Towards a novel wave-extraction method for numerical relativity

TL;DR

This paper introduces a new wave extraction method in numerical relativity using Weyl scalars, emphasizing the importance of choosing the correct null tetrad to accurately measure gravitational radiation.

Contribution

It proposes a general procedure for selecting a null tetrad in wave extraction, improving the accuracy of gravitational wave measurements in numerical simulations.

Findings

Successful application to a black hole simulation

Demonstrated the importance of tetrad choice for accurate results

Compared Weyl scalar results with the news function

Abstract

We present the recent results of a research project aimed at constructing a robust wave extraction technique for numerical relativity. Our procedure makes use of Weyl scalars to achieve wave extraction. It is well known that, with a correct choice of null tetrad, Weyl scalars are directly associated to physical properties of the space-time under analysis in some well understood way. In particular it is possible to associate $\Psi_4$ with the outgoing gravitational radiation degrees of freedom, thus making it a promising tool for numerical wave--extraction. The right choice of the tetrad is, however, the problem to be addressed. We have made progress towards identifying a general procedure for choosing this tetrad, by looking at transverse tetrads where $\Psi_1=\Psi_3=0$. As a direct application of these concepts, we present a numerical study of the evolution of a non-linearly disturbed black hole described by the Bondi--Sachs metric. This particular scenario allows us to compare the results coming from Weyl scalars with the results coming from the news function which, in this particular case, is directly associated with the radiative degrees of freedom. We show that, if we did not take particular care in choosing the right tetrad, we would end up with incorrect results.