The Quadrupole Moment of Compact Binaries to the Fourth post-Newtonian Order: I. Non-Locality in Time and Infra-Red Divergencies

Understand

With the aim of providing high accuracy post-Newtonian (PN) templates for the analysis of gravitational waves generated by compact binary systems, we complete the analytical derivation of the source type mass quadrupole moment of compact binaries (without spins) at the fourth PN order of general relativity.

• Similarly to the case of the conservative 4PN equations of motion, we show that the quadrupole moment at that order contains a non-local (in time) contribution, arising from the tail-transported interaction entering the conservative part of the dynamics.
• Furthermore, we investigate the infra-red (IR) divergences of the quadrupole moment.
• In a previous work, this moment has been computed using a Hadamard partie finie procedure for the IR divergences, but the knowledge of the conservative equations of motion indicates that those divergences have to be dealt with by means of dimensional regularization.