At 4PN order, the binding energy in the flux-balance law differs from the conservative energy by a hereditary 'pseudo-Schott' term, which exactly reproduces the previously postulated energy-frequency relation and confirms the 4.5PN phasing.
Thus, we perform the time integra- tion as follows: Z ∞ 0 dρf y(t−ρ) = Z y 0 dy′ f(y′) dy′/dt, (5.5) where dy′/dt is given at the required order in Eq
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Schott term in the binding energy for compact binaries on circular orbits at fourth post-Newtonian order
At 4PN order, the binding energy in the flux-balance law differs from the conservative energy by a hereditary 'pseudo-Schott' term, which exactly reproduces the previously postulated energy-frequency relation and confirms the 4.5PN phasing.