In the presence of confinement, the Einstein field equations are expected to exhibit turbulent dynamics. The simplest example of such behaviour is described by the AdS instability conjecture, put forward by Dafermos and Holzegel in 2006; this conjecture suggests that generic small perturbations of the AdS initial data lead to the formation of trapped surfaces when reflecting boundary conditions are imposed at conformal infinity. However, whether a similar scenario also holds in the more complicated case of the exterior region of an asymptotically AdS black hole spacetime has been the subject of debate.
In this talk, we will show that weak turbulence does emerge in the dynamics of a quasilinear toy model for the vacuum Einstein equations on the Schwarzschild-AdS exterior spacetimes for an open and dense set of black hole mass parameters. This is joint work with Christoph Kehle.