IX Black Hole Workshop

Guimarães 19-20 December 2016

I will present the latest results on the Fokker Lagrangian describing the dynamics of non-spinning compact binary systems at the fourth post-Newtonian order in harmonic coordinates. This work is important in view of the detection and precise determination of the physical parameters of gravitational waves by the current and next generations of interferometric detectors. In this talk, I will focus on two main issues that arise in the derivation of the Fokker action at 4PN. First, I will precise the impact of the non-local character of the Fokker action, due to the presence of the tail effect at the 4PN order, on both the conserved energy and the relativistic periastron precession for circular orbits. Then, I will show that the regularization procedure for the infra-red divergences in the calculation of the gravitational part of the action is problematic, and requires the introduction of a second ambiguity parameter. After fixing the two ambiguity parameters by using gravitational self-force results, our final Lagrangian is physically entirely equivalent to the one obtained in the ADM approach.