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

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