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It is well-known that the SU(2) Reissner-Nordstr\"om black-hole solutions ofthe Einstein-Yang-Mills theory are characterized by an infinite set of unstable(imaginary) eigenvalues $\{\omega_n(T_{\text{BH}})\}_{n=0}^{n=\infty}$ (here$T_{\text{BH}}$ is the black-hole temperature). In this paper we analyze theexcited instability spectrum of these magnetically charged black holes. Thenumerical results suggest the existence of a universal behavior for theseblack-hole excited eigenvalues. In particular, we show that unstableeigenvalues in the regime $\omega_n\ll T_{\text{BH}}$ are characterized, to avery good degree of accuracy, by the simple universal relation$\omega_n(r_+-r_-)={\text{constant}}$, where $r_{\pm}$ are the horizon radii ofthe black hole.

Numerical evidence for universality in the excited instability spectrum of magnetically charged Reissner-Nordstr\"om black holes