It is well-known that the SU(2) Reissner-Nordstr\"om black-hole solutions of the 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 the excited instability spectrum of these magnetically charged black holes. The numerical results suggest the existence of a universal behavior for these black-hole excited eigenvalues. In particular, we show that unstable eigenvalues in the regime $\omega_n\ll T_{ \text{ BH}}$ are characterized, to a very good degree of accuracy, by the simple universal relation $\omega_n(r_+-r_-)={ \text{ constant}}$, where $r_{ \pm}$ are the horizon radii of the black hole.
Categories: gr-qc astro-ph.HE hep-th