Towards a wave--extraction method for numerical relativity: III. Analytical examples for the Beetle--Burko radiation scalar

TL;DR

This paper evaluates the Beetle--Burko radiation scalar in various analytical spacetimes to demonstrate its potential as a diagnostic tool for gravitational wave content in numerical relativity.

Contribution

It applies the Beetle--Burko scalar to multiple analytical solutions, showing its effectiveness in identifying gravitational radiation in numerical relativity data.

Findings

Scalar successfully detects gravitational waves in linearized models

Scalar provides insights into initial data quality

Scalar can distinguish radiative from non-radiative spacetimes

Abstract

Beetle and Burko recently introduced a background--independent scalar curvature invariant for general relativity that carries information only about the gravitational radiation in generic spacetimes, in cases where such radiation is incontrovertibly defined. In this paper we adopt a formalism that only uses spatial data as they are used in numerical relativity and compute the Beetle--Burko radiation scalar for a number of analytical examples, specifically linearized Einstein--Rosen cylindrical waves, linearized quadrupole waves, the Kerr spacetime, Bowen--York initial data, and the Kasner spacetime. These examples illustrate how the Beetle--Burko radiation scalar can be used to examine the gravitational wave content of numerically generated spacetimes, and how it may provide a useful diagnostic for initial data sets.