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

TL;DR

This paper extends the effective field theory approach to include spin effects in Post-Minkowskian gravitational dynamics, providing new calculations for scattering, orbital properties, and finite-size effects of spinning compact objects.

Contribution

It generalizes the EFT formalism to Post-Minkowskian regime with spins, introduces a systematic method for momentum and spin change calculations, and computes the radial action and related orbital parameters including finite-size corrections.

Findings

Derived the aligned-spin radial action from scattering data.

Calculated periastron advance and binding energy for circular orbits.

Extended PM dynamics knowledge to quadratic order in spins.

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.