An ultrarelativistic relativistic study of axisymmetric Bondi--Hoyle accretion onto a moving Kerr black hole is presented. The equations of general relativistic hydrodynamics are solved using high resolution shock capturing methods. In this treatment we consider the ultrarelativistic limit wherein one may neglect the baryon rest mass density. This approximation is valid in the regime where the internal energy of the system dominates over the rest mass energy contribution from the baryons. The parameters of interest in this study are the adiabatic constant $Γ$, and the asymptotic speed of the fluid, $v_\infty$. We perform our simulations in three different regimes, subsonic, marginally supersonic, and supersonic, but the primary focus of this study is the parameter regime in which the flow is supersonic, that is when $v_\infty \ge c_{s}^{\infty}$. As expected from previous studies the supersonic regimes reveal interesting dynamics, but even more interesting is the presence of a bow shock in marginally supersonic systems. A range of parameter values were investigated to attempt to capture possible deviations from steady state solutions, none were found. To show the steady state behaviour of each of the flows studied we calculate the energy accretion rates on the Schwarzschild radius. Additionally, we also find that the accretion flows are dependent on the location of the computational boundary, that if the computational boundary is located too close to the black hole the calculated flow profiles are marred with numerical artifacts. This is a problem not found in previous relativistic models for ultrarelativistic hydrodynamic systems.

16 pages, 15 figures, Typos corrected