Bondi-type accretion onto a Kerr black hole in the kinetic regime

TL;DR

This work develops an exact Bondi-type accretion model for a kinetic (Vlasov) gas onto a Kerr black hole, with a gas that originates from infinity in a homogeneous, at-rest state. By solving the Vlasov equation and exploiting constants of motion, the authors express particle fluxes and accretion rates as explicit integrals and derive analytic approximations for the mass, energy, and angular momentum accretion, enabling characteristic growth and spin-down timescales. They provide a detailed treatment of unbound Kerr geodesics, distinguish absorbed and scattered populations, and obtain both exact and slow-rotation approximations, including asymptotic limits for high and low host temperatures. The work further analyzes the implications for black hole evolution in cosmological contexts, presenting two scenarios for mass growth and spin evolution and showing that significant growth requires extremely cold dark matter; these results offer a tractable kinetic framework for assessing SMBH growth and spin changes in realistic ambient media.

Abstract

We derive an exact solution representing a Bondi-type stationary accretion of a kinetic (Vlasov) gas onto the Kerr black hole. The solution is exact in the sense that relevant physical quantities, such as the particle current density or the accretion rates, are expressed as explicit integrals, which can be evaluated numerically. We provide an analytic approximation which allows us to obtain simple formulas for the mass, energy, and angular momentum accretion rates. These formulas are used to derive characteristic time scales of the black hole mass growth and the associated spin-down in two different scenarios: assuming that the ambient energy density is either constant or decreases on a cosmological scale.

Figures (2)

• Figure 1: Compression ratio at the meridional plane close to the black hole horizon (white dashed line) for the Maxwell-Jüttner model with $z = 1$ and $\alpha = 0.95$. We denote $x = r/M$. The solid dark lines mark contours of constant $n$. This plot can be compared with Fig. 11 in mainpaper obtained for monoenergetic distributions.
• Figure 2: Energy accretion rates for the Maxwell-Jüttner model with small (left) and large (right) values of $z$. Discrete marks denote exact values. Lines correspond to the slow-rotation approximation.