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

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.

34 pages, close to published version

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• Quasi-Keplerian parametrization for eccentric compact binaries in scalar-tensor theories at second post-Newtonian order and applications
• Nonlocal-in-time effective one body Hamiltonian in scalar-tensor gravity at third post-Newtonian order
• Bootstrapping spinning two body problem in dynamical Chern-Simons gravity using worldline QFT
• Post-Keplerian waveform model for binary compact object as sources of space-based gravitational wave detector and its implications
• Quasi-Keplerian parametrization for compact binaries on hyperbolic orbits in scalar-tensor theories at second post-Newtonian order