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The detection of quadratic quasi-normal modes would provide a direct probe into black hole nonlinear perturbations. We report the first observational evidence of a set of quadratic quasi-normal modes in the gravitational-wave ringdown of a…

General Relativity and Quantum Cosmology · Physics 2026-01-12 Yi-Fan Wang , Sizheng Ma , Neev Khera , Huan Yang

The ringdown phase of a gravitational wave signal from a binary black hole merger offers a unique laboratory for testing general relativity in the strong-field regime and probing the properties of the final remnant black hole. In this…

General Relativity and Quantum Cosmology · Physics 2025-09-03 Hai-Tian Wang , Shao-Peng Tang , Peng-Cheng Li , Yi-Zhong Fan

We report evidence for nonlinear modes in the ringdown stage of the gravitational waveform produced by the merger of two comparable-mass black holes. We consider both the coalescence of black hole binaries in quasicircular orbits and…

The ringdown gravitational wave signal arising e.g., in the final stage of a black hole binary merger, contains important information about the properties of the remnant, and can potentially be used to perform clean tests of general…

General Relativity and Quantum Cosmology · Physics 2024-11-22 Taillte May , Sizheng Ma , Justin L. Ripley , William E. East

Due to the nature of gravity, non-linear effects are left imprinted in the quasi-normal modes generated in the ringdown phase of the merger of two black holes. We offer an analytical treatment of the quasi-normal modes at second-order in…

General Relativity and Quantum Cosmology · Physics 2024-04-09 Davide Perrone , Thomas Barreira , Alex Kehagias , Antonio Riotto

In the aftermath of a binary black hole merger event, the gravitational wave signal emitted by the remnant black hole is modeled as a superposition of damped sinusoids known as quasinormal modes. While the dominant quasinormal modes…

General Relativity and Quantum Cosmology · Physics 2024-06-18 Sophia Yi , Adrien Kuntz , Enrico Barausse , Emanuele Berti , Mark Ho-Yeuk Cheung , Konstantinos Kritos , Andrea Maselli

The nonlinear nature of general relativity manifests prominently throughout the merger of two black holes, from the inspiral phase to the final ringdown. Notably, the quasi-normal modes generated during the ringdown phase display…

General Relativity and Quantum Cosmology · Physics 2024-11-13 A. Kehagias , A. Riotto

The modeling of gravitational wave ringdown has traditionally relied on linear perturbation theory, which mainly describes the late-time behavior of a perturbed black hole after a binary merger. However, the need for more accurate ringdown…

General Relativity and Quantum Cosmology · Physics 2026-04-03 Macarena Lagos

Black hole (BH) oscillations known as quasi-normal modes (QNMs) are one of the most important gravitational wave (GW) sources. We propose that higher perturbative order of QNMs, generated by nonlinear gravitational interaction near the BHs,…

Astrophysics · Physics 2008-12-18 Kunihito Ioka , Hiroyuki Nakano

Gravitational-wave observations of black hole ringdowns are commonly used to characterize binary merger remnants and to test general relativity. These analyses assume linear black hole perturbation theory, in particular that the ringdown…

General Relativity and Quantum Cosmology · Physics 2022-08-31 Laura Sberna , Pablo Bosch , William E. East , Stephen R. Green , Luis Lehner

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…

General Relativity and Quantum Cosmology · Physics 2024-10-10 Collin D. Capano , Jahed Abedi , Shilpa Kastha , Alexander H. Nitz , Julian Westerweck , Yi-Fan Wang , Miriam Cabero , Alex B. Nielsen , Badri Krishnan

We estimate the degree of squeezing possible in gravitational waves due to nonlinear gravitational effects in the weakly perturbative regime. Using the predicted amplitude ratios for higher harmonic generation in the ringdown phase of a…

General Relativity and Quantum Cosmology · Physics 2026-04-17 Sreenath K. Manikandan , Frank Wilczek

The recent first detection of gravitational waves (GWs) from binary black hole mergers has spurred a renewed interest in possible deviations from General Relativity (GR), since they could be detected in the GWs emitted by such systems. Of…

General Relativity and Quantum Cosmology · Physics 2022-11-03 Hugo Roussille

The gravitational wave strain emitted by a perturbed black hole (BH) ringing down is typically modeled analytically using first-order BH perturbation theory. In this Letter we show that second-order effects are necessary for modeling…

After black holes collide, the remnant settles to a stationary state by emitting gravitational waves. Once non-linearities subside, these ringdown waves are dominated by exponentially-damped sinusoids, or quasinormal modes. We develop a…

General Relativity and Quantum Cosmology · Physics 2024-11-05 Adrian Ka-Wai Chung , Nicolas Yunes

The remnant black hole from a binary coalescence emits ringdown gravitational waves characterized by quasinormal modes, which depend solely on the remnant's mass and spin. In contrast, the ringdown amplitudes and phases are determined by…

General Relativity and Quantum Cosmology · Physics 2024-12-04 Costantino Pacilio , Swetha Bhagwat , Francesco Nobili , Davide Gerosa

We present a new method to search for gravitational waves from quasinormal modes in the ringdowns of the remnants of the mergers of the binary black hole systems. The method is based on maximum likelihood estimation. We derive a time-domain…

General Relativity and Quantum Cosmology · Physics 2026-04-28 A. Królak , O. Dorosh

It has been recently shown that nonlinear effects emerging at the time of the generation of the quasi-normal modes are necessary to model ringdowns from black hole mergers. In this note, we describe how nonlinerarities also arise when…

General Relativity and Quantum Cosmology · Physics 2023-02-03 Alex Kehagias , Antonio Riotto

The gravitational waves emitted by a perturbed black hole ringing down are well described by damped sinusoids, whose frequencies are those of quasinormal modes. Typically, first-order black hole perturbation theory is used to calculate…

Observations of gravitational waves (GWs) generated by binary black hole (BBH) mergers provide us with a powerful way to explore the strong and highly dynamical regime of gravity theories. The ringdown of BBH merger, consisting of a series…

General Relativity and Quantum Cosmology · Physics 2026-02-24 Zexin Hu , Daniela D. Doneva , Stoytcho S. Yazadjiev , Lijing Shao
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