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

TL;DR

The work addresses the NNLO (3.5PN) spin-orbit coupling in the two-body problem of spinning compact objects by deriving an explicit Hamiltonian within the ADM canonical formalism. It employs a $d$-dimensional extension and UV-regularization to manage ambiguities, and uses delta-type, Riesz-type, and generalized Riesz-type integrals, with a 68-parameter center-of-mass vector fixed via the global Poincaré algebra. The resulting Hamiltonian, validated against Kerr-test spin results and Poincaré-consistency checks, extends the spin-orbit dynamics to 3.5PN for binaries of black holes or neutron stars (excluding tidal and higher-spin effects). This contribution supports high-precision modeling of spinning binaries and informs effective-one-body approaches pending future higher-order point-mass results.

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.