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arXiv · 2605.15160

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

Leonardo Wimmer·Hideyuki Tagoshi
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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.

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Leonardo Wimmer, Hideyuki Tagoshi. 2026-05-14. N-body next-to-leading order gravitational spin-orbit interaction via effective field theory. https://arxiv.org/abs/2605.15160

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