2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/36450We investigated the stability of the spherically symmetric non-abelian (Bartnik-McKinnon) black hole solution of the SU(2) Einstein-Yang-Mills system using the multiple-scale analysis. It is found, in contrast with the vacuum situation, that a spherically symmetric oscillatory perturbation to second order cannot be constructed. The singular behavior of gravitational waves is induced by the coupling of the gravitational waves to the Yang-Mills waves.5 pages in REVTEX. To appear in the proceedings of the XXXIV-th Rencontres de Moriond on "Gravitational Waves and Experimental Gravity", Les Arcs, France [January 23-30, 1999]General Relativity and Quantum Cosmologytext