Hyperbolic slicings of spacetime: singularity avoidance and gauge shocks

TL;DR

This paper analyzes hyperbolic slicing conditions in spacetime, focusing on avoiding singularities and gauge shocks, and identifies conditions for effective singularity avoidance and shock elimination, including practical slicing choices like the 1+log family.

Contribution

It extends the analysis of Bona-Masso slicing conditions, providing new insights into singularity avoidance and gauge shock elimination, and explores practical slicing options.

Findings

Both marginal and strong singularity avoidance are achievable with certain slicing behaviors.

A previously known gauge shock elimination condition is re-derived, limiting slicing choices.

Approximate satisfaction of the shock elimination condition allows for practical slicing conditions like the 1+log family.

Abstract

I study the Bona-Masso family of hyperbolic slicing conditions, considering in particular its properties when approaching two different types of singularities: focusing singularities and gauge shocks. For focusing singularities, I extend the original analysis of Bona et. al and show that both marginal and strong singularity avoidance can be obtained for certain types of behavior of the slicing condition as the lapse approaches zero. For the case of gauge shocks, I re-derive a condition found previously that eliminates them. Unfortunately, such a condition limits considerably the type of slicings allowed. However, useful slicing conditions can still be found if one asks for this condition to be satisfied only approximately. Such less restrictive conditions include a particular member of the 1+log family, which in the past has been found empirically to be extremely robust for both Brill wave and black hole simulations.