Dynamics of compact binary systems in scalar-tensor theories: I. Equations of motion to the third post-Newtonian order

TL;DR

This paper derives the equations of motion for nonspinning compact binary systems in scalar-tensor theories up to the third post-Newtonian order, incorporating tail effects and regularisation techniques, to aid gravitational waveform modeling.

Contribution

It extends the post-Newtonian formalism to scalar-tensor theories at 3PN order, including tail effects and regularisation, for the first time.

Findings

Derived 3PN equations of motion in scalar-tensor theories.

Included tail effects with non-local terms.

Facilitates computation of scalar gravitational waveforms.

Abstract

Scalar-tensor theories are one of the most natural and well-constrained alternative theories of gravity, while still allowing for significant deviations from general relativity. We present the equations of motion of nonspinning compact binary systems at the third post-Newtonian (PN) order in massless scalar-tensor theories. We adapt the Fokker action of point particles in harmonic coordinates in general relativity to the specificities of scalar-tensor theories. We use dimensional regularisation to treat both the infrared and ultraviolet divergences, and we consistently include the tail effects that contribute by a non-local term to the dynamics. This work is crucial in order to compute the scalar gravitational waveform and the energy flux at 2PN order.