Simple conversion of gravitational waveforms to a transverse frame in numerical relativity

The dominant method of extracting gravitational waveforms from numerical simulations of compact-object mergers is through calculating the "outgoing" Weyl curvature scalar $psi_4$ at large but finite coordinate radii. While independent of the spacetime coordinates, this application of the Newman-Penrose formalism still depends on the choice of a suitable null tetrad field to define the "outgoing" direction, and a poorly chosen tetrad leads to pollution of the true outgoing radiation by other curvature quantities. In principle, this can be corrected by solving an eigenvalue problem involving all the numerical Weyl scalars, and using it to create a new null tetrad field in a transverse frame that eliminates the pollution of $psi_4$; however this is an unwieldy procedure that is usually not worth the additional computational effort. Here, we demonstrate a shortcut that allows a much simpler generation of the "unpolluted" $psi_4$ from the original $psi_i$ without explicit regeneration of the tetrad field.