Improved Moving Puncture Gauge Conditions for Compact Binary Evolutions

TL;DR

This paper introduces improved moving-puncture gauge conditions that significantly reduce noise and errors in binary black hole simulations, enhancing gravitational waveform accuracy and stability.

Contribution

The authors develop and implement new gauge conditions that better manage outgoing gauge waves, reducing noise and errors in numerical relativity simulations of compact binaries.

Findings

40% lower waveform phase and amplitude errors

Constraint violations reduced by over an order of magnitude

Less fluctuation in convergence order during inspiral

Abstract

Robust gauge conditions are critically important to the stability and accuracy of numerical relativity (NR) simulations involving compact objects. Most of the NR community use the highly robust---though decade-old---moving-puncture (MP) gauge conditions for such simulations. It has been argued that in binary black hole (BBH) evolutions adopting this gauge, noise generated near adaptive-mesh-refinement (AMR) boundaries does not converge away cleanly with increasing resolution, severely limiting gravitational waveform accuracy at computationally feasible resolutions. We link this noise to a sharp (short-wavelength), initial outgoing gauge wave crossing into progressively lower resolution AMR grids, and present improvements to the standard MP gauge conditions that focus on stretching, smoothing, and more rapidly settling this outgoing wave. Our best gauge choice greatly reduces gravitational waveform noise during inspiral, yielding less fluctuation in convergence order and $\sim 40%$ lower waveform phase and amplitude errors at typical resolutions. Noise in other physical quantities of interest is also reduced, and constraint violations drop by more than an order of magnitude. We expect these improvements will carry over to simulations of all types of compact binary systems, as well as other $N$+1 formulations of gravity for which MP-like gauge conditions can be chosen.