Schott term in the binding energy for compact binaries on circular orbits at fourth post-Newtonian order

Abstract

The phasing for compact binary systems on circular orbits was obtained in [Phys. Rev. Lett. 131, 121402 (2023)] at fourth-and-a-half post-Newtonian (4.5PN) order thanks to two main ingredients: the 4PN conservative energy (associated to a nonradiative spacetime) in terms of the orbital frequency and the 4.5PN flux in terms of the waveform frequency [i.e., the half-frequency of the (ℓ