  We study the problem of a spherically-symmetric distribution of a perfect
relativistic fluid accreting onto a (potentially spinning) black hole within a
fully discrete spacetime setting. This problem has previously been studied
extensively in the context of continuum spacetimes, beginning with the purely
analytic work of Bondi in the spherically-symmetric Newtonian case, Michel in
the spherically-symmetric general relativistic case, and Petrich, Shapiro and
Teukolsky in the axially-symmetric general relativistic case relevant for
spinning black holes. However, the purpose of the present work is to determine
the effect of discretization of the underlying spacetime upon the mass/energy
and momentum accretion rates, the overall morphology and characteristics of the
accretion flow, and the drag force exerted on the black hole in the case of
non-zero spin. In order to achieve this, we first develop a novel formulation
of the equations of general relativistic hydrodynamics that is more directly
amenable to rigorous analysis within a discrete spacetime setting, and we then
proceed to implement this formulation into the Gravitas computational general
relativity framework. Through a combination of mathematical analysis and
explicit numerical simulation in Gravitas, we discover that the mass/energy and
momentum accretion rates both decrease monotonically as functions of the
underlying spacetime discretization scale, with this effect becoming more
pronounced for higher values of the black hole spin parameter, higher fluid
temperatures, and stiffer equation of state parameters. We also find that the
exerted drag force is highly sensitive to the value of the underlying
discretization scale in the case of spinning black hole spacetimes, with
certain instabilities becoming significantly more pronounced at certain
critical values of the discretization parameter.
