Cauchy Evolution of Asymptotically Global AdS Spacetimes with No Symmetries

TL;DR

This paper demonstrates the first stable, long-term numerical simulations of fully general asymptotically AdS spacetimes without symmetry constraints, advancing the study of gravitational dynamics in such backgrounds.

Contribution

It introduces a novel numerical scheme based on generalized harmonic Einstein equations that enables symmetry-free evolution of AdS spacetimes, including matter couplings and higher dimensions.

Findings

First long-time stable 3+1 AdS simulations with scalar fields

Successful gravitational collapse simulations without symmetry

Observation of black hole ringdown to static state

Abstract

We present the first proof-of-principle Cauchy evolutions of asymptotically global AdS spacetimes with no imposed symmetries, employing a numerical scheme based on the generalized harmonic form of the Einstein equations. In this scheme, the main difficulty in removing all symmetry assumptions can be phrased in terms of finding a set of generalized harmonic source functions that are consistent with AdS boundary conditions. In four spacetime dimensions, we detail an explicit set of source functions that achieves evolution in full generality. A similar prescription should also lead to stable evolution in higher spacetime dimensions, various couplings with matter fields, and on the Poincare patch. We apply this scheme to obtain the first long-time stable 3+1 simulations of four dimensional spacetimes with a negative cosmological constant, using initial data sourced by a massless scalar field. We present preliminary results of gravitational collapse with no symmetry assumptions, and the subsequent quasi-normal mode ringdown to a static black hole in the bulk, which corresponds to evolution towards a homogeneous state on the boundary.