Multitrace deformations and the nonlinear stability of Anti-de Sitter space

TL;DR

This paper studies how multitrace deformations influence the nonlinear stability of Anti-de Sitter space, revealing that relevant deformations can disrupt instability while marginal and irrelevant ones do not.

Contribution

It demonstrates the effect of multitrace deformations on AdS stability using numerical simulations and links these effects to changes in the resonant spectrum.

Findings

Marginal and irrelevant deformations preserve the original instability.

Relevant deformations disrupt the nonlinear instability.

The impact correlates with changes in the eigenfrequency spectrum.

Abstract

We investigate the nonlinear stability of global Anti-de Sitter space in the presence of multitrace deformations utilizing an Einstein-Klein-Gordon system with a top-down scalar potential. Our numerical simulations show that marginal and irrelevant deformations retain the nonlinear instability originally found by Bizo\'n and Rostworowski, while relevant deformations disrupt it. We show that the nonlinear impact of multitrace deformations is in one-to-one correspondence with how they affect the resonant character of the global Anti-de Sitter normal mode eigenfrequency spectrum.