Numerical solution of gravitational dynamics in asymptotically anti-de Sitter spacetimes

TL;DR

This paper presents a numerical approach for solving gravitational dynamics in asymptotically anti-de Sitter spacetimes, demonstrating its effectiveness through examples related to gauge theories and fluid dynamics.

Contribution

It introduces a unified numerical method using null slicing, residual diffeomorphism exploitation, and spectral methods for AdS gravitational problems, with detailed discussion and practical examples.

Findings

Effective numerical solutions for AdS gravitational problems

Application to isotropization, shock collisions, and turbulence

Demonstrated accuracy and efficiency of the method

Abstract

A variety of gravitational dynamics problems in asymptotically anti-de Sitter (AdS) spacetime are amenable to efficient numerical solution using a common approach involving a null slicing of spacetime based on infalling geodesics, convenient exploitation of the residual diffeomorphism freedom, and use of spectral methods for discretizing and solving the resulting differential equations. Relevant issues and choices leading to this approach are discussed in detail. Three examples, motivated by applications to non-equilibrium dynamics in strongly coupled gauge theories, are discussed as instructive test cases. These are gravitational descriptions of homogeneous isotropization, collisions of planar shocks, and turbulent fluid flows in two spatial dimensions.