Strategies for the Characteristic Extraction of Gravitational Waveforms

TL;DR

This paper introduces new numerical and geometric techniques to enhance the accuracy of gravitational waveform extraction in characteristic evolution, including boundary treatments and the use of Weyl tensor components.

Contribution

It presents novel boundary handling and waveform extraction methods using $ ext{Psi}_4$, improving the precision of gravitational wave simulations.

Findings

Circular boundary implementation reduces grid irregularities.

Angular dissipation dampens high-frequency errors.

Waveform extraction via $ ext{Psi}_4$ yields accurate results.

Abstract

We develop, test and compare new numerical and geometrical methods for improving the accuracy of extracting waveforms using characteristic evolution. The new numerical method involves use of circular boundaries to the stereographic grid patches which cover the spherical cross-sections of the outgoing null cones. We show how an angular version of numerical dissipation can be introduced into the characteristic code to damp the high frequency error arising form the irregular way the circular patch boundary cuts through the grid. The new geometric method involves use of the Weyl tensor component $\Psi_4$ to extract the waveform as opposed to the original approach via the Bondi news function. We develop the necessary analytic and computational formula to compute the $O(1/r)$ radiative part of $\Psi_4$ in terms of a conformally compactified treatment of null infinity. These methods are compared and calibrated in test problems based upon linearized waves.