Gravitational spin-orbit coupling in binary systems, post-Minkowskian approximation, and effective one-body theory

A novel approach for extracting gauge-invariant information about spin-orbit coupling in gravitationally interacting binary systems is introduced. This approach is based on the ``scattering holonomy'', i. e. the integration (from the infinite past to the infinite future) of the differential spin evolution along the two worldlines of a binary system in hyperboliclike motion. We apply this approach to the computation, at the first post-Minkowskian approximation (i. e. first order in G and all orders in v/c), of the values of the two gyrogravitomagnetic ratios describing spin-orbit coupling in the effective one-body formalism. These gyrogravitomagnetic ratios are found to tend to zero in the ultrarelativistic limit.