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

TL;DR

This paper extends Monte Carlo simulation techniques to model stationary collisionless gas accretion onto a moving Schwarzschild black hole, demonstrating the method's flexibility beyond symmetric cases.

Contribution

It introduces an extended Monte Carlo approach for stationary relativistic Vlasov systems applicable to non-symmetric accretion scenarios.

Findings

Successful simulation of planar accretion onto a moving black hole

Extension of Monte Carlo methods beyond symmetric assumptions

Development of a coarse graining scheme for observable calculations

Abstract

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 the appropriate parametrization of particle trajectories and a selection of parameters consistent with assumed requirements on the distribution function.