发表机构
Kyoto University; Kindai University; RIKEN iTHEMS; The Hakubi Center for Advanced Research, Kyoto University（京都大学; 近畿大学; 理化学研究所 iTHEMS; 京都大学博雅研究高级中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出极点分裂方法分离Kerr黑洞振铃波形，揭示直接波频率与衰减率可探测能层及红移效应。
AI 中文摘要
我们阐述了极端质量比并合情形下直接波（DW）的理论方面。直接波是一种源驱动的波形，其特征为复频率$\omega_{\rm G}$，该频率反映了粒子在黑洞附近的轨道运动，包括轨道在能层内部的部分：其实部由参考系拖曳决定，虚部由源的引力红移决定。利用格林函数技术，我们推导了源驱动频率$\omega_{\rm G}$，描述了势垒对其的屏蔽作用，并讨论了其与动力学激发的准正则模（QNMs）的关系。我们还讨论了直接波的晚期衰减，并预测其以三阶视界模衰减。随后，我们引入了一种极点分裂方法，该方法将整个波形划分为QNM极点部分和非QNM部分。与QNM滤波（将波形频谱乘以滤波函数，从而通过依赖于频率的时间平移（即群延迟）使波形变形）不同，我们的极点分裂方法仅将传递函数划分为极点部分和非极点部分，从而分离出完整波形。模拟中等自旋和快速自旋Kerr黑洞的准圆旋入，我们发现主导模$\ell = m = 2$中非极点部分的频率和衰减率与$\omega_{\rm G}$或其屏蔽对应量$\omega_{\rm screen}$一致演化，从而确立了直接波作为能层和黑洞周围红移效应的探针。
英文摘要
We formulate the theoretical aspects of direct waves (DWs) in the case of extreme-mass merger. A DW is a source-driven waveform characterized by a complex frequency $ω_{\rm G}$, which reflects the orbital motion of the particle in the vicinity of the black hole, including a part of the orbit inside the ergoregion: its real part is governed by frame dragging and its imaginary part by the redshift of the source. Using the Green's function technique, we derive the source-driven frequency $ω_{\rm G}$, describe its screening by the potential barrier, and discuss its relation to dynamically excited quasinormal modes (QNMs). We then introduce a pole-splitting method that divides the full waveform into a QNM-pole sector and a non-QNM sector. Unlike QNM filtering, which multiplies the waveform spectrum by a filter function and thereby deforms it through a frequency-dependent time shift (i.e., group delay), our pole-splitting method merely divides the transfer function into pole and non-pole parts, separating the full waveform. Simulating a quasi-circular plunge into a Kerr black hole with medium and rapid spins, we find that the frequency and decay rate of the non-pole sector in the dominant mode, $\ell = m = 2$, evolve consistently with $ω_{\rm G}$-or with its screened counterpart $ω_{\rm screen}$-establishing the DW as a probe of the ergoregion and of the redshift effect around a black hole.
Comments17 pages, 8 figures. Sec. II F and all related discussion have been removed because the analysis in that section was incorrect. The main results and conclusions are unaffected
