Gravitational turbulent instability of AdS${}_5$

We consider the problem of stability of anti-de Sitter spacetime in five dimensions under small purely gravitational perturbations satisfying the cohomogeneity-two biaxial Bianchi IX ansatz. In analogy to spherically symmetric scalar perturbations, we observe numerically a black hole formation on the time-scale $\mathcal{O}({\epsilon }^{-2})$, where $\epsilon$ is the size of the perturbation.