A "horizon-adapted" approach to the study of relativistic accretion flows onto rotating black holes

We present a new geometrical approach to the study of accretion flows onto rotating black holes. instead of Boyer-Lindquist coordinates, the standard choice in all existing numerical simulations in the literature, we employ t he simplest example of a horizon-adapted coordinate system, the Kerr-Schild coordinates. This choice eliminates unphysical divergent behavior at the e vent horizon. Computations of Bondi-Hoyle accretion onto extreme Kerr black holes, performed here for the first time, demonstrate the key advantages o f this procedure. We argue that it offers the best approach to the numerica l study of the observationally increasingly, more accessible, relativistic inner region around black holes.