Gravitational Wave Flux and Quadrupole Modes from Quasi-Circular Non-Spinning Compact Binaries to the Fourth Post-Newtonian Order

Abstract

This article provides the details on the technical derivation of the gravitational waveform and total gravitational-wave energy flux of non-spinning compact binary systems to the 4PN (fourth post-Newtonian) order beyond the Einstein quadrupole formula. In particular: (i) we overview the link between the radiative multipole moments measured at infinity and the source moments in the framework of dimensional regularization; (ii) we compute special corrections to the source moments due to "infrared" commutators arising at the 4PN order; (iii) we derive a "post-adiabatic" correction needed to evaluate the tail integral with 2.5PN relative precision; (iv) we discuss the relation between the binary's orbital frequency in quasi-circular orbit and the gravitational-wave frequency measured at infinity; (v) we compute the hereditary effects at the 4PN order, including those coming from the recently derived tails-of-memory; and (vi) we describe the various tests we have performed to ensure the correctness of the results. Those results are collected in an ancillary file.

arXiv comment32 pages, no figure. v2: reference of the companion letter updated. v3: post-referee version. v4: bibliographic typo corrected

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