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

## TL;DR

This paper derives an exact analytical solution for stationary kinetic gas accretion onto a Kerr black hole, providing explicit formulas for accretion rates and analyzing black hole growth and spin evolution.

## Contribution

It presents the first exact solution for Bondi-type accretion of a kinetic (Vlasov) gas onto a Kerr black hole with explicit integral expressions and simple formulas for key accretion parameters.

## Key findings

- Explicit integral expressions for particle current and accretion rates.
- Analytic formulas for mass, energy, and angular momentum accretion rates.
- Estimates of black hole growth and spin-down timescales under different ambient energy conditions.

## 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.