Perturbative Hyperboloidal Extraction of Gravitational Waves in 3+1 Numerical Relativity

TL;DR

This paper introduces a perturbative hyperboloidal method for extracting gravitational waves at null infinity from 3+1 numerical relativity simulations, improving data quality and efficiency over traditional extrapolation techniques.

Contribution

The authors develop a new hyperboloidal extraction framework that uses perturbative Regge-Wheeler-Zerilli equations to reach null infinity, enhancing gravitational wave extraction in numerical relativity.

Findings

Waveforms from various astrophysical scenarios are successfully extracted.

The method achieves data quality comparable to existing characteristic extraction.

It offers a simple and efficient alternative for gravitational wave computation.

Abstract

We present a framework to propagate to null infinity gravitational waves computed at timelike worldtubes in the interior of a 3+1 (Cauchy) numerical relativity simulations. In our method, numerical relativity data are used as the inner inflowing boundary of a perturbative time-domain Regge-Wheeler-Zerilli simulation in hyperboloidal coordinates that reaches null infinity. We showcase waveforms from (3+1)D simulations of gravitational collapse of rotating neutron stars, binary black holes mergers and scattering, and binary neutron star mergers and compare them to other extrapolation methods. Our perturbative hyperboloidal extraction provides a simple yet efficient procedure to compute gravitational waves with data quality comparable to the Cauchy characteristic extraction for several practical applications. Nonlinear effects in the wave propagation are not captured by our method, but the present work is a stepping stone towards more sophisticated hyperboloidal schemes for gravitational-wave extraction.