The Teukolsky equation on Kerr black hole spacetimes
Abstract: The Teukolsky equation is one of the fundamental equations governing linear gravitational perturbations of the Kerr black hole family. We study fixed frequency solutions and obtain estimates which are uniform in the frequency parameters. Due to the separability of the Teukolsky equation, as a corollary we show that solutions are bounded and decay in time; this is a key first step in establishing linear stability of Kerr. Moreover, our estimates can also shed light on more delicate features of the Teukolsky equation, such as their scattering properties.
This is joint work with Yakov Shlapentokh-Rothman (Princeton).