Abstract

An extreme mass ratio inspiral terminates when the small compact object plunges into the large black hole (BH) it orbited. Its trajectory, hence also the emitted gravitational waveform, starts (quite) universally from the innermost stable circular orbit. Next, the binary merges and the final black hole rings down until it reaches steady state. In this stage the geometry constitutes an open resonant cavity for gravitational perturbations, which are described by quasinormal modes (QNMs). For a plunge into non-rotating BHs, I present (semi-) analytical results for the QNM ringdown amplitudes and hence the late time waveform, and successfully compare to amplitudes extracted from numerical waveforms. For near-extremal Kerr BHs, I present analytical results for the amplitudes, excited in the highly symmetric near-horizon region. I show part of the computation can be carried out at exact extremality and carried to near-extremality by diffeomorphism.