  We present a new geometrical approach to the study of accretion flows onto
rotating (Kerr) black holes. Instead of Boyer-Lindquist coordinates, the
standard choice in all existing numerical simulations in the literature, we
employ the simplest example of a horizon adapted coordinate system, the
Kerr-Schild coordinates. This choice eliminates boundary ambiguities and
unphysical divergent behavior at the event horizon. Computations of Bondi-Hoyle
accretion onto extreme Kerr black holes, performed here for the first time,
demonstrate the key advantages of this procedure. We argue it offers the best
approach to the numerical study of the, observationally, increasingly more
accesible relativistic inner region around black holes.
