发表机构
School of Physics and Astronomy, Beijing Normal University; School of Mathematics, Yunnan Normal University; Institute for Frontiers in Astronomy and Astrophysics, Beijing Normal University; School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, UCAS; Department of Physics, Key Laboratory of Low Dimensional Quantum Structures and Quantum Control of Ministry of Education, Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University（北京师范大学物理与天文学院; 云南师范大学数学学院; 北京师范大学前沿天文与天体物理研究所; 中国科学院大学杭州高等研究院基础科学与数学学院; 湖南师范大学物理学系、教育部低维量子结构与量子控制重点实验室、量子效应与应用协同创新中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究构造了Kerr黑洞引力全透射模式的完整谱，发现四个全局连续族，修正了先前分类，并揭示了发散分支与异常近邻关系。
AI 中文摘要
我们构造了Kerr黑洞引力全透射模式（TTMs）的完整谱，并发现了四个全局连续族，$n_\infty=1,2,3,4$。与Cook和Lu [Phys. Rev. D 107, 044043 (2023)]的三族分类相比，我们的全局延拓将固定$m$下的复共轭与连接$m$和$-m$谱的镜像对称性分开，从而在不引入额外非对称相关根的情况下，得到统一的四族分类。$n_\infty=3$族趋近于Schwarzschild代数特殊频率，而$n_\infty=1,2,$和$4$族沿下半平面方向$-150^\circ$、$-90^\circ$和$-30^\circ$发散，渐近行为为$\omega\propto a^{-4/3}$。高达$\ell=32$的高精度数据恢复了Cook-Lu小自旋渐近性，并展示了发散分支如何嵌入全局四族谱中。球面极限的极向标记和大$|a\omega|$角向排序以依赖于族的方式相关联。对于轴对称扰动，我们表明$n_\infty=2$和$n_\infty=3$分支在例外点处合并，随后演化至不同的小自旋极限，而非表现出Cook和Lu提出的泛音多重态分裂。最后，我们识别出$n_\infty=3$ TTM族与非常规Kerr准正则模序列之间先前未报道的异常接近，分离度达到$10^{-8}$量级，同时数值上仍可清晰分辨。
英文摘要
We construct the complete spectrum of gravitational total-transmission modes (TTMs) of Kerr black holes and find four globally continuous families, $n_\infty=1,2,3,4$, each with two complex-conjugate frequency branches. Compared with the three-family classification of Cook and Lu, our global continuation resolves the mirror-related sectors of their $n=2$ family into separate families without introducing additional symmetry-unrelated roots. This organization distinguishes complex conjugation at fixed $m$ from the mirror symmetry connecting the $m$ and $-m$ spectra. The $n_\infty=3$ family approaches the Schwarzschild algebraically special frequency, whereas the $n_\infty=1,2,$ and $4$ families diverge as $ω\propto a^{-4/3}$ along lower-half-plane directions $-150^\circ$, $-90^\circ$, and $-30^\circ$, respectively. High-precision data up to $\ell=32$ confirm the Cook--Lu small-spin asymptotics and reveal how the divergent branches are embedded in the global four-family spectrum, with a family-dependent relation between the spherical-limit angular labels and the large-$|aω|$ ordering. For axisymmetric perturbations, the $n_\infty=2$ and $n_\infty=3$ branches coalesce at genuine exceptional points, where the scattering spectral function develops a second-order zero and the TTM excitation factors are strongly enhanced, offering a different interpretation of the structure previously described by Cook and Lu as an overtone-multiplet splitting. Finally, we identify a previously unreported anomalous proximity between the $n_\infty=3$ TTM family and an unconventional Kerr quasinormal-mode sequence, with frequency separations reaching order $10^{-8}$ in the representative case studied.
Comments24 pages,13 figures
