Perturbation theory for self-gravitating gauge fields: The odd-parity sector - art. no. 084001

A gauge- and coordinate-invariant perturbation theory for self-gravitating non-Abelian gauge fields with the gauge group SU(2) is developed and used t o analyze local uniqueness and linear stability properties of non-Abelian e quilibrium configurations. It is shown that all admissible stationary odd-p arity excitations of the static and spherically symmetric Einstein-Yang-Mil ls soliton and black hole solutions have a total angular momentum number l = 1, and are characterized by nonvanishing asymptotic flux integrals. Local uniqueness and stability results with respect to non-Abelian perturbations are also established for the Schwarzschild and Reissner-Nordstrom solution s. Finally, unstable modes with l = 1 are excluded for the static and spher ically symmetric non-Abelian solitons and black holes.