On weakly turbulent instability of anti-de Sitter space

TL;DR

This paper demonstrates that anti-de Sitter space is nonlinearly unstable under small perturbations, likely due to resonant mode mixing causing energy transfer to higher frequencies, based on numerical simulations.

Contribution

It provides the first detailed numerical evidence of the weakly turbulent instability of AdS space under generic small perturbations.

Findings

AdS spacetime is unstable under small perturbations.

Resonant mode mixing causes energy diffusion to high frequencies.

Numerical simulations support the weak turbulence conjecture.

Abstract

We study the nonlinear evolution of a weakly perturbed anti-de Sitter (AdS) spacetime by solving numerically the four-dimensional spherically symmetric Einstein-massless-scalar field equations with negative cosmological constant. Our results suggest that AdS spacetime is unstable under arbitrarily small generic perturbations. We conjecture that this instability is triggered by a resonant mode mixing which gives rise to diffusion of energy from low to high frequencies.