  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 $\Gamma$, 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.
