The odd-parity sector

TL;DR

This paper develops a gauge-invariant perturbation theory for self-gravitating non-Abelian gauge fields, analyzing stability and uniqueness of Einstein-Yang-Mills solutions, and finds specific stability properties for black holes and solitons.

Contribution

It introduces a novel gauge and coordinate invariant perturbation framework for self-gravitating gauge fields and applies it to analyze stability and uniqueness of solutions.

Findings

All odd-parity excitations have angular momentum number ℓ=1.

Schwarzschild and Reissner-Nordström solutions are linearly stable.

Unstable modes with ℓ=1 are excluded for certain solutions.

Abstract

A gauge and coordinate invariant perturbation theory for self-gravitating non-Abelian gauge fields is developed and used to analyze local uniqueness and linear stability properties of non-Abelian equilibrium configurations. It is shown that all admissible stationary odd-parity excitations of the static and spherically symmetric Einstein-Yang-Mills soliton and black hole solutions have total angular momentum number $\ell = 1$, and are characterized by non-vanishing asymptotic flux integrals. Local uniqueness results with respect to non-Abelian perturbations are also established for the Schwarzschild and the Reissner-Nordstr\"om solutions, which, in addition, are shown to be linearly stable under dynamical Einstein-Yang-Mills perturbations. Finally, unstable modes with $\ell = 1$ are also excluded for the static and spherically symmetric non-Abelian solitons and black holes.