Numerical evidence for universality in the excited instability spectrum of magnetically charged Reissner–Nordström black holes

It is well known that the SU(2) Reissner– Nordström black-hole solutions of the Einstein–Yang–Mills theory are characterized by an infinite set of unstable (imaginary) eigenvalues {ωn(TBH)}n=∞ n=0 (here TBH 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 ωn TBH are characterized, to a very good degree of accuracy, by the simple universal relation ωn(r+ − r−) = constant, where r± are the horizon radii of the black hole.