Abstract
The magnetically charged SU(2) Reissner-Nordström black-hole solutions of the coupled nonlinear Einstein-Yang-Mills field equations are known to be characterized by infinite spectra of unstable (imaginary) resonances {ω n (r +, r −)} n = ∞ n = 0 (here r ± are the black-hole horizon radii). Based on direct numerical computations of the black-hole 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 ω n (r + − r −) = λ n , where {λ n } are dimensionless constants which are independent of the black-hole parameters. In the present paper we study analytically the instability spectra of the magnetically charged SU(2) Reissner-Nordström black holes. In particular, we provide a rigorous analytical proof for the numerically-suggested universal behavior ω n (r + − r −) = λ n in the small frequency ω n r + ≪ (r + − r −)/r + regime. Interestingly, it is shown that the excited black-√hole resonances are characterized by the simple universal relation ω n + 1/ω n = e − 2π/3. Finally, we confirm our analytical results for the black-hole instability spectra with numerical computations.
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Hod, S. Analytic treatment of the excited instability spectra of the magnetically charged SU(2) Reissner-Nordström black holes. J. High Energ. Phys. 2017, 72 (2017). https://doi.org/10.1007/JHEP03(2017)072
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DOI: https://doi.org/10.1007/JHEP03(2017)072