Quasinormal modes are the gravitational wave analogue to the overtones heard after striking a bell. They dominate the signal observed during the ringdown phase after a dynamical event and are characterised by complex frequencies, which encode oscillation and exponential decay in time. As horizons become extremal, various computations (both analytic and numerical) have shown that in many cases, there exists a sequence of frequencies which become purely oscillatory in the limit and which cluster on a line in the complex plane. These are zero-damped modes and are conjectured to exist generically for near-extremal horizons. In this talk, we shall discuss rigorous results that can be obtained toward resolving this question.

https://indico.math.cnrs.fr/event/10707/