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Towards a novel wave-extraction method for numerical relativity. I. Foundations and initial-value formulation

Christopher Beetle·Marco Bruni·Lior M. Burko·Andrea Nerozzi
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Abstract

The Teukolsky formalism of black hole perturbation theory describes weak gravitational radiation generated by a mildly dynamical hole near equilibrium. A particular null tetrad of the background Kerr geometry, due to Kinnersley, plays a singularly important role within this formalism. In order to apply the rich physical intuition of Teukolsky's approach to the results of fully non-linear numerical simulations, one must approximate this Kinnersley tetrad using raw numerical data, with no a priori knowledge of a background. This paper addresses this issue by identifying the directions of the tetrad fields in a quasi-Kinnersley frame. This frame provides a unique, analytic extension of Kinnersley's definition for the Kerr geometry to a much broader class of space-times including not only arbitrary perturbations, but also many examples which differ non-perturbatively from Kerr. This paper establishes concrete limits delineating this class and outlines a scheme to calculate the quasi-Kinnersley frame in numerical codes based on the initial-value formulation of geometrodynamics.

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Christopher Beetle, Marco Bruni, Lior M. Burko, Andrea Nerozzi. 2005-05-11. Towards a novel wave-extraction method for numerical relativity. I. Foundations and initial-value formulation. https://doi.org/10.1103/physrevd.72.024013

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