The Teukolsky master equations describe the linear behavior of extremal perturbations of the Kerr black hole family.
In this talk, we focus on separable solutions to the Teukolsky equations, for which superradiance and trapping phenomena can be understood. Particular emphasis will be given to mode stability, that is non-existence of exponentially growing or bounded but non-decaying separable solutions. A corollary of our analysis is that general solutions to the Teukolsky equations are bounded and decay in time; this is a key first step in establishing linear stability of Kerr.
This talk contains joint work with Marc Casals (CBPF/UC Dublin) and Yakov Shlapentokh-Rothman (Toronto).