The quadrupole moment of compact binaries to the fourth post-Newtonian order: II. Dimensional regularization and renormalization

Abstract The regularization and renormalization of the radiative mass-type quadrupole moment inspiralling compact binaries (without spins) is investigated at fourth post-Newtonian (4PN) approximation general relativity. As clear from conservative 4PN equations motion, a dimensional has to be implemented in order properly treat non-linear interactions experienced by gravitational waves during their propagation towards future null infinity. By implementing such procedure, we show that poles coming source (computed companion paper) are exactly cancelled moment, as expected for physical quantity. We thus define obtain ‘ renormalized ’ quadrupole, three-dimensional nature, which an important step computation gravitational-wave flux with accuracy. Furthermore, explicitly prove equivalence between previously used Hadamard partie finie scheme up 3PN order.