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

Abstract

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