We derive an effective field theory describing a pair of gravitationally interacting point particles in an expansion in their mass ratio, also known as the self-force (SF) expansion. The 0SF dynamics are trivially obtained to all orders in Newton’s constant by the geodesic motion of the light body in a Schwarzschild background encoding the gravitational field of the heavy body. The corrections at 1SF and higher are generated by perturbations about this configuration—that is, the geodesic deviation of the light body and the fluctuation graviton—but crucially supplemented by an operator describing the recoil of the heavy body as it interacts with the smaller companion. Using this formalism we compute new results at third post-Minkowskian order for the conservative dynamics of a system of gravitationally interacting massive particles coupled to a set of additional scalar and vector fields.

• Received 27 November 2023
• Accepted 23 January 2024

DOI:https://doi.org/10.1103/PhysRevLett.132.091402

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Published by the American Physical Society