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Explore the analytical modeling of quasinormal mode excitation during black hole binary mergers in this 21-minute conference lecture from the Workshop on "Hyperboloidal Foliations and their Application" at the Erwin Schrödinger International Institute. Discover how the first analytical model predicts dynamical excitation of quasinormal modes throughout plunge-merger-ringdown stages for generic orbits, including highly eccentric configurations, working within the perturbative limit. Learn about the behavior of quasinormal modes as they travel on hyperboloidal slices in minimal gauge, with amplitudes functioning as activation functions near waveform peaks. Examine the emergence of an infinite tower of non-oscillatory, exponentially damped terms in the stationary ringdown regime, resulting from source redshift at the horizon and their potential to overwhelm overtone contributions. Understand how this theoretical prediction demonstrates good agreement with perturbative numerical solutions of binary mergers, while identifying the need for correct prompt response modeling to fully reproduce the merger stage. Conclude with the presentation of a closed-form model for prompt response in Schwarzschild spacetime, specifically valid for sources localized far from the black hole, providing insights into gravitational wave physics and black hole dynamics.
