Nonlinear Stability of Kerr-de Sitter Spacetimes

Explore the nonlinear stability of slowly-rotating Kerr-de Sitter black holes in this 48-minute conference talk from the Thematic Programme on "Spectral Theory and Mathematical Relativity" at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into recent developments in black hole stability, focusing on a new proof that combines the vectorfield method with frequency-space approaches. Discover how this innovative technique uncovers the high-frequency spectral gap in Kerr-de Sitter spacetimes and employs a bootstrap scheme to demonstrate nonlinear stability without relying on Nash-Moser methods. Compare this approach to the 2016 proof by Hintz and Vasy, which utilized microlocal techniques, and gain insights into the evolving landscape of mathematical relativity and black hole physics.