Researchers have developed a method to determine the radiation-reaction force at the 3.5 post-Newtonian order for general orbits, considering its coordinate dependence. The radiation-reaction force describes how a system loses energy and angular momentum through the emission of gravitational waves. This work is based on the balance method, which relates the energy and angular momentum lost by the system to the energy and angular momentum fluxes at infinity, as well as the Schott terms. The novelty lies in how the gauge (or coordinate system) dependence of these terms, which has traditionally complicated their calculation, is handled.

The study addresses the gauge-dependent nature of both the radiation-reaction force and the Schott terms, encoded in a set of gauge parameters. The authors demonstrate how to relate the losses of mechanical energy and angular momentum in harmonic coordinates to the radial and azimuthal components of the radiation-reaction force in a different coordinate system. The advantage of this approach is that only the coordinate transformation between the harmonic system and the new system is needed, without having to re-solve the balance equations. This significantly simplifies the calculation process.

Necessary transformations are derived for both Arnowitt-Deser-Misner (ADM) and Effective-One-Body (EOB) coordinates. In the EOB case, simplifying choices of gauge parameters used in current gravitational waveform models are discussed. Finally, the work shows how to obtain the radiation-reaction correction to the orbit in the new coordinate system simply by transforming the known solution in harmonic coordinates, representing a remarkable simplification by avoiding the need to re-solve the radiation-reacted dynamics.