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

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