A new proof for the nonlinear stability of slowly-rotating Kerr-de Sitter

Abstract: The stability of black hole spacetimes is a critical question in mathematical relativity. The nonlinear stability of the slowly-rotating Kerr-de Sitter family was first proven by Hintz and Vasy in 2016 using microlocal techniques. In my talk, I will present a novel proof of the nonlinear stability of slowly-rotating Kerr-de Sitter spacetimes that avoids frequency-space techniques outside of a neighborhood of the trapped set. The proof utilizes spectral methods to uncover a spectral gap corresponding to exponential decay at the level of the linearized equation. The exponential decay of solutions to the linearized problem is then used in a bootstrap proof to conclude nonlinear stability.