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) Reissner-Nordström 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.

4 pages

References in corpus (1)

• Formation and decay of Einstein-Yang-Mills black holes