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Stellar-mass binaries evolving in the vicinity of supermassive black holes (SMBHs) may be common in the universe, either in active galactic nuclei or in other astrophysical environments. Here, we study in detail the resonant excitation of SMBH modes driven by a nearby stellar-mass binary. The resulting resonant energy fluxes vary with the orbital location and frequency of the binary, exhibiting a rich and complex structure. In particular, we find that the total energy flux radiated to infinity is maximized at a gravitational-wave frequency that is close, but not exactly equal to, the real part of the corresponding quasi-normal-mode frequency. Moreover, as the binary is moved farther away from the SMBH, this offset from the mode frequency becomes increasingly pronounced. In addition, for suitable orientations, the binary can effectively “feed” the light ring of the SMBH, selectively exciting particular oscillation modes. For rotating (Kerr) black holes, the mode spectrum is significantly more intricate; however, individual modes are also less strongly damped, leading to an enhanced—but more difficult to interpret—resonant response. 

We uncover late-time gravitational-wave tails in fully nonlinear $3+1$ dimensional numerical relativity simulations of merging black holes, using the highly accurate p code. We achieve this result by exploiting the strong magnification of late-time tails due to binary eccentricity, recently observed in perturbative evolutions, and showcase here the tail presence in head-on configurations for several mass ratios close to unity. We validate the result through a large battery of numerical tests and detailed comparison with a perturbative evolution, which display striking agreement with full nonlinear ones in the ringdown regime, and very similar tail morphologies. Our results offer yet another confirmation of the highly predictive power of black hole perturbation theory in the presence of a source, even when applied to nonlinear solutions. The late-time tail signal is much more prominent than anticipated until recently, and possibly within reach of gravitational-wave detector measurements, unlocking observational investigations of an additional set of general relativistic predictions on the long-range gravitational dynamics. 

Abstract The ‘ringdown’ radiation emitted by oscillating black holes has great scientific potential. By carefully predicting the frequencies and amplitudes of black hole quasinormal modes and comparing them with gravitational-wave (GW) data from compact binary mergers we can advance our understanding of the two-body problem in general relativity, verify the predictions of the theory in the regime of strong and dynamical gravitational fields, and search for physics beyond the Standard Model or new gravitational degrees of freedom. We summarize the state of the art in our understanding of black hole quasinormal modes in general relativity and modified gravity, their excitation, and the modeling of ringdown waveforms. We also review the status of LIGO-Virgo-KAGRA ringdown observations, data analysis techniques, and the bright prospects of the field in the era of LISA and next-generation ground-based GW detectors.