Nonlinear instability of Schwarzschild–AdS

For each $s\in\mathbb N$, let $J^{\mathrm{EVE}}_s\subset(0,+\infty)$ be a set of black-hole masses, and let $(\gamma_0,K_0)$ denote Schwarzschild–AdS initial data of mass $M$. The data $(\gamma_\epsilon,K_\epsilon)$ are asymptotically AdS initial data, and their evolution is taken under the vacuum Einstein equations with reflecting boundary conditions at $\mathcal I$.

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 there exists a one-parameter family of asymptotically AdS initial data $(\gamma_\epsilon,K_\epsilon)$ converging in the $H^s$ topology to $(\gamma_0,K_0)$, whose evolution leads to the creation of a trapped surface far from the background event horizon.

This is a maximalistic conjectural formulation of weakly turbulent instability for the full Einstein vacuum equations, motivated by the paper's scalar model and by the expected concentration of energy associated with trapped-surface formation. The supplied text does not establish the conjecture.