Quasi-normal modes and exponential energy decay for the Kerr-de Sitter black hole

Understand

We provide a rigorous definition of quasi-normal modes for a rotating black hole.

• They are given by the poles of a certain meromorphic family of operators and agree with the heuristic definition in the physics literature.
• If the black hole rotates slowly enough, we show that these poles form a discrete subset of the complex plane.
• As an application we prove that the local energy of linear waves in that background decays exponentially once orthogonality to the zero resonance is imposed.