Tensor-Multi-Scalar Gravity: Equations of Motion to 2.5 post-Newtonian Order

TL;DR

This paper extends the post-Newtonian formalism to tensor-multi-scalar gravity theories with multiple scalar fields, deriving equations of motion up to 2.5 post-Newtonian order to facilitate future gravitational waveform calculations.

Contribution

It introduces the first derivation of equations of motion at 2.5 post-Newtonian order for tensor-multi-scalar theories, expanding the framework beyond single scalar field models.

Findings

Derived equations of motion up to 2.5 post-Newtonian order

Established a formalism for tensor-multi-scalar gravitational theories

Paved the way for gravitational waveform modeling in these theories

Abstract

In the present paper we take a step towards the generalization of the post-Newtonian formalism to tensor-multi-scalar theories. These are theories where we have more than one scalar field being mediators of the gravitational interaction in addition to the spacetime metric. They are very natural extensions of Einstein's gravity allowing for the existence of new classes of compact objects and offering interesting phenomenology reaching far beyond the single scalar field theories. We calculate the expansion up to 2.5 post-Newtonian order in the near zone using the so-called direct integration of the relaxed Einstein equations formalism and derive the equation of motion. This work is the first step towards the calculation of gravitational waveforms in tensor-multi-scalar theories.