Next-to-leading order spin-orbit and spin(a)-spin(b) Hamiltonians for n gravitating spinning compact objects

Abstract

We derive the post-Newtonian next-to-leading order conservative spin-orbit and spin(a)-spin(b) gravitational interaction Hamiltonians for arbitrary many compact objects. The spin-orbit Hamiltonian completes the knowledge of Hamiltonians up to and including 2.5PN for the general relativistic three-body problem. The new Hamiltonians include highly nontrivial three-body interactions, in contrast to the leading order consisting of two-body interactions only. This may be important for the study of effects like Kozai resonances in mergers of black holes with binary black holes.