Azimuthal instabilities of extremal Kerr black holes

Kerr solutions to Einstein's equations of general relativity describe stationary, rotating black holes in vacuum. When Kerr black holes rotate at their maximally allowed angular velocity, they are said to be extremal. Extremal black holes can be thought of as critical solutions, featuring dynamics that are rich with interesting phenomena. I will introduce upcoming work on the existence of strong asymptotic instabilities of a non-axisymmetric nature for scalar waves propagating on extremal Kerr black hole backgrounds and I will discuss the connection of instabilities with the precise shape of late-time power law tails in the emitted radiation.