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

We present a numerical study of the evolution of a nonlinearly 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 nonlinearly 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.