Gravitational turbulent instability of AdS${}_5$

TL;DR

This paper investigates the stability of five-dimensional anti-de Sitter spacetime under small gravitational perturbations, revealing that such perturbations can lead to black hole formation on a specific time scale.

Contribution

It demonstrates the gravitational turbulent instability of AdS${}_5$ and provides numerical evidence for black hole formation due to small perturbations.

Findings

Black hole formation occurs on the order of (-2) time scale.

Small gravitational perturbations can destabilize AdS${}_5$.

Numerical simulations support the turbulent instability hypothesis.

Abstract

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 $\mathcal{O}(\varepsilon^{-2})$, where $\varepsilon$ is the size of the perturbation.