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Through detection by low gravitational wave space interferometers, thecapture of stars by supermassive black holes will constitute a giant stepforward in the understanding of gravitation in strong field. The impact of theperturbations on the motion of the star is computed via the tail, theback-scattered part of the perturbations, or via a radiative Green function. Inthe former approach, the self-force acts upon the background geodesic, while inthe latter, the geodesic is conceived in the total (background plusperturbations) field. Regularisations (mode-sum and Riemann-Hurwitz $\zeta$function) intervene to cancel divergencies coming from the infinitesimal sizeof the particle. The non-adiabatic trajectories require the most sophisticatedtechniques for studying the evolution of the motion, like the self-consistentapproach.

Self-force and motion of stars around black holes