Mode stability for the Teukolsky equation on extremal and subextremal Kerr spacetimes

Understand

We prove that there are no exponentially growing modes nor modes on the real axis for the Teukolsky equation on Kerr black hole spacetimes, both in the extremal and subextremal case.

• We also give a quantitative refinement of mode stability.
• As an immediate application, we show that the transmission and reflection coefficients of the scattering problem are bounded, independently of the specific angular momentum of the black hole, in any compact set of real frequencies excluding zero frequency and the superradiant threshold.
• While in the subextremal setting these results were known previously, the extremal case is more involved and has remained an open problem.