Accretion of the relativistic collisionless gas in the equatorial plane of the Kerr black hole

I will discuss a model of stationary accretion of a collisionless Vlasov gas onto the Kerr black hole, occurring in the equatorial plane. The solution is specified by imposing asymptotic boundary conditions: at infinity the gas obeys the Maxwell-Jüttner distribution, restricted to the equatorial plane (both in positions and momenta). We compute accretion rates of the rest-mass, the energy, and the angular momentum, as well as the particle number surface density, focusing on the dependence of these quantities on the asymptotic temperature of the gas and the black hole spin. Our model belongs to a larger research project aiming at a kinetic description of black hole accretion processes, with emphasis put on possible physical signatures of dark matter accretion onto black holes. The talk will be mainly based on the results published in Phys. Rev. D 106, 104056 (2022).