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arXiv · 2605.16005

Stable colored black holes with quartic self-interactions

Jose F. Rodriguez-Ruiz·Gabriel Gomez
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Abstract

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 $Q_{\rm NA}^2$ 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-Nordstr\"{o}m 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 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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Jose F. Rodriguez-Ruiz, Gabriel Gomez. 2026-05-15. Stable colored black holes with quartic self-interactions. https://doi.org/10.1103/t21m-d4hd

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