A Balescu-Lenard-type kinetic equation for the collisional evolution of stable self-gravitating systems

A kinetic equation for the collisional evolution of stable, bound, self-gravitating and slowly relaxing systems is established, which is valid when the number of constituents is very large. It accounts for the detailed dynamics and self-consistent dressing by collective gravitational interaction of the colliding particles, for the system's inhomogeneity and for different constituents' masses. It describes the coupled evolution of collisionally interacting populations, such as stars in a thick disc and the molecular clouds off which they scatter.