Gravitational Turbulent Instability of Anti-de Sitter Space

TL;DR

This paper provides evidence that anti-de Sitter space is nonlinearly unstable due to gravitational turbulence, leading to black hole formation, with implications for the dual field theory.

Contribution

It demonstrates that multi-mode initial conditions in AdS lead to turbulent instability and black hole formation, extending previous single-mode analyses.

Findings

Single-mode perturbations can form nonlinear geons.

Multi-mode perturbations induce energy transfer to smaller scales.

Turbulent instability suggests a route to black hole formation in AdS.

Abstract

Bizon and Rostworowski have recently suggested that anti-de Sitter spacetime might be nonlinearly unstable to transfering energy to smaller and smaller scales and eventually forming a small black hole. We consider pure gravity with a negative cosmological constant and find strong support for this idea. While one can start with a single linearized mode and add higher order corrections to construct a nonlinear geon, this is not possible starting with a linear combination of two or more modes. One is forced to add higher frequency modes with growing amplitude. The implications of this turbulent instability for the dual field theory are discussed.