Coordinate Conditions and Their Implementation in 3D Numerical Relativity

TL;DR

This paper discusses coordinate conditions in 3D numerical relativity, emphasizing active enforcement methods, especially for the determinant of the spatial metric, and introduces an efficient approach for implementing elliptic conditions in large-scale simulations.

Contribution

It proposes a novel, highly efficient method for implementing elliptic coordinate conditions, enhancing long-term stability and accuracy in 3D numerical relativity simulations.

Findings

Active enforcement of coordinate properties improves simulation stability.

The proposed method is significantly more efficient than existing techniques.

Implementation of elliptic conditions becomes feasible for large-scale 3D simulations.

Abstract

We put forth a few ideas on coordinate conditions and their implementation in numerical relativity. Coordinate conditions are important for the long time scale simulations of relativistic systems, e.g., for the determination of gravitational waveforms from astrophysical events to be measured by LIGO/VIRGO. We demonstrate the importance of, and propose methods for, the {\it active enforcement} of coordinate properties. In particular, the constancy of the determinant of the spatial 3-metric is investigated as such a property. We propose an exceedingly simple but powerful idea for implementing elliptic coordinate conditions that not only makes possible the use of complicated elliptic conditions, but is also {\it orders of magnitude} more efficient than existing methods for large scale 3D simulations.