Radiation reaction for spinning bodies in effective field theory I: Spin-orbit effects

TL;DR

This work develops an effective field theory framework for radiation reaction in gravity that incorporates spinning bodies at linear order in spin, computing the leading spin-orbit contributions to the radiation-reaction acceleration and spin evolution at $4PN$ order. The analysis is carried out in both Newton-Wigner and covariant spin supplementary conditions, using a doubled-degree-of-freedom, nonconservative action and a Routhian formalism to derive the RR effects from first principles. A nontrivial consistency check shows that the RR-induced power matches the far-zone radiated power up to Schott terms, and the spin evolution receives no net contribution at this order, with spin-spin back-reaction left to a companion paper. The results refine high-precision waveform modeling for gravitational waves and establish a solid EFT-based approach for future higher-order spin effects in compact binaries.

Abstract

We compute the leading Post-Newtonian (PN) contributions at linear order in the spin to the radiation-reaction acceleration and spin evolution for binary systems, which enter at fourth PN order. The calculation is carried out, from first principles, using the effective field theory framework for spinning compact objects, in both the Newton-Wigner and covariant spin supplementary conditions. A non-trivial consistency check is performed on our results by showing that the energy loss induced by the resulting radiation-reaction force is equivalent to the total emitted power in the far zone, up to so-called "Schott terms." We also find that, at this order, the radiation reaction has no net effect on the evolution of the spins. The spin-spin contributions to radiation reaction are reported in a companion paper.