Using curvature invariants for wave extraction in numerical relativity

TL;DR

This paper introduces a new method for extracting gravitational wave signals in numerical relativity using curvature invariants and a fully fixed transverse tetrad, improving the accuracy of wave extraction.

Contribution

It provides a novel explicit expression for Psi_4 based on curvature invariants and a completely fixed tetrad, enhancing wave extraction techniques in numerical relativity.

Findings

New formula for Psi_4 using invariants I and J

Complete fixing of the tetrad including spin-boost transformations

Improved accuracy in gravitational wave extraction

Abstract

We present a new expression for the Weyl scalar Psi_4 that can be used in numerical relativity to extract the gravitational wave content of a spacetime. The formula relies upon the identification of transverse tetrads, namely the ones in which Psi_1=Psi_3=0. It is well known that tetrads with this property always exist in a general Petrov type I spacetime. A sub-class of these tetrads naturally converges to the Kinnersley tetrad in the limit of Petrov type D spacetime. However, the transverse condition fixes only four of the six parameters coming from the Lorentz group of transformations applied to tetrads. Here we fix the tetrad completely, in particular by giving the expression for the spin-boost transformation that was still unclear. The value of Psi_4 in this optimal tetrad is given as a function of the two curvature invariants I and J.