  We have studied numerically the so-called Bondi-Hoyle (wind) accretion on to
a rotating (Kerr) black hole in general relativity. We have used the
Kerr-Schild form of the Kerr metric, free of coordinate singularities at the
black hole horizon. The `test-fluid' approximation has been adopted, assuming
no dynamical evolution of the gravitational field. We have used a recent
formulation of the general relativistic hydrodynamic equations which casts them
into a first-order hyperbolic system of conservation laws. Our studies have
been performed using a Godunov-type scheme based on Marquina's flux-formula.
  We find 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 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.
