# Spherical steady-state accretion of a relativistic collisionless gas into a Schwarzschild black hole

## TL;DR

This paper numerically analyzes steady-state, spherical accretion of a relativistic collisionless gas into a Schwarzschild black hole, comparing kinetic and fluid models and exploring the effects of temperature on accretion observables.

## Contribution

It provides explicit numerical computations of accretion observables for a collisionless gas, extending previous theoretical solutions to detailed, temperature-dependent profiles.

## Key findings

- Accretion observables vary significantly with temperature.
- Kinetic model results differ from perfect fluid approximations.
- Behavior of stress-energy tensor analyzed across radial distances.

## Abstract

In previous work, we derived the most general solution of the collisionless Boltzmann equation describing the accretion of a kinetic gas into a Schwarzschild black hole background, and we gave explicit expressions for the corresponding observables (the current density and stress energy-momentum tensor) in terms of certain integrals over the distribution function. In this article, we numerically compute these integrals for the particular case of the steady-state, spherical symmetric accretion flows which, at infinity, are described by an equilibrium distribution function of given temperature. We analyze in detail the behavior of the observables as a function of the temperature and the radial coordinate, comparing our results with the perfect fluid model of Bondi-Michel accretion.