A Monte Carlo approach to stationary kinetic disks in the Kerr spacetime

Abstract

We extend a recently proposed Monte Carlo scheme for computing stationary solutions of the general-relativistic Vlasov equation to the Kerr spacetime. As an example, we focus on razor-thin configurations of a gas confined to the equatorial plane and extending to spatial infinity. We consider monoenergetic models as well as solutions corresponding to planar Maxwell-J\"{u}ttner distributions at infinity. In both cases, the components of the particle current surface density are recovered within the proposed Monte Carlo framework. Some aspects of razor-thin kinetic disk models, including an analysis of the bulk angular momentum and angular velocity, are briefly covered.