Coordinate Singularities in Harmonically-sliced Cosmologies

TL;DR

This paper investigates the limitations of harmonic slicing in numerical relativity, showing that coordinate singularities often develop in Kasner and Gowdy cosmologies, affecting simulation duration and interpretation.

Contribution

It provides analytic and numerical analysis demonstrating that harmonic slicings typically develop coordinate singularities in certain cosmological spacetimes, limiting simulation effectiveness.

Findings

Harmonic slicings often develop coordinate singularities in Kasner and Gowdy spacetimes.

Coordinate singularities restrict the maximum duration of numerical simulations.

Features caused by singularities can be mistaken for physical effects.

Abstract

Harmonic slicing has in recent years become a standard way of prescribing the lapse function in numerical simulations of general relativity. However, as was first noticed by Alcubierre (1997), numerical solutions generated using this slicing condition can show pathological behaviour. In this paper, analytic and numerical methods are used to examine harmonic slicings of Kasner and Gowdy cosmological spacetimes. It is shown that in general the slicings are prevented from covering the whole of the spacetimes by the appearance of coordinate singularities. As well as limiting the maximum running times of numerical simulations, the coordinate singularities can lead to features being produced in numerically evolved solutions which must be distinguished from genuine physical effects.