Leading-order spin-orbit and spin(1)-spin(2) radiation-reaction Hamiltonians

TL;DR

This work derives the leading-order post-Newtonian radiation-reaction Hamiltonians for spin-orbit and spin(1)–spin(2) interactions using the ADM canonical formalism, with results valid for arbitrary numbers of spinning bodies. By performing near-zone expansions and solving the field constraints, the authors obtain the 2.5PN and 3.5PN dissipative Hamiltonians, including spin contributions, and compute the corresponding instantaneous energy loss, demonstrating agreement with the standard far-zone energy flux in harmonic coordinates up to a gauge-dependent total time derivative. The spin-dependent parts are expressed through a set of integrals and auxiliary quantities (e.g., h^{TT}_{ij}, B_{(4)ij}, B_{(6)ij}, chi, Pi, R, Q), providing compact, gauge-consistent equations of motion for spinning binaries and extending previous conservative results to the dissipative sector. These results are relevant for gravitational-wave template accuracy in the late inspiral of rapidly rotating compact binaries, and lay groundwork for higher-order spin Hamiltonians (e.g., 4PN) and broader multi-body applications.

Abstract

In the present paper, the leading-order post-Newtonian spin-orbit and spin(1)-spin(2) radiation-reaction Hamiltonians are calculated. We utilize the canonical formalism of Arnowitt, Deser, and Misner (ADM), which has shown to be valuable for this kind of calculation. The results are valid for arbitrary many objects. The energy loss is then computed and compared to well-known results for the energy flux as a check.