Center-of-Mass Equations of Motion and Conserved Integrals of Compact Binary Systems at the Fourth Post-Newtonian Order

TL;DR

This paper derives the equations of motion and conserved quantities for compact binary systems at the 4PN order in general relativity, including tail effects and radiation reaction, providing a comprehensive framework for their dynamics.

Contribution

It presents the first complete derivation of the center-of-mass equations, conserved integrals, and reduction to quasi-circular orbits at 4PN order, incorporating tail effects and dissipation.

Findings

Derived the ten Poincaré constants of motion at 4PN order.

Formulated the center-of-mass equations of motion and conserved quantities.

Included tail effects and radiation-reaction contributions in the dynamics.

Abstract

The dynamics of compact binary systems at the fourth post-Newtonian (4PN) approximation of general relativity has been recently completed in a self-consistent way. In this paper, we compute the ten Poincar\'e constants of the motion and present the equations of motion in the frame of the center of mass (CM), together with the corresponding CM Lagrangian, conserved energy and conserved angular momentum. Next, we investigate the reduction of the CM dynamics to the case of quasi-circular orbits. The non local (in time) tail effect at the 4PN order is consistently included, as well as the relevant radiation-reaction dissipative contributions to the energy and angular momentum.