4 problems

The AdS instability conjecture. There exist arbitrarily small perturbations of Anti-de Sitter spacetime solving the vacuum Einstein equations with reflecting boundary conditions at…

Nonlinear instability of Schwarzschild–AdS. For any $s\in\mathbb N$, there exists an open and dense set $J^{\mathrm{EVE}}_s\subset(0,+\infty)$ of black-hole masses $M$ such that th…

Holzegel–Smulevici's instability conjecture. The family of Kerr–AdS spacetimes is nonlinearly unstable for generic perturbations.

Let $\Sigma_0$ be a complete $2$-ended asymptotically flat Cauchy hypersurface in a Kerr spacetime with $0<|a|<M$, and let $\psi$ solve the linear wave equation … The relevant assu…