Next-to-next-to-leading order post-Newtonian spin-orbit Hamiltonian for self-gravitating binaries

TL;DR

This paper derives the next-to-next-to-leading order post-Newtonian spin-orbit Hamiltonian for binary systems of spinning compact objects, completing the 3.5PN order understanding crucial for gravitational wave modeling.

Contribution

It provides the first complete 3.5PN order spin-orbit Hamiltonian for binary black holes, including rapid spins, using a novel combination of tests and algebraic consistency checks.

Findings

Hamiltonian matches known test-spin results

Ensures Poincare algebra consistency

Completes 3.5PN spin-orbit interaction description

Abstract

We present the next-to-next-to-leading order post-Newtonian (PN) spin-orbit Hamiltonian for two self-gravitating spinning compact objects. If at least one of the objects is rapidly rotating, then the corresponding interaction is comparable in strength to a 3.5PN effect. The result in the present paper in fact completes the knowledge of the post-Newtonian Hamiltonian for binary spinning black holes up to and including 3.5PN. The Hamiltonian is checked via known results for the test-spin case and via the global Poincare algebra with the center-of-mass vector uniquely determined by an ansatz.