arXiv 1701.014472017-01-05hep-thastro-ph.HEgr-qc

磁荷SU（2）Reissner-Nordström黑洞激发不稳定谱的解析处理

Analytic treatment of the excited instability spectra of the magnetically charged SU(2) Reissner-Nordström black holes

Shahar Hod

备注：: 7 pages
发表信息：: Journal of High Energy Physics 03, 072 (2017)

摘要：

耦合的非线性爱因斯坦-杨-米尔斯场方程的磁荷SU（2）Reissner-Nordström黑洞解被描述为不稳定（虚）共振的无限谱$\{ω_n(r_+,r_-)\}_{n=0}^{n=\infty}$（这里$r_{\pm}$是黑洞视界半径）。基于对黑洞不稳定性谱的直接{ \it数值}计算，最近观察到磁荷黑洞的激发不稳定性本征值具有简单的普适性。特别地，数值计算的磁荷黑洞的不稳定性特征值具有小频率普适关系$ω_n(r_+-r_-)=λ_n$的特征，其中$\{λ_n\}$是与黑洞参数无关的无量纲常数.本文研究了带电SU（2）Reissner-Nordström黑洞的不稳定性谱。特别是，我们提供了一个严格的{ \it分析}证明的{ \it数值}建议的普遍行为$ω_n(r_+-r_-)=λ_n$在小频率$ω_n r_+\ll (r_+-r_-)/r_+$制度。有趣的是，它表明，激发黑洞共振的特点是简单的普适关系$ω_{n+1}/ω_n=e^{-2π/\sqrt{3}}$。最后，我们用数值计算证实了我们对黑洞不稳定性谱的分析结果。

英文摘要：

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 $\{ω_n(r_+,r_-)\}_{n=0}^{n=\infty}$ (here $r_{\pm}$ are the black-hole horizon radii). Based on direct {\it 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 {\it analytical} proof for the {\it numerically}-suggested universal behavior $ω_n(r_+-r_-)=λ_n$ in the small frequency $ω_n r_+\ll (r_+-r_-)/r_+$ regime. Interestingly, it is shown that the excited black-hole resonances are characterized by the simple universal relation $ω_{n+1}/ω_n=e^{-2π/\sqrt{3}}$. Finally, we confirm our analytical results for the black-hole instability spectra with numerical computations.

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