A hyperbolic slicing condition adapted to Killing fields and densitized lapses

TL;DR

This paper introduces a modified hyperbolic slicing condition for Einstein's equations that preserves static or stationary spacetimes and is compatible with densitized lapses, enhancing stability and consistency in numerical relativity.

Contribution

The paper proposes a new hyperbolic slicing condition that maintains stationarity and is adapted to densitized lapses, improving numerical relativity simulations.

Findings

Ensures static and stationary spacetimes remain unchanged during evolution.

Compatible with densitized lapse variables in hyperbolic formulations.

Potentially improves stability of Einstein evolution equations.

Abstract

We study the properties of a modified version of the Bona-Masso family of hyperbolic slicing conditions. This modified slicing condition has two very important features: In the first place, it guarantees that if a spacetime is static or stationary, and one starts the evolution in a coordinate system in which the metric coefficients are already time independent, then they will remain time independent during the subsequent evolution, {\em i.e.} the lapse will not evolve and will therefore not drive the time lines away from the Killing direction. Second, the modified condition is naturally adapted to the use of a densitized lapse as a fundamental variable, which in turn makes it a good candidate for a dynamic slicing condition that can be used in conjunction with some recently proposed hyperbolic reformulations of the Einstein evolution equations.