Turbulence in general relativity

In the presence of confinement, the Einstein field equations are expected to exhibit turbulent dynamics. One way to introduce confinement to the equations is by imposing a negative value for the cosmological constant and study the evolution of solutions with Anti-de Sitter asymptotics. In this talk, we will focus on two settings where turbulence emerges in the dynamics of the Einstein equations. First, in the case of small perturbations of Anti de-Sitter spacetime, we will establish the AdS instability conjecture for the spherically symmetric Einstein-scalar field system. We will, then, proceed to show how weak turbulence arises in a quasilinear toy model for the vacuum Einstein equations in the exterior of a Schwarzschild-AdS black hole. This is joint work with Christoph Kehle.