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

TL;DR

This paper develops a Monte Carlo method to compute stationary solutions of the relativistic Vlasov equation in Kerr spacetime, focusing on thin disk models and their physical properties.

Contribution

It extends a Monte Carlo scheme to Kerr spacetime and applies it to thin disk configurations, providing new computational tools for relativistic kinetic models.

Findings

Successfully recovers particle current surface density components.

Analyzes bulk angular momentum and angular velocity of kinetic disks.

Demonstrates applicability to monoenergetic and Maxwell-Jüttner distributions.

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.