Accretion of the relativistic Vlasov gas onto a Kerr black hole

TL;DR

This paper analyzes the accretion process of relativistic Vlasov gas onto a Kerr black hole using a full 3+1 dimensional relativistic framework, deriving explicit formulas and numerical results that reveal how accretion rates depend on angle and temperature.

Contribution

It provides the first full 3+1 dimensional solution of the relativistic Vlasov equation in Kerr geometry and calculates detailed accretion rates and their angular dependence.

Findings

Unit mass accretion rate matches Schwarzschild in low temperature limit.

Accretion rates vary with angle, slowing down the black hole more near the equator.

Analytic results agree with numerical simulations at large distances.

Abstract

We study the accretion of relativistic Vlasov gas onto a Kerr black hole, regarding the particles as distributed throughout all the space, other than just in the equatorial plane. We solve the relativistic Liouville equation in the full $3+1$ dimensional framework of Kerr geometry. For the flow that is stationary and axial symmetric, we prove that the distribution function is independent of the conjugate coordinates. For an explicit distribution that can approximate to Maxwell-J\"{u}ttner distribution, we further calculate the particle current density, the stress energy momentum tensor and the unit accretion rates of mass, energy and angular momentum. The analytic results at large distance are shown to be consistent with the limits of the numerical ones computed at finite distance. Especially, we show that the unit mass accretion rate agrees with the Schwarzschild result in the case of low temperature limit. Furthermore, we find from the numerical results that the three unit accretion rates vary with the angle in Kerr metric and the accretion of Vlasov gas would slow down the Kerr black hole. The closer to the equator, the faster it slows down the black hole.