Accretion of a Vlasov gas by a Kerr black hole

TL;DR

This paper studies how a collisionless relativistic gas accretes onto a rotating Kerr black hole, providing analytical and numerical insights into the effects of black hole spin on accretion rates and flow morphology.

Contribution

It offers a novel analysis of collisionless gas accretion onto Kerr black holes, including closed-form integral expressions and slow-rotation approximations for key physical quantities.

Findings

Angular momentum accretion reduces black hole spin.

Black hole rotation slightly affects mass and energy accretion rates.

Flow morphology is influenced by black hole rotation.

Abstract

We investigate the accretion of a collisionless, relativistic kinetic gas by a rotating Kerr black hole, assuming that at infinity the state of the gas is described by a distribution function depending only on the energy of the particles. Neglecting the self-gravity of the gas, we show that relevant physical observables, including the particle current density and the accretion rates associated with the mass, the energy, and the angular momentum, can be expressed in the form of closed integrals that can be evaluated numerically or approximated analytically in the slow-rotation limit. The accretion rates are computed in this manner for both monoenergetic particles and the Maxwell-J\"uttner distribution and compared with the corresponding results in the non-rotating case. We show that the angular momentum accretion rate decreases the absolute value of the black hole spin parameter. It is also found that the rotation of the black hole has a small but non-vanishing effect on the mass and the energy accretion rates, which is remarkably well described by an analytic calculation in the slow-rotation approximation to quadratic order in the rotation parameter. The effects of rotation on the morphology of the accretion flow are also analyzed.