Extending Gravitational Wave Extraction Using Weyl Characteristic Fields

TL;DR

This paper introduces a comprehensive method for extracting all Newman-Penrose Weyl scalars from numerical spacetimes, facilitating improved gravitational waveform analysis crucial for gravitational wave astronomy.

Contribution

It extends existing extraction techniques to produce the full set of Weyl scalars without strict tetrad conditions, enhancing waveform accuracy and analysis capabilities.

Findings

Successfully extracted all Weyl scalars from numerical simulations.

Produced waveforms compatible with current gravitational wave detectors.

Demonstrated the method's viability compared to more complex approaches.

Abstract

We present a detailed methodology for extracting the full set of Newman-Penrose Weyl scalars from numerically generated spacetimes without requiring a tetrad that is completely orthonormal or perfectly aligned to the principal null directions. We also describe how to implement an extrapolation technique for computing the Weyl scalars' contribution at asymptotic null infinity in postprocessing. These methods have been used to produce $\Psi_4$ and $h$ waveforms for the Simulating eXtreme Spacetimes (SXS) waveform catalog and now have been expanded to produce the entire set of Weyl scalars. These new waveform quantities are critical for the future of gravitational wave astronomy in order to understand the finite-amplitude gauge differences that can occur in numerical waveforms. We also present a new analysis of the accuracy of waveforms produced by the Spectral Einstein Code. While ultimately we expect Cauchy characteristic extraction to yield more accurate waveforms, the extraction techniques described here are far easier to implement and have already proven to be a viable way to produce production-level waveforms that can meet the demands of current gravitational-wave detectors.