标题： 关于近极端Kerr黑洞准正则共振的分支 显示英文标题

标题： On the branching of the quasinormal resonances of near-extremal Kerr black holes

摘要： 最近由Yang等人[Phys. Rev. D{\bf 87}, 041502(R) (2013)]证明，旋转的Kerr黑洞由两组不同的准正则共振特征。这两种准正则共振家族在极端（$a/M\to 1$）黑洞极限中表现出定性不同的渐近行为：零阻尼模（ZDMs）的特点是弛豫时间趋向于无穷大，在极端黑洞极限中（$\Im\omega\to 0$作为$a/M\to 1$），而阻尼模（DMs）的特点是非零阻尼率（$\Im\omega\to$为有限值作为$a/M\to 1$）。在本文中，我们反驳了Yang等人提出的说法。 共旋的暗模（DMs）仅限于有限范围$0\leq \mu\lesssim\mu_{\text{c}}\approx 0.74$，其中$\mu\equiv m/l$是扰动模的方位调和指数$m$与球面调和指数$l$之间的无量纲比值。 特别是，我们使用 Detweiler 最初推导出的解析公式，以证明近极端黑洞在$\mu>\mu_{\text{c}}$范围内存在 DMs（阻尼准正则共振，其特征是$a/M\to 1$极限下有限的$\Im\omega$值），这个范围曾被 Yang 等人声称不包含阻尼模。 我们表明，在 regime$\mu>\mu_{\text{c}}$范围内，这些共旋 DMs 预期将表征快速旋转（近极端）黑洞的共振谱，其中$a/M\gtrsim 1-10^{-9}$。 显示英文摘要

摘要： It has recently been shown by Yang. et. al. [Phys. Rev. D {\bf 87}, 041502(R) (2013)] that rotating Kerr black holes are characterized by two distinct sets of quasinormal resonances. These two families of quasinormal resonances display qualitatively different asymptotic behaviors in the extremal ($a/M\to 1$) black-hole limit: The zero-damping modes (ZDMs) are characterized by relaxation times which tend to infinity in the extremal black-hole limit ($\Im\omega\to 0$ as $a/M\to 1$), whereas the damped modes (DMs) are characterized by non-zero damping rates ($\Im\omega\to$ finite-values as $a/M\to 1$). In this paper we refute the claim made by Yang et. al. that co-rotating DMs of near-extremal black holes are restricted to the limited range $0\leq \mu\lesssim\mu_{\text{c}}\approx 0.74$, where $\mu\equiv m/l$ is the dimensionless ratio between the azimuthal harmonic index $m$ and the spheroidal harmonic index $l$ of the perturbation mode. In particular, we use an analytical formula originally derived by Detweiler in order to prove the existence of DMs (damped quasinormal resonances which are characterized by finite $\Im\omega$ values in the $a/M\to 1$ limit) of near-extremal black holes in the $\mu>\mu_{\text{c}}$ regime, the regime which was claimed by Yang et. al. not to contain damped modes. We show that these co-rotating DMs (in the regime $\mu>\mu_{\text{c}}$) are expected to characterize the resonance spectra of rapidly-rotating (near-extremal) black holes with $a/M\gtrsim 1-10^{-9}$.