Gravitational radiation reaction along general orbits in the effective one-body formalism

TL;DR

This work extends the Effective One Body framework to general binary orbits by deriving a 2PN-accurate gravitational radiation-reaction force grounded in energy–angular-momentum balance, while omitting tails. A key innovation is a constructive decomposition of the combined flux $\Phi_{EJ}$ into minimal, gauge-friendly components that yield explicit expressions for the radial RR force ${\mathcal{F}}_r$, the azimuthal RR force ${\mathcal{F}}_\phi$, and the Schott energy $E_{\rm (schott)}$ in EOB variables. The authors also analyze gauge freedoms, show that a minimal choice with ${J}_{\rm (schott)}^{\rm EOB}=0$ and ${\mathcal{F}}_\phi=-\Phi_J$ fixes a consistent RR scheme, and apply the results to quasi-circular inspirals and hyperbolic scattering, including a PN-consistent treatment of conservative hyperbolic dynamics and RR-induced corrections to the scattering angle. These developments enable more accurate modeling of noncircular binary dynamics within EOB and lay groundwork for incorporating tails and waveform extensions in future work. Overall, the paper delivers a practical, PN-consistent path to RR forces for general orbits, with direct implications for high-precision waveform modeling and interpretation of hyperbolic encounters.

Abstract

We derive the gravitational radiation-reaction force modifying the Effective One Body (EOB) description of the conservative dynamics of binary systems. Our result is applicable to general orbits (elliptic or hyperbolic) and keeps terms of fractional second post-Newtonian order (but does not include tail effects). Our derivation of radiation-reaction is based on a new way of requiring energy and angular momentum balance. We give several applications of our results, notably the value of the (minimal) "Schott" contribution to the energy, the radial component of the radiation-reaction force, and the radiative contribution to the angle of scattering during hyperbolic encounters. We present also new results about the conservative relativistic dynamics of hyperbolic motions.