Repeated ringing of black holes: Quasinormal bursts from highly eccentric, extreme mass-ratio binaries

Recent studies of scalar and gravitational waveforms from high-eccentricity, extreme mass-ratio black-hole binaries show the presence of quasinormal bursts (QNBs), lingering high-frequency decaying oscillations (also known as “wiggles”), soon after each periapsis passage. One puzzle associated with these QNBs is that in the case of a nearly extreme rotating central black hole the frequency of the QNBs has been found to be in a range which is lower than the corresponding range of relevant quasinormal modes. We reproduce these results using a different approach and perform a detailed analysis to find evidence for the resolution of the puzzle and for the origin of the QNBs. We find that the QNB frequency as measured at future null infinity evolves in (retarded) time and approaches the dominant quasinormal frequency exponentially in time. We also show that the QNB amplitude decays inversely in (retarded) time. We discuss the time dependence of both the QNB waveform frequency and its amplitude and argue that this behavior arises as a result of the excitation of many quasinormal overtones and the summation thereof.