An Improved Gauge Driver for the Generalized Harmonic Einstein System

TL;DR

This paper introduces a new gauge driver for the generalized harmonic Einstein system that enhances stability, allows dual-frame evolution, and is validated through numerical black-hole simulations.

Contribution

A novel gauge driver for the GH Einstein system that maintains hyperbolicity, improves stability, and supports dual-frame evolution techniques.

Findings

Demonstrates improved stability in black-hole evolutions

Constructs new boundary conditions for gauge components

Validates effectiveness through numerical tests

Abstract

A new gauge driver is introduced for the generalized harmonic (GH) representation of Einstein's equation. This new driver allows a rather general class of gauge conditions to be implemented in a way that maintains the hyperbolicity of the combined evolution system. This driver is more stable and effective, and unlike previous drivers, allows stable evolutions using the dual-frame evolution technique. Appropriate boundary conditions for this new gauge driver are constructed, and a new boundary condition for the ``gauge'' components of the spacetime metric in the GH Einstein system is introduced. The stability and effectiveness of this new gauge driver are demonstrated through numerical tests, which impose a new damped-wave gauge condition on the evolutions of single black-hole spacetimes.