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

TL;DR

This paper develops a method to approximate the Kinnersley tetrad in numerical relativity simulations, enabling better extraction of gravitational wave signals from complex, non-linear spacetime evolutions.

Contribution

It introduces a quasi-Kinnersley frame that extends the Kinnersley tetrad concept to a broader class of spacetimes, including non-perturbative deviations from Kerr.

Findings

Defines the quasi-Kinnersley frame for numerical relativity.

Provides a scheme to compute this frame from initial-value data.

Establishes limits for applicability to various spacetime perturbations.

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.