N-body next-to-leading order gravitational spin-orbit interaction via effective field theory

TL;DR

This paper extends the effective field theory approach to derive the NLO spin-orbit interaction Hamiltonian for N gravitating bodies, including three-body effects, in general relativity.

Contribution

It generalizes the EFT treatment of spin-orbit interactions from binary to N-body systems and compares two derivation methods.

Findings

Derived the NLO spin-orbit potential and Hamiltonian for N bodies.

Identified three-body interaction diagrams as the new contributions.

Confirmed agreement with the ADM N-body Hamiltonian up to a canonical transformation.

Abstract

Using the post-Newtonian effective field theory (PN-EFT) formalism for spinning gravitating bodies, we derive the next-to-leading-order (NLO) spin-orbit potential and Hamiltonian for a system of N spinning bodies in general relativity. This extends the EFT treatment of the binary case to arbitrary N. We present two derivations: one in the generalized canonical gauge, and one based on the covariant spin supplementary condition (SSC), followed by a noncanonical transformation to canonical variables. In both approaches, the only new contributions beyond the binary case are three-body interaction diagrams. The canonical Hamiltonians obtained from the two EFT routes agree with the known ADM N-body Hamiltonian of Hartung and Steinhoff up to a canonical transformation.