Exact analytical expression for the helical flux in compact binaries

Derive the exact analytical expression for the helical flux F_xi = Ė − Ω(u) · L̇ carried by gravitational waves to future null infinity for quasi-circular, non-precessing compact binary inspirals within the post-Newtonian multipolar post-Minkowskian framework, extending beyond currently available 4.5PN results so that robust analytical comparison with numerical relativity is possible.

Background

The paper studies approximate helical symmetry in compact binary inspirals and quantifies its breaking via the flux of the associated BMS charge at future null infinity. For quasi-circular, non-precessing binaries, the authors compute energy and angular-momentum fluxes up to 4.5PN and find that the helical flux vanishes through this order, with analytic and numerical evidence indicating that the leading non-vanishing contribution arises at relative 5PN.

However, a complete, exact analytical expression for the helical flux has not been derived due to the current limitations of post-Newtonian results. The authors therefore explicitly defer the computation of the exact analytical helical flux to future work, noting that such a result is necessary for robust analytical comparison with numerical relativity waveforms and for validating semi-analytic models.