In black hole perturbation formalism, the gravitational waveform is obtained by the convolution of the Green's function and the source term causing radiation emission. Hence, the ringdown properties, namely its start time, depend on both functions. The unknown time-shift encoded in the Green's function introduces a "time-shift problem" for ringdown. We study the ringdown time-shift problem by reconstructing a waveform via the excitation factors of quasi-normal modes (QNMs) of a spinning black hole. For the first time, we reconstruct ringdown with a significant number of QNMs weighted with their excitation factors and confirm its excellent convergence. We then precisely identify the ringdown starting time. We also find (i) that for moderate or large spins and $\ell=m=2$, QNMs should be included up to around the $20$th prograde overtones and around fifth retrograde overtones to reconstruct the ringdown waveform for the delta-function source with a mismatch threshold $ M < O(10^{-3})$. For higher angular modes, a more significant number of QNMs are necessary to reconstruct it; (ii) that the time shift of ringdown caused by the Green's function is the same for different $(\ell, m, n)$ modes but that nontrivial sources can change this conclusion. Finally, we demonstrate (iii) that the greybody factor can be reconstructed with the superposed QNM spectrum in the frequency domain.
Shaping black hole resonances I. Black hole ringdown as a spectral filtering process
Universitat de les Illes Balears（巴利阿里群岛大学）；Gran Sasso Science Institute (GSSI)（格兰萨索科学研究所）；INFN, Laboratori Nazionali del Gran Sasso（意大利国家核物理研究所，格兰萨索国家实验室）
Ringdown of a postinnermost stable circular orbit of a rapidly spinning black hole: Mass ratio dependence of higher harmonic quasinormal mode excitation
Identifying Exceptional Points in Black Hole Ringdowns
Nankai University（南开大学）；Yantai University（烟台大学）；The Hong Kong University of Science and Technology（香港科技大学）；The HKUST Jockey Club Institute for Advanced Study（香港科技大学赛马会高等研究院）
Avoided crossings and resonances in black hole ringdown with coupled fields: A case study of the Einstein-Maxwell-axion system
Research Center for the Early Universe (RESCEU), Graduate School of Science, The University of Tokyo（东京大学理学研究系早期宇宙研究中心）；Department of Physics, Tokyo Metropolitan University（东京都立大学物理学系）
Quasi-Normal Mode Ringing of Binary Black Hole Mergers in Scalar-Gauss-Bonnet Gravity
Peking University（北京大学）；Kavli Institute for Astronomy and Astrophysics, Peking University（北京大学科维理天文与天体物理研究所）；Eberhard Karls University of Tübingen（蒂宾根大学）；INRNE - Bulgarian Academy of Sciences（保加利亚科学院核研究与核能研究所）；Sofia University “St. Kliment Ohridski”（索菲亚大学）；Institute of Mathematics and Informatics, Bulgarian Academy of Sciences（保加利亚科学院数学与信息学研究所）；National Astronomical Observatories, Chinese Academy of Sciences（中国科学院国家天文台）
Vanishing of all redshift modes in Schwarzschild ringdown
CENTRA, Departamento de Física, Instituto Superior Técnico – IST, Universidade de Lisboa – UL（里斯本大学高等理工学院物理系CENTRA）；Dipartimento di Fisica, Sapienza Università di Roma（罗马智慧大学物理系）；INFN, Sezione di Roma（罗马意大利国家核物理研究所）
Excitation factors for horizonless compact objects: long-lived modes, echoes, and greybody factors
Dipartimento di Fisica, Sapienza Università di Roma（罗马大学物理系）；INFN, Sezione di Roma（意大利国家核物理研究所罗马分部）；Indian Institute of Technology, Gandhinagar（印度理工学院甘地纳加尔分校）；School of Physical Sciences, Indian Association for the Cultivation of Science（印度科学培养协会物理科学学院）
Exceptional Lines and Excitation of (Nearly) Double-Pole Quasinormal Modes: A Semi-Analytic Study in the Nariai Black Hole
Kyoto University（京都大学）；Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所）；The Hakubi Center for Advanced Research, Kyoto University（京都大学博雅中心）；RIKEN iTHEMS（理化学研究所iTHEMS）；Kindai University（近畿大学）
Universitat de les Illes Balears（巴利阿里群岛大学）；Gran Sasso Science Institute (GSSI)（格兰萨索科学研究所）；INFN, Laboratori Nazionali del Gran Sasso（意大利国家核物理研究所，格兰萨索国家实验室）
Niels Bohr Institute（尼尔斯·玻尔研究所）；CENTRA, Departamento de Fisica, Instituto Superior Técnico – IST, Universidade de Lisboa – UL（科英布拉天体物理与中心研究中心，物理学系，高等技术学院，里斯本大学）；University of Birmingham（伯明翰大学）；University of Nottingham（诺丁汉大学）
Quasinormal modes and their excitation beyond general relativity. II: isospectrality loss in gravitational waveforms
The Grainger College of Engineering, University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校格兰杰工程学院）；Max Planck Institute for Gravitational Physics (Albert Einstein Institute)（马克斯·普朗克引力物理研究所（爱因斯坦研究所））；ETH Zürich（苏黎世联邦理工学院）；Universidad de Murcia（穆尔西亚大学）；University of Tübingen（蒂宾根大学）；University of Virginia（弗吉尼亚大学）
Gravitational waves in massive gravity: Waveforms generated by a particle plunging into a black hole and the excitation of quasinormal modes and quasibound states
Gravitational perturbations of a regular T-duality inspired black hole: Quasinormal modes, excitation factors, and time-domain evolution
University of Hradec Králové（赫拉德茨克拉洛韦大学）；National Research University TIIAME（塔什干国立技术大学TIIAME）；Tashkent State Technical University（塔什干国立技术大学）；National University of Uzbekistan（乌兹别克斯坦国立大学）；University of Tashkent for Applied Sciences（塔什干应用科学大学）；Kimyo International University in Tashkent（塔什干化学国际大学）；Samarkand State Pedagogical Institute（撒马尔罕国立师范学院）；University of Economics and Pedagogy（经济与师范大学）
研究正则 T 对偶启发的黑洞轴向引力微扰，用高阶 WKB - Padé 方法计算准正则模等，通过时域演化验证主导模。发现开启零点长度时，特定引力模式频率实部增加、阻尼率变化有特点，且激发因子大小变化相对准正则频率较小。
