Analytic treatment of the excited instability spectra of the magnetically charged SU(2) ReissnerNordström black holes
Abstract
The magnetically charged SU(2) ReissnerNordström blackhole solutions of the coupled nonlinear EinsteinYangMills field equations are known to be characterized by infinite spectra of unstable (imaginary) resonances $\{\omega_n(r_+,r_)\}_{n=0}^{n=\infty}$ (here $r_{\pm}$ are the blackhole horizon radii). Based on direct {\it numerical} computations of the blackhole instability spectra, it has recently been observed that the excited instability eigenvalues of the magnetically charged black holes exhibit a simple universal behavior. In particular, it was shown that the numerically computed instability eigenvalues of the magnetically charged black holes are characterized by the small frequency universal relation $\omega_n(r_+r_)=\lambda_n$, where $\{\lambda_n\}$ are dimensionless constants which are independent of the blackhole parameters. In the present paper we study analytically the instability spectra of the magnetically charged SU(2) ReissnerNordström black holes. In particular, we provide a rigorous {\it analytical} proof for the {\it numerically}suggested universal behavior $\omega_n(r_+r_)=\lambda_n$ in the small frequency $\omega_n r_+\ll (r_+r_)/r_+$ regime. Interestingly, it is shown that the excited blackhole resonances are characterized by the simple universal relation $\omega_{n+1}/\omega_n=e^{2\pi/\sqrt{3}}$. Finally, we confirm our analytical results for the blackhole instability spectra with numerical computations.
 Publication:

arXiv eprints
 Pub Date:
 January 2017
 arXiv:
 arXiv:1701.01447
 Bibcode:
 2017arXiv170101447H
 Keywords:

 High Energy Physics  Theory;
 Astrophysics  High Energy Astrophysical Phenomena;
 General Relativity and Quantum Cosmology
 EPrint:
 7 pages