Wave zone extraction of gravitational radiation in three-dimensional numerical relativity

TL;DR

This paper introduces a highly accurate method for extracting gravitational waveforms from 3D numerical relativity simulations, utilizing novel algorithms and fixed mesh refinement to improve precision and applicability to black hole collisions.

Contribution

It presents a new approach combining a three-plus-one Einstein equations decomposition, Misner's spherical harmonic algorithm, and fixed mesh refinement for better gravitational wave extraction.

Findings

Waveforms last for multiple periods with 2% error ratio

Method successfully applied to Teukolsky wave and black hole collision

Results demonstrate high accuracy and potential as standard test cases

Abstract

We present convergent gravitational waveforms extracted from three-dimensional, numerical simulations in the wave zone and with causally disconnected boundaries. These waveforms last for multiple periods and are very accurate, showing a peak error to peak amplitude ratio of 2% or better. Our approach includes defining the Weyl scalar Psi_4 in terms of a three-plus-one decomposition of the Einstein equations; applying, for the first time, a novel algorithm due to Misner for computing spherical harmonic components of our wave data; and using fixed mesh refinement to focus resolution on non-linear sources while simultaneously resolving the wave zone and maintaining a causally disconnected computational boundary. We apply our techniques to a (linear) Teukolsky wave, and then to an equal mass, head-on collision of two black holes. We argue both for the quality of our results and for the value of these problems as standard test cases for wave extraction techniques.