Resonant dynamics and the instability of anti-de Sitter spacetime

TL;DR

This paper investigates the potential instability of five-dimensional anti-de Sitter spacetime by analyzing small perturbations and demonstrating the development of singularities through a resonant approximation.

Contribution

It introduces a resonant approximation method to study the evolution of perturbations in AdS spacetime and shows the development of singularities, suggesting instability.

Findings

Resonant system solutions develop finite-time singularities.

Small perturbations can lead to instability in AdS spacetime.

The approach provides insights into the nonlinear dynamics of AdS.

Abstract

We consider spherically symmetric Einstein-massless-scalar field equations with negative cosmological constant in five dimensions and analyze evolution of small perturbations of anti-de Sitter spacetime using the recently proposed resonant approximation. We show that for typical initial data the solution of the resonant system develops an oscillatory singularity in finite time. This result hints at a possible route to establishing instability of AdS under arbitrarily small perturbations.