Numerical Cauchy evolution of asymptotically AdS spacetimes with no symmetries

TL;DR

This thesis introduces a novel numerical scheme for simulating asymptotically AdS spacetimes without symmetry constraints, enabling long-term stable 3+1 evolutions and applications to gravitational collapse and black hole phenomena.

Contribution

It develops the first general method for stable Cauchy evolution of AdS spacetimes without symmetry, using a new prescription for harmonic source functions.

Findings

Achieved stable long-time 3+1 simulations of AdS spacetimes.

Demonstrated gravitational collapse and black hole ringdown without symmetry.

Supported potential studies of black hole superradiance in Kerr-AdS.

Abstract

In this thesis, I present the first numerical scheme able to perform Cauchy evolutions of asymptotically AdS spacetimes with reflective boundary conditions under no symmetry requirements on the solution. The scheme is based on the generalised harmonic formulation of the Einstein equations. The main difficulty in removing all symmetry assumptions can be phrased in terms of finding a set of generalised harmonic source functions that are consistent with the AdS boundary conditions. I detail a prescription to obtain the set of source functions that achieves stable evolution in full generality. This prescription leads to the first long-time stable 3+1 simulations of four dimensional spacetimes with a negative cosmological constant in Cartesian coordinates. I show results of gravitational collapse with no symmetry assumptions, and the subsequent ringdown to a static black hole in the bulk, which corresponds to evolution towards a homogeneous state on the boundary. Furthermore, it is argued that this scheme is well-suited for the study of black hole superradiance -- the amplification of waves scattering off a rotating black hole -- in Kerr-AdS spacetime. This statement is supported by the results of a preliminary simulation of perturbed Kerr-AdS.