Islands of stability and recurrence times in AdS

TL;DR

This paper investigates the stability of AdS spacetime under scalar perturbations, identifying stable quasi-periodic solutions and predicting recurrence times, thus shedding light on the weak turbulence and collapse phenomena in AdS.

Contribution

It demonstrates the existence of stable quasi-periodic solutions in AdS within the TTF approximation and links their stability to recurrence times in the full system.

Findings

Stable quasi-periodic solutions exist in AdS.

Recurrence times can be predicted from eigenmodes.

Breakdown of TTF indicates potential black hole formation.

Abstract

We study the stability of anti-de Sitter (AdS) spacetime to spherically symmetric perturbations of a real scalar field in general relativity. Further, we work within the context of the "two time framework" (TTF) approximation, which describes the leading nonlinear effects for small amplitude perturbations, and is therefore suitable for studying the weakly turbulent instability of AdS---including both collapsing and non-collapsing solutions. We have previously identified a class of quasi-periodic (QP) solutions to the TTF equations, and in this work we analyze their stability. We show that there exist several families of QP solutions that are stable to linear order, and we argue that these solutions represent islands of stability in TTF. We extract the eigenmodes of small oscillations about QP solutions, and we use them to predict approximate recurrence times for generic non-collapsing initial data in the full (non-TTF) system. Alternatively, when sufficient energy is driven to high-frequency modes, as occurs for initial data far from a QP solution, the TTF description breaks down as an approximation to the full system. Depending on the higher order dynamics of the full system, this often signals an imminent collapse to a black hole.