Impact of densitized lapse slicings on evolutions of a wobbling black hole

TL;DR

This paper demonstrates that using a densitized lapse function significantly enhances the stability and duration of black hole simulations, introduces a new singularity tracking method, and improves static black hole stability.

Contribution

The study shows that densitized lapse functions extend black hole simulation lifetimes and presents a new, inexpensive singularity tracking approach for mildly distorted black holes.

Findings

Densitized lapse extends simulation lifetime.

Improved stability for static black holes with algebraic densitized lapse.

Introduced a simple method for tracking black hole singularities.

Abstract

We present long-term stable and second-order convergent evolutions of an excised wobbling black hole. Our results clearly demonstrate that the use of a densitized lapse function extends the lifetime of simulations dramatically. We also show the improvement in the stability of single static black holes when an algebraic densitized lapse condition is applied. In addition, we introduce a computationally inexpensive approach for tracking the location of the singularity suitable for mildly distorted black holes. The method is based on investigating the fall-off behavior and asymmetry of appropriate grid variables. This simple tracking method allows one to adjust the location of the excision region to follow the coordinate motion of the singularity.