10 problems

Let $(\mathcal{M}_{AdS},g_{AdS})$ denote the trivial anti-de Sitter solution, let $\mathcal{I}$ be its conformal boundary, and consider arbitrarily small perturbations of its initi…

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

The paper considers Anti-de Sitter spacetime with either reflective or optimally dissipative boundary conditions. Nonlinear instability and dissipative stability conjecture. Anti-d…

Bizon–Rostworowski's resonant-instability conjecture. The instability is driven by a mechanism of resonant interactions of spherically symmetric modes, leading to weakly turbulent…

Anti-de Sitter instability conjecture. Anti-de Sitter spacetime is unstable under reflective boundary conditions.

Vacuum Anti-de Sitter spacetime has a timelike boundary. Vacuum AdS instability conjecture. Perturbations of its initial data can lead to the formation of a black hole, so vacuum A…

Let $n+1$ be the dimension of Anti-de Sitter spacetime, and consider spherically symmetric perturbations of a self-gravitating, minimally coupled, massless scalar field with approp…

Let $(\mathcal{M}_{Sch},g_{Sch})$ denote Schwarzschild–anti-de Sitter spacetime. Nonlinear stability means that sufficiently small perturbations remain controlled and approach the…

Let $\tilde H^{1,2m}$ be the universal anti de Sitter spacetime of dimension $2m+1$, and let a compact quotient be a manifold of the form $\Gamma\setminus\tilde H^{1,2m}$. Such a q…

Let $AdS_D$ denote anti-de Sitter spacetime in dimension $D\geq 4$, and consider arbitrarily small perturbations of it in the setting of a spherically symmetric massless scalar fie…