Extraction of Gravitational Waves in Numerical Relativity

TL;DR

This paper reviews various methods for extracting gravitational wave signals from numerical relativity simulations, discussing their theoretical foundations, implementation details, and comparative advantages and disadvantages.

Contribution

It provides a comprehensive comparison and analysis of existing gravitational wave extraction techniques in numerical relativity.

Findings

Quadrupole formulas are simple but approximate.

Gauge-invariant metric perturbations offer more accuracy.

Characteristic extraction provides precise waveforms at null infinity.

Abstract

A numerical-relativity calculation yields in general a solution of the Einstein equations including also a radiative part, which is in practice computed in a region of finite extent. Since gravitational radiation is properly defined only at null infinity and in an appropriate coordinate system, the accurate estimation of the emitted gravitational waves represents an old and non-trivial problem in numerical relativity. A number of methods have been developed over the years to "extract" the radiative part of the solution from a numerical simulation and these include: quadrupole formulas, gauge-invariant metric perturbations, Weyl scalars, and characteristic extraction. We review and discuss each method, in terms of both its theoretical background as well as its implementation. Finally, we provide a brief comparison of the various methods in terms of their inherent advantages and disadvantages.