Equatorial accretion on the Kerr black hole

We investigate stationary accretion of the collisionless Vlasov gas onto the Kerr black hole, occurring in the equatorial plane. At infinity the gas obeys the Maxwell-J\"{u}ttner distribution, restricted to the equatorial plane. In the vicinity of the black hole, the motion of the gas is governed by the spacetime geometry. 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. The accretion slows down the rotation of the black hole. We present preliminary results for a Vlasov gas accretion onto a Kerr black hole moving with a velocity parallel to the equatorial plane.