Oliver Lindblad Petersen: Conditional non-linear stability of Kerr–de Sitter spacetimes in the full subextremal range

Abstract: Einstein's equations is a system of non-linear PDE whose solutions describe gravity in (a part of) the universe. The Kerr–de Sitter geometry is such a solution, modeling a rotating black hole in an expanding universe. When analyzing the dynamics of such black holes, quasinormal modes (QNMs) play a crucial role. These are particular solutions to the linearized version of the Einstein equations, with a simple oscillating behavior in the time variable. One can think of QNMs as analogues to wave modes on a compact subset of \(\mathbb{R}^n\) with Dirichlet or Neumann boundary conditions, but with the important difference that QNMs typically are expected to decay in time as energy falls into the black hole or escapes to infinity.

In this talk, I will present a recent result saying that if all quasinormal modes decay on a subextremal Kerr–de Sitter spacetime, then the Kerr–de Sitter spacetime is stable to (non-linear) gravitational perturbations and settles down to a new black hole. This generalizes a previous result by Hintz–Vasy valid for slowly rotating black holes. Our result reduces the Black Hole Stability Conjecture in the case of a positive cosmological constant to the Mode Stability Conjecture.

This is joint work with Peter Hintz and András Vasy.