Speaker
Description
The quasinormal mode (QNM) spectra of black holes have been studied since the 1970s. In 2015 the imprint of the fundamental quadrupolar QNM was observed in the gravitational-wave signal from a binary merger. QNM (and Regge-pole) resonances have a local dependence on the potential maximum associated with the black hole light-ring, and also a global dependence on boundary conditions. In this talk we investigate how the resonance spectrum can be strongly disrupted by a weak perturbation in the potential (the Elephant-and-Flea phenomenon). For the case of delta-function perturbation of strength A, we formulate a dynamical system in which resonances follow continuous trajectories with A in the complex plane. We define attracting and repelling points for this dynamical system. The repelling points typically lie close to the unperturbed QNM frequencies, leading to extreme sensitivity in the spectrum to A (i.e. failure of linearised approximations even for tiny values of A). These repelling points appear to be closely related to the Exceptional Points identified by Motohashi (arXiv:2407.15191) which are associated with avoided-crossings of resonances (cf. level-repulsion in quantum mechanics) and enhanced mode contributions in the time-domain (Macedo et al, arXiv:2512.02110). This talk is based on work with T. Torres and arXiv:2601.04892.