Turbulence and Chaos in Anti-de-Sitter Gravity

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.