Monte Carlo methods for stationary solutions of general-relativistic Vlasov systems: Planar accretion onto a moving Schwarzschild black hole

We perform Monte Carlo simulations of stationary planar accretion of a collisionless gas onto a moving Schwarzschild black hole. In this work---a sequel to our previous paper on the Monte Carlo method for stationary general-relativistic Vlasov systems---we demonstrate that our approach can be extended beyond the simplifying assumptions of the spherical symmetry or axial symmetry in the planar case. Our method of computing observable quantities, such as the particle current density, can be regarded as a rigorous coarse graining scheme, adapted to a numerical grid. Main difficulties are related to an appropriate parametrization of particle trajectories and a selection of parameters consistent with assumed requirements on the distribution function.