Gauge Drivers for the Generalized Harmonic Einstein Equations

TL;DR

This paper introduces a new gauge driver method for the generalized harmonic Einstein equations that maintains hyperbolicity across a broad range of gauge conditions, enhancing stability and applicability in numerical relativity.

Contribution

A novel gauge driver approach that preserves hyperbolicity for many standard gauge conditions in the generalized harmonic formulation of Einstein's equations.

Findings

The new method maintains stability in numerical simulations.

It successfully incorporates various standard gauge conditions.

Analytical and numerical tests confirm effectiveness.

Abstract

The generalized harmonic representation of Einstein's equation is manifestly hyperbolic for a large class of gauge conditions. Unfortunately most of the useful gauges developed over the past several decades by the numerical relativity community are incompatible with the hyperbolicity of the equations in this form. This paper presents a new method of imposing gauge conditions that preserves hyperbolicity for a much wider class of conditions, including as special cases many of the standard ones used in numerical relativity: e.g., K-freezing, Gamma-freezing, Bona-Masso slicing, conformal Gamma-drivers, etc. Analytical and numerical results are presented which test the stability and the effectiveness of this new gauge driver evolution system.