Towards a wave-extraction method for numerical relativity: IV. Testing the quasi-Kinnersley method in the Bondi-Sachs framework

TL;DR

This paper compares gravitational wave extraction methods in numerical relativity, demonstrating that the quasi-Kinnersley approach in the Bondi-Sachs framework aligns well with the news function, unlike non-quasi-Kinnersley tetrads.

Contribution

It tests and validates the quasi-Kinnersley wave-extraction method within the Bondi-Sachs framework against the traditional news function approach.

Findings

Quasi-Kinnersley method agrees well with the news function in wave extraction.

Non-quasi-Kinnersley tetrads produce significantly different results.

The method is robust across different formulations of Einstein's equations.

Abstract

We present a numerical study of the evolution of a non-linearly disturbed black hole described by the Bondi--Sachs metric, for which the outgoing gravitational waves can readily be found using the news function. We compare the gravitational wave output obtained with the use of the news function in the Bondi--Sachs framework, with that obtained from the Weyl scalars, where the latter are evaluated in a quasi-Kinnersley tetrad. The latter method has the advantage of being applicable to any formulation of Einstein's equations---including the ADM formulation and its various descendants---in addition to being robust. Using the non-linearly disturbed Bondi--Sachs black hole as a test-bed, we show that the two approaches give wave-extraction results which are in very good agreement. When wave extraction through the Weyl scalars is done in a non quasi-Kinnersley tetrad, the results are markedly different from those obtained using the news function.