Collimation of a spherical collisionless particles stream in Kerr space-time

TL;DR

This paper studies how collisionless particles emitted from a spherical shell propagate in Kerr space-time, revealing that black hole spin causes an anti-collimation effect on the particle stream, especially at larger emission radii.

Contribution

It demonstrates the influence of black hole spin on particle stream collimation and confirms the effect in both strong and weak gravitational fields.

Findings

Particles tend to deviate from uniform distribution at infinity.

Black hole spin causes anti-collimation of particle streams.

The effect is confirmed in the weak field limit.

Abstract

We examine the propagation of collisionless particles emitted from a spherical shell to infinity. The number distribution at infinity, calculated as a function of the polar angle, exhibits a small deviation from uniformity. The number of particles moving from the polar region toward the equatorial plane is slightly larger than that of particles in the opposite direction, for an emission radius $ > 4.5M$ in extreme Kerr space-time. This means that the black hole spin exerts an anti-collimation effect on the particles stream propagating along the rotation axis. We also confirm this property in the weak field limit. The quadrupole moment of the central object produces a force toward the equatorial plane. For a smaller emission radius $r<4.5M$, the absorption of particles into the black hole, the non-uniformity and/or the anisotropy of the emission distribution become much more important.