Turbulence and Chaos in Anti-de-Sitter Gravity

TL;DR

This paper explores the instability of Anti-de-Sitter spacetimes using spectral methods, modeling the problem as coupled harmonic oscillators, and emphasizes the need for interdisciplinary research to fully understand turbulence and chaos in this context.

Contribution

It demonstrates the effectiveness of spectral methods in analyzing AdS spacetime instability and models the problem as a system of nonlinear coupled harmonic oscillators.

Findings

Spectral methods effectively analyze nonlinear dynamics in AdS spacetimes.

Modeling as coupled oscillators provides new insights into turbulence and chaos.

Highlights open questions requiring interdisciplinary collaboration.

Abstract

Due to the AdS/CFT correspondence the question of instability of Anti-de-Sitter spacetimes sits in the intersection of mathematical and numerical relativity, string theory, field theory and condensed matter physics. In this essay we revisit that important question emphasizing the power of spectral methods and highlighting the effectiveness of standard techniques for studying nonlinear dynamical systems. In particular we display explicitly how the problem can be modeled as a system on nonlinearly coupled harmonic oscillators. We highlight some of the many open questions that stem from this result and point out that a full understanding will necessarily required the interdisciplinary cooperation of various communities.