Scalar functions for wave extraction in numerical relativity

TL;DR

This paper simplifies the process of extracting gravitational wave signals in numerical relativity by reducing the complexity of choosing the quasi-Kinnersley tetrad, making waveform analysis more efficient and straightforward.

Contribution

It demonstrates that the quasi-Kinnersley tetrad can be constructed more simply by focusing on the choice of the time-like vector, with the remaining vectors derived easily from the Weyl tensor.

Findings

Simplified the construction of the quasi-Kinnersley tetrad.

Expressed Weyl scalars as functions of electric and magnetic parts.

Enhanced efficiency in gravitational wave extraction procedures.

Abstract

Wave extraction plays a fundamental role in the binary black hole simulations currently performed in numerical relativity. Having a well defined procedure for wave extraction, which matches simplicity with efficiency, is critical especially when comparing waveforms from different simulations. Recently, progress has been made in defining a general technique which uses Weyl scalars to extract the gravitational wave signal, through the introduction of the {\it quasi-Kinnersley tetrad}. This procedure has been used successfully in current numerical simulations; however, it involves complicated calculations. The work in this paper simplifies the procedure by showing that the choice of the {\it quasi-Kinnersley tetrad} is reduced to the choice of the time-like vector used to create it. The space-like vectors needed to complete the tetrad are then easily identified, and it is possible to write the expression for the Weyl scalars in the right tetrad, as simple functions of the electric and magnetic parts of the Weyl tensor.