Covariant and Gauge-invariant Metric-based Gravitational-waves Extraction in Numerical Relativity

TL;DR

This paper presents a gauge-invariant metric-based method for extracting gravitational waves in numerical relativity, validated across diverse scenarios, offering a robust alternative to curvature-based techniques with improved systematic error identification.

Contribution

The authors develop a gauge-invariant metric perturbation approach for gravitational-wave extraction that does not assume Schwarzschild coordinates, validated with comprehensive 3D simulations.

Findings

Metric extraction is robust and comparable to curvature extraction.

The method effectively identifies waveform systematics.

Good agreement between different gauge-invariant master functions in even-parity sector.

Abstract

We revisit the problem of gravitational-wave extraction in numerical relativity with gauge-invariant metric perturbation theory of spherical spacetimes. Our extraction algorithm allows the computation of even-parity (Zerilli-Moncrief) and odd-parity (Regge-Wheeler) multipoles of the strain from a (3+1) metric without the assumption that the spherical background is in Schwarzschild coordinates. The algorithm is validated with a comprehensive suite of 3D problems including fluid ($f$-modes) and spacetime ($w$-modes) perturbations of neutron stars, gravitational collapse of rotating neutron stars, circular binary black holes mergers and black hole dynamical captures and binary neutron star mergers. We find that metric extraction is robust in all the considered scenarios and delivers waveforms of overall quality similar to curvature (Weyl) extraction. Metric extraction is particularly valuable in identifying waveform systematics for problems in which the reconstruction of the strain from the Weyl multipoles is ambiguous. Direct comparison of different choices for the gauge-invariant master functions show very good agreement in the even-parity sector. Instead, in the odd-parity sector, assuming the background in Schwarzschild coordinates can minimize gauge effects related to the use of the $\Gamma$-driver shift. Moreover, for optimal choices of the extraction radius, a simple extrapolation to null infinity can deliver waveforms compatible to Cauchy-characteristic extrapolated waveforms.