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In this Reply we include the corrections suggested in the Comment [Phys. Rev. Lett. 131, 169001]. We show that their impact on our results is small, and that the overall conclusion of the Article [Phys. Rev. Lett. 129, 111102] are robust.…

广义相对论与量子宇宙学 · 物理学 2023-11-01 Gregorio Carullo , Roberto Cotesta , Emanuele Berti , Vitor Cardoso

Black hole spectroscopy with gravitational waves is an important tool to measure the mass and spin of astrophysical black holes and to test their Kerr nature. Next-generation ground- and space-based detectors will observe binary black hole…

广义相对论与量子宇宙学 · 物理学 2022-10-26 Emanuele Berti , Vitor Cardoso , Mark Ho-Yeuk Cheung , Francesco Di Filippo , Francisco Duque , Paul Martens , Shinji Mukohyama

The ringdown phase of a gravitational wave (GW) signal from a binary black hole merger provides valuable insights into the properties of the final black hole and serves as a critical test of general relativity in the strong-field regime. A…

广义相对论与量子宇宙学 · 物理学 2025-03-12 Hai-Tian Wang , Ziming Wang , Yiming Dong , Garvin Yim , Lijing Shao

Distorted black holes radiate gravitational waves. In the so-called ringdown phase radiation is emitted in a discrete set of complex quasinormal frequencies, whose values depend only on the black hole's mass and angular momentum. Ringdown…

广义相对论与量子宇宙学 · 物理学 2009-11-11 Emanuele Berti , Vitor Cardoso

We propose a new way of analyzing, and analytically representing, the ringdown part of the gravitational wave signal emitted by coalescing black hole binaries.By contrast with the usual {\it linear} decomposition of the multipolar complex…

广义相对论与量子宇宙学 · 物理学 2015-06-19 Thibault Damour , Alessandro Nagar

A major aim of gravitational wave astronomy is to test observationally the Kerr nature of black holes. The strongest such test, with minimal additional assumptions, is provided by observations of multiple ringdown modes, also known as black…

While black hole perturbation theory predicts a rich quasi-normal mode structure, technical challenges have limited the numerical study of excitations to the fundamental, lowest order modes caused by the coalescence of black holes. Here, we…

广义相对论与量子宇宙学 · 物理学 2017-02-22 Lionel London , James Healy , Deirdre Shoemaker

The excitation factors of black hole quasinormal modes quantify the $\textit{ease of excitation}$ of the quasinormal modes and are independent of the source of perturbation. We compute the excitation factors of Kerr black holes up to the…

广义相对论与量子宇宙学 · 物理学 2022-06-07 Naritaka Oshita

We study how quasinormal-mode frequencies may encode information about the effective matter source responsible for black-hole hair. Using the established eikonal correspondence between quasinormal modes and unstable null geodesics, we…

广义相对论与量子宇宙学 · 物理学 2026-05-20 Ariadna Uxue Palomino Ylla , Kosuke Makino , Akane Tanaka , Akihiro Ishibashi , Chul-Moon Yoo

Quasinormal modes are a set of damped resonances that describe how an excited open system is driven back to equilibrium. In gravitational physics these modes characterise the ringdown of a perturbed black hole, e.g. following a binary black…

广义相对论与量子宇宙学 · 物理学 2018-08-09 Sam Patrick , Antonin Coutant , Mauricio Richartz , Silke Weinfurtner

GW231123 is a short-duration, low-frequency gravitational wave signal consistent with a binary black hole coalescence and dominated by the merger-ringdown regime due to the high mass of the source. We demonstrate that fits of this ringdown…

广义相对论与量子宇宙学 · 物理学 2025-11-05 Harrison Siegel , Nicole M. Khusid , Maximiliano Isi , Will M. Farr

We develop a search method for gravitational ringing of black holes. The gravitational ringing is due to complex frequency modes called the quasi-normal modes that are excited when a black hole geometry is perturbed. The detection of it…

广义相对论与量子宇宙学 · 物理学 2009-10-09 Hiroyuki Nakano , Hirotaka Takahashi , Hideyuki Tagoshi , Misao Sasaki

The analytical understanding of quasinormal mode ringing requires an accurate knowledge of the Green's function describing the response of the black hole to external perturbations. We carry out a comprehensive study of quasinormal mode…

广义相对论与量子宇宙学 · 物理学 2014-01-23 Zhongyang Zhang , Emanuele Berti , Vitor Cardoso

The ringdown of a perturbed black hole consists of a superposition of quasi-normal modes (QNMs), with complex frequencies determined by the black hole's mass and spin, while phases and amplitudes depend on binary parameters. Traditional…

广义相对论与量子宇宙学 · 物理学 2025-09-23 Koustav Chandra , Juan Calderón Bustillo

Quasinormal modes of rapidly rotating black holes are crucial in understanding the ringdown phase after a merger. While for Kerr black holes these modes have been known for a long time, their calculation has remained a challenge in…

广义相对论与量子宇宙学 · 物理学 2025-01-22 Jose Luis Blázquez-Salcedo , Fech Scen Khoo , Burkhard Kleihaus , Jutta Kunz

In this paper, we investigate the quasinormal mode (QNM) spectra for scalar perturbation over a quantum-corrected black hole (BH). The fundamental modes of this quantum-corrected BH exhibit two key properties. Firstly, there is a…

广义相对论与量子宇宙学 · 物理学 2024-01-09 Huajie Gong , Shulan Li , Dan Zhang , Guoyang Fu , Jian-Pin Wu

We employ the isomonodromic method to study linear scalar massive perturbations of Kerr black holes for generic scalar masses $M\mu$ and generic black hole spins $a/M$. We find that the longest-living quasinormal mode and the first overtone…

广义相对论与量子宇宙学 · 物理学 2024-12-31 João Paulo Cavalcante , Maurício Richartz , Bruno Carneiro da Cunha

This study delves into the existence of dark matter around supermassive black holes in galactic cores using a novel gravitational model. By analyzing gravitational waves emitted during the ringdown phase of black holes under different field…

广义相对论与量子宇宙学 · 物理学 2025-03-14 Jie Liang , Dong Liu , Hao-Jie Lin , Zheng-Wen Long

Quasinormal modes of perturbed black holes have recently gained much interest because of their tight relations with the gravitational wave signals emitted during the post-merger phase of a binary black hole coalescence. One of the…

广义相对论与量子宇宙学 · 物理学 2021-03-03 Che-Yu Chen , Mariam Bouhmadi-López , Pisin Chen

Quasinormal modes are excited during the ringdown phase of black holes after merger. Determination of quasinormal modes of rapidly rotating black holes in alternative theories of gravity has remained a challenge for a long time. Here we…

广义相对论与量子宇宙学 · 物理学 2025-03-06 Jose Luis Blázquez-Salcedo , Fech Scen Khoo , Burkhard Kleihaus , Jutta Kunz