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

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-Nordström 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.

23 pages, revtex, no figures

References in corpus (2)

• Measurement Theory and General Relativity
• The generalization of the Regge-Wheeler equation for self-gravitating matter fields

Cited by in corpus (8)

• Critical phenomena in gravitational collapse (Physics Reports)
• Gauge invariant perturbations of Schwarzschild black holes in horizon-penetrating coordinates
• On the linear stability of solitons and hairy black holes with a negative cosmological constant: the odd-parity sector
• Outer boundary conditions for Einstein's field equations in harmonic coordinates
• On the linear stability of solitons and hairy black holes with a negative cosmological constant: the even-parity sector
• Physical interpretation of gauge invariant perturbations of spherically symmetric space-times
• Self-adjoint wave equations for dynamical perturbations of self-gravitating fields
• Non-Abelian Magnetized Blackholes and Unstable Attractors