General Fourier expansion of post-Newtonian binary dynamics based on a quasi-Keplerian framework

Abstract

We have introduced a new method for computing gravitational-wave emission from nonspinning binaries which systematically unifies the various integrals arising in the Fourier expansions of post-Newtonian dynamics, providing a simple, practical scheme for calculations at arbitrary precision. Using this approach, we derived the full set of 3PN dynamical quantities and gravitational-wave Fourier modes and have released the corresponding numerical code as open source. Furthermore, when radiation-reaction effects is not included, we found that the tail contribution to the energy and angular momentum fluxes can be resummed into an exceptionally compact expression with the help of the new method. These advances pave the way for more convenient and accurate frequency-domain waveform modeling in the future.