Spectral Cauchy-characteristic extraction of the gravitational wave news function

TL;DR

This paper introduces an improved spectral algorithm for extracting gravitational wave signals in numerical relativity, enhancing accuracy and convergence at critical regions and increasing temporal resolution.

Contribution

The paper presents a novel spectral algorithm for Cauchy-characteristic extraction that improves convergence and accuracy in gravitational wave simulations.

Findings

Enhanced spectral convergence at poles and null infinity

Increased temporal resolution of the gravitational wave extraction code

Demonstrated accuracy improvements over existing implementations

Abstract

We present an improved spectral algorithm for Cauchy-characteristic extraction and characteristic evolution of gravitational waves in numerical relativity. The new algorithms improve spectral convergence both at the poles of the spherical-polar grid and at future null infinity, as well as increase the temporal resolution of the code. The key to the success of these algorithms is a new set of high-accuracy tests, which we present here. We demonstrate the accuracy of the code and compare with the existing PittNull implementation.