  We investigate accretion of dark matter onto a moving Schwarzschild black
hole. The dark matter is modeled by the collisionless Vlasov gas, assumed to be
in thermal equilibrium at infinity. We derive an exact stationary solution and
provide a compact formula for the mass accretion rate. In general, the mass
accretion rate is a nonmonotonic function of the black hole velocity. A
monotonic relation (the accretion rate proportional to the Lorentz factor
associated with the velocity of the black hole) is obtained for high asymptotic
temperatures of the gas. The derived accretion rates are relevant for the
growth of primordial black holes in the early Universe.
