  In our program of studying numerically the so-called Bondi-Hoyle accretion in
the fully relativistic regime, we present here first results concerning the
evolution of matter accreting supersonically onto a rotating (Kerr) black hole.
These computations generalize previous results where the non-rotating
(Schwarzschild) case was extensively considered. We parametrize our initial
data by the asymptotic conditions for the fluid and explore the dependence of
the solution on the angular momentum of the black hole. Towards quantifying the
robustness of our numerical results, we use two different geometrical
foliations of the black hole spacetime, the standard form of the Kerr metric in
Boyer-Lindquist coordinates as well as its Kerr-Schild form, which is free of
coordinate singularities at the black hole horizon. We demonstrate some
important advantages of using such horizon adapted coordinate systems.
  Our numerical study indicates that regardless of the value of the black hole
spin the final accretion pattern is always stable, leading to constant
accretion rates of mass and momentum. The flow is characterized by a strong
tail shock, which, unlike the Schwarzschild case, is increasingly wrapped
around the central black hole as the hole angular momentum increases. The
rotation induced asymmetry in the pressure field implies that besides the well
known drag, the black hole will experience also a lift normal to the flow
direction. This situation exhibits some analogies with the Magnus effect of
classical fluid dynamics.
