We analytically prove the linear radial stability of non-Abelian black holes with quartic self-interactions. The background, constructed from the Wu-Yang magnetic monopole ansatz, is an exact black-hole solution carrying a non-Abelian magnetic charge $Q_{\mathrm{NA}}^2$ controlled by a single coupling parameter $\chi$, and admits two distinct branches. The odd sector is always stable, while in the even sector the effective potential is positive for branch I and negative for branch II, establishing stability and potential instability, respectively. The potential instability of branch II is consistent with its connection to the perturbatively unstable Einstein–Yang-Mills Reissner-Nordström solution. Branch I remains linearly stable throughout the physical domain of $\chi$ where the solutions are regular and free of naked singularities. The stability of branch I is further confirmed through a numerical computation of the quasinormal mode spectrum using Leaver’s continued fraction method and time-domain evolution supplemented with Prony’s method, showing no unstable modes. Our results prove the existence of the first linearly stable asymptotically flat hairy black holes in four dimensions with a minimally coupled non-Abelian Proca self-interaction.

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• Alternative gravity theories
• Classical black holes
• General relativity
• General relativity equations & solutions
• General relativity formalism