Resonant relaxation of stars around a supermassive black hole
In the vicinity of a supermassive black hole, stars move on nearly Keplerian orbits. Yet, because of the enclosed stellar mass and general relativity, the potential slightly deviates from the Keplerian one, which causes the stellar orbits to precess. Similarly, as a result of the finite number of stars, the mutual gravitational torques between pairs of stars also drive a rapid reshuffling of the stars' orbital orientation, much faster than the standard two-body relaxation driven by local scatterings. Overall, the combination of these two effects leads to a stochastic evolution of stellar orbital angular momentum vectors, through a process named ``resonant relaxation". Owing to recent developments in the diffusion theory of self-gravitating systems, I will show how one can fully describe such dynamics, in particular scalar resonant relaxation (relaxation of the norm of the angular momentum) and vector resonant relaxation (relaxation of the direction of the angular momentum vector). I will also highlight some astrophysical applications of these new methods, for example to understand the inefficiency of resonant relaxation to induce stellar tidal disruptions, or the spontaneous dissolution of stellar discs in galactic nuclei.