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

In our programme of studying numerically the so-called Bondi-Hoyle accretio n in the fully relativistic regime, we present here the first results conce rning the evolution of matter accreting supersonically on to a rotating (Ke rr) black hole. These computations generalize previous results where the no n-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. Towa rds quantifying the robustness of our numerical results, we use two differe nt geometrical foliations of the black hole space-time, the standard form o f 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 coo rdinate systems. Our numerical study indicates that regardless of the value of the black hol e spin the final accretion pattern is always stable, leading to constant ac cretion rates of mass and momentum. The flow is characterized by a strong t ail shock, which, unlike the Schwarzschild case, is increasingly wrapped ar ound the central black hole as the hole angular momentum increases. The rot ation-induced asymmetry in the pressure field implies that, besides the wel l-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.