The Teukolsky equation on Kerr black hole spacetimes

The black hole stability conjecture is one of the outstanding open problems in the General Relativity, and an active area of research since the late 1950s. Key to this endeavor is a quantitative understanding of solutions to the so-called Teukolsky master equation in linearized gravity around Kerr. In this talk, we discuss a uniform-in-frequency analysis of separable solutions to the Teukolsky equations which captures superradiance and trapping phenomena. 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. Particular emphasis will be given to mode stability, that is non-existence of exponentially growing or bounded but non-decaying separable solutions. This talk contains joint work with Marc Casals (Leipzig) and Yakov Shlapentokh-Rothman (Toronto).