Leading-order term expansion for the Teukolsky equation on subextremal Kerr black holes

In this note, we present a result based on [47] providing the large time leading-order term for initially localized solutions of the Teukolsky equation on a general subextremal Kerr black hole. This equation is important in the study of Maxwell’s equations and Einstein’s equations on a Kerr background. The method used is based on a careful analysis of the resolvent operator permitted by recent advances in microlocal analysis including non elliptic Fredholm theory, radial point estimates and semiclassical analysis near the trapped set together with a result about the absence of modes for the Teukolsky equation.