AdS nonlinear instability: moving beyond spherical symmetry

TL;DR

This paper investigates the nonlinear stability of Anti-de Sitter space beyond spherical symmetry, revealing that gravitational perturbations exhibit complex resonances and turbulent cascades, differing from scalar field behaviors.

Contribution

It demonstrates that gravitational normal modes in AdS cannot all be extended into smooth periodic solutions and identifies multiple resonances and turbulent cascades in gravitational perturbations.

Findings

Not all gravitational normal modes extend into periodic solutions.

Single-mode seeds can develop secular resonances.

Two-mode seeds can generate multiple resonances at third order.

Abstract

Anti-de Sitter (AdS) is conjectured to be nonlinear unstable to a weakly turbulent mechanism that develops a cascade towards high frequencies, leading to black hole formation [1,2]. We give evidence that the gravitational sector of perturbations behaves differently from the scalar one studied in [2]. In contrast with [2], we find that not all gravitational normal modes of AdS can be nonlinearly extended into periodic horizonless smooth solutions of the Einstein equation. In particular, we show that even seeds with a single normal mode can develop secular resonances, unlike the spherically symmetric scalar field collapse studied in [2]. Moreover, if the seed has two normal modes, more than one resonance can be generated at third order, unlike the spherical collapse of [2]. We also show that weak turbulent perturbative theory predicts the existence of direct and inverse cascades, with the former dominating the latter for equal energy two-mode seeds.