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

TL;DR

This paper derives advanced Hamiltonians describing the gravitational interactions involving spins for multiple compact objects, enhancing the understanding of three-body effects in relativistic astrophysics.

Contribution

It provides the first derivation of next-to-leading order spin-orbit and spin(a)-spin(b) Hamiltonians for many-body systems, including complex three-body interactions.

Findings

Hamiltonians complete up to 2.5PN order for three-body systems.

Inclusion of nontrivial three-body spin interactions.

Potential implications for black hole merger dynamics.

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.