Non-axisymmetric relativistic Bondi-Hoyle accretion on to a Kerr black hole

In our programme of studying numerically the so-called Bondi-Hoyle accretion in the fully relativistic regime, we present here the first results concerning the evolution of matter accreting supersonically on to 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 space-time, 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 how direction. This situation exhibits some analogies with the Magnus effect of classical fluid dynamics.