Hadamard regularization of the third post-Newtonian gravitational wave generation of two point masses

Continuing previous work on the 3PN-accurate gravitational-wave generation from point-particle binaries, we obtain the binary’s 3PN mass-type quadrupole and dipole moments for general (not necessarily circular) orbits in harmonic coordinates. The final expressions are given in terms of their core parts, resulting from the application of the pure-Hadamard-Schwartz self-field regularization scheme, and augmented by an ambiguous part. In the case of the 3PN quadrupole we find three ambiguity parameters, $\xi$, $\kappa$ and $\zeta$, but only one for the 3PN dipole, in the form of the particular combination $\xi +\kappa$. Requiring that the dipole moment agree with the center-of-mass position deduced from the 3PN equations of motion in harmonic coordinates yields the relation $\xi +\kappa =-9871/9240$. Our results will form the basis of the complete calculation of the 3PN radiation field of compact binaries by means of dimensional regularization.