Asymptotic frame selection for binary black hole spacetimes II: Post-Newtonian limit

TL;DR

This paper investigates how to select a preferred frame in gravitational wave signals from binary black hole systems using a principal axes approach, focusing on the post-Newtonian approximation and its behavior during inspiral.

Contribution

It evaluates the principal axes method for frame selection in binary black hole spacetimes within the post-Newtonian limit, including precessing and nonprecessing cases.

Findings

Dominant eigenvector aligns with orbital angular momentum in nonprecessing binaries.

In precessing binaries, the preferred frame deviates from orbital and total angular momentum.

Frame differences grow as the binary approaches merger, influenced by precession and higher harmonics.

Abstract

One way to select a preferred frame from gravitational radiation is via the principal axes of < L L>, an average of the action of rotation group generators on the Weyl tensor at asymptotic infinity. In this paper we evaluate this time-domain average for a quasicircular binary using approximate (post-Newtonian) waveforms. For nonprecessing unequal-mass binaries, we show the dominant eigenvector of this tensor lies along the orbital angular momentum. For precessing binaries, this frame is not generally aligned with either the orbital or total angular momentum, working to leading order in the spins. The difference between these two quantities grows with time, as the binary approaches the end of the inspiral and both precession and higher harmonics become more significant.