In a binary black hole merger event, the gravitational waves emitted consist of three major stages: inspiral, merger, and ringdown. The final ringdown stage corresponds to the oscillation of the remnant black hole, which encodes rich information about the system in an extreme gravity regime.
The ringdown gravitational waves are described by a superposition of exponentially damped sinusoids – a set of complex-valued quasinormal modes (QNMs). These modes, labelled by two angular numbers l, m, and an overtone index n, are solutions to the linearized Einstein’s equations in the background of a Kerr black hole and are fully determined by the mass and spin of the remnant black hole due to the no-hair theorem. Thus, studying the modes observed in a ringdown gravitational wave to test the black hole no-hair theorem is also known as “black hole spectroscopy.” Measuring the frequency and decay rate of the QNMs provides a way to estimate the mass and spin of the remnant black hole formed in the merger.
With the improving sensitivity of the gravitational-wave detector network, the observation of an increasing number of binary black hole mergers, especially the increasing signal-to-noise ratio in the ringdown signal, will allow us to test Einstein’s general theory of relativity and explore the nature of gravity in full detail using these real detections.
At the Centre for Gravitational Astrophysics, we are actively studying the numerical waveforms of the black hole ringdown, implementing tools and analysis frameworks, and analyzing the latest gravitational wave detector data [1-4].
 S. Ma, L. Sun, Y. Chen, Black hole spectroscopy by mode cleaning, Phys. Rev. Lett. 130, 141401 (2023), arXiv:2301.06705
 S. Ma, L. Sun, Y. Chen, Using rational filters to uncover the first ringdown overtone in GW150914, Phys. Rev. D 107, 084010 (2023), arXiv:2301.06639
 S. Ma, K. Mitman, L. Sun, N. Deppe, F. Hébert, L. E. Kidder, J. Moxon, W. Throwe, N. L. Vu, Y. Chen, Quasinormal-mode filters: A new approach to analyze the gravitational-wave ringdown of binary black-hole mergers, Phys. Rev. D 106, 084036 (2022), arXiv:2207.10870
 X. Li, L. Sun, R. K. L. Lo, E. Payne, Y. Chen, Angular emission patterns of remnant black holes, Phys. Rev. D 105, 024016 (2022), arXiv:2110.03116