# Dynamics of compact binary systems in scalar-tensor theories: II. Center-of-mass and conserved quantities to 3PN order

## TL;DR

This paper extends the analysis of nonspinning compact binary systems in scalar-tensor theories by deriving conserved quantities and equations of motion at 3PN order, focusing on the center-of-mass frame and circular orbits.

## Contribution

It provides the complete set of integrals of motion and reduces the equations to quasi-circular orbits at 3PN order in scalar-tensor theories, advancing the theoretical understanding.

## Key findings

- Derived the ten integrals of motion at 3PN order.
- Reduced equations to quasi-circular orbits.
- Determined conserved energy and angular momentum for circular orbits.

## Abstract

The equations of motion of nonspinning compact binary systems at the third post-Newtonian (PN) order in massless scalar-tensor theories have recently been obtained. In the present paper, we complete this work by computing at 3PN order the ten integrals of motion together with the equations of motion in the center-of-mass frame. We then perform the reduction of the center-of-mass equations to quasi-circular orbits and determine the conserved energy and angular momentum for circular orbits.