Spin Effects in the Effective Field Theory Approach to Post-Minkowskian Conservative Dynamics

TL;DR

The paper advances the post-Minkowskian treatment of binary dynamics by incorporating spinning compact objects into the worldline EFT framework. It derives momentum and spin impulses to 2PM order, including linear and bilinear spin effects and finite-size corrections, and establishes a covariant, on-shell boundary-to-bound mapping for aligned spins to obtain bound-state observables. The aligned-spin analysis yields the radial action, periastron advance, and circular-orbit binding energy, with results matching and extending existing literature. The work also provides a canonical-variable translation and a detailed Impetus (CoM momentum) expansion, laying the groundwork for a Hamiltonian formulation consistent with PM spin dynamics and offering new insights into Kerr-like finite-size effects.

Abstract

Building upon the worldline effective field theory (EFT) formalism for spinning bodies developed for the Post-Newtonian regime, we generalize the EFT approach to Post-Minkowskian (PM) dynamics to include rotational degrees of freedom in a manifestly covariant framework. We introduce a systematic procedure to compute the total change in momentum and spin in the gravitational scattering of compact objects. For the special case of spins aligned with the orbital angular momentum, we show how to construct the radial action for elliptic-like orbits using the Boundary-to-Bound correspondence. As a paradigmatic example, we solve the scattering problem to next-to-leading PM order with linear and bilinear spin effects and arbitrary initial conditions, incorporating for the first time finite-size corrections. We obtain the aligned-spin radial action from the resulting scattering data, and derive the periastron advance and binding energy for circular orbits. We also provide the (square of the) center-of-mass momentum to ${\cal O}(G^2)$, which may be used to reconstruct a Hamiltonian. Our results are in perfect agreement with the existent literature, while at the same time extend the knowledge of the PM dynamics of compact binaries at quadratic order in spins.

Figures (1)

• Figure 1: Feynman topologies needed to 2PM order. (See text.)