https://hal-insu.archives-ouvertes.fr/insu-03645679Shah, Abhay G.Abhay G.ShahIAP - Institut d'Astrophysique de Paris - INSU - CNRS - Institut national des sciences de l'Univers - SU - Sorbonne Université - CNRS - Centre National de la Recherche ScientifiqueFriedman, John L.John L.FriedmanIAP - Institut d'Astrophysique de Paris - INSU - CNRS - Institut national des sciences de l'Univers - SU - Sorbonne Université - CNRS - Centre National de la Recherche ScientifiqueWhiting, Bernard F.Bernard F.WhitingIAP - Institut d'Astrophysique de Paris - INSU - CNRS - Institut national des sciences de l'Univers - SU - Sorbonne Université - CNRS - Centre National de la Recherche ScientifiqueFinding high-order analytic post-Newtonian parameters from a high-precision numerical self-force calculationHAL CCSD201404.25.Nx04.30.Db04.70.BwPost-Newtonian approximationperturbation theoryrelated approximationsWave generation and sourcesClassical black holesGeneral Relativity and Quantum Cosmology[SDU] Sciences of the Universe [physics]Gestionnaire, Hal Sorbonne Université2022-04-24 11:41:292023-03-13 11:17:182022-04-24 11:41:29enJournal articleshttps://hal-insu.archives-ouvertes.fr/insu-03645679/document10.1103/PhysRevD.89.064042application/pdf1We present a novel analytic extraction of high-order post-Newtonian (pN) parameters that govern quasicircular binary systems. Coefficients in the pN expansion of the energy of a binary system can be found from corresponding coefficients in an extreme-mass-ratio inspiral computation of the change ΔU in the redshift factor of a circular orbit at fixed angular velocity. Remarkably, by computing this essentially gauge-invariant quantity to accuracy greater than one part in <SUP>10225</SUP>, and by assuming that a subset of pN coefficients are rational numbers or products of π and a rational, we obtain the exact analytic coefficients. We find the previously unexpected result that the post-Newtonian expansion of ΔU (and of the change ΔΩ in the angular velocity at fixed redshift factor) have conservative terms at half-integral pN order beginning with a 5.5 pN term. This implies the existence of a corresponding 5.5 pN term in the expansion of the energy of a binary system. Coefficients in the pN series that do not belong to the subset just described are obtained to accuracy better than 1 part in 10<SUP>265-23n</SUP> at nth pN order. We work in a radiation gauge, finding the radiative part of the metric perturbation from the gauge-invariant Weyl scalar ψ<SUB>0</SUB> via a Hertz potential. We use mode-sum renormalization, and find high-order renormalization coefficients by matching a series in L=ℓ+1/2 to the large-L behavior of the expression for ΔU. The nonradiative parts of the perturbed metric associated with changes in mass and angular momentum are calculated in the Schwarzschild gauge.