Stationary hyperboloidal slicings with evolved gauge conditions

TL;DR

This paper investigates stationary hyperboloidal slicings of Schwarzschild spacetime using Bona-Masso slicing conditions, focusing on gauge choices that include null infinity for better gravitational wave observation.

Contribution

It demonstrates that standard 1+log slicing cannot produce regular hyperboloidal slices, but combining it with harmonic slicing yields a singularity-avoiding hyperboloidal foliation connecting the black hole to scri.

Findings

Standard 1+log slicing is incompatible with regular hyperboloidal slices.

A combined gauge condition with harmonic slicing creates a singularity-avoiding hyperboloidal foliation.

The resulting slicing includes null infinity, useful for gravitational wave studies.

Abstract

We analyze stationary slicings of the Schwarzschild spacetime defined by members of the Bona-Masso family of slicing conditions. Our main focus is on the influence of a non-vanishing offset to the extrinsic curvature, which forbids the existence of standard Cauchy foliations but at the same time allows gauge choices that are adapted to include null infinity (scri) in the evolution. These hyperboloidal slicings are especially interesting for observing outgoing gravitational waves. We show that the standard 1+log slicing condition admits no overall regular hyperboloidal slicing, but by appropriately combining with harmonic slicing, we construct a gauge condition that leads to a strongly singularity-avoiding hyperboloidal foliation that connects the black hole to scri.