Effective Field Theory for Extreme Mass Ratios

TL;DR

This paper develops an effective field theory framework for modeling gravitational interactions in systems with extreme mass ratios, enabling systematic calculations of dynamics including self-force effects and higher-order corrections.

Contribution

It introduces a novel EFT approach for extreme mass ratio systems, incorporating recoil effects and perturbations, and computes third post-Minkowskian order results for conservative dynamics.

Findings

Derived an EFT for gravitationally interacting particles with mass ratio expansion.

Included recoil effects of the heavy body in the formalism.

Computed third post-Minkowskian order conservative dynamics results.

Abstract

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.