# Relativistic wind accretion on to a Schwarzschild black hole

## TL;DR

This paper introduces a new relativistic wind accretion model onto a Schwarzschild black hole, extending classical theories with analytic solutions, and confirms its accuracy through numerical simulations, showing increased accretion rates at high wind speeds.

## Contribution

It provides the first analytic relativistic extension of the classical wind accretion model, including explicit expressions and numerical schemes, validated against hydrodynamic simulations.

## Key findings

- Relativistic accretion rates are significantly higher than Newtonian predictions at high wind speeds.
- Analytic streamlines and accretion rates match well with numerical simulations within 10%.
- The model is valid for steady, axisymmetric, ballistic flows around Schwarzschild black holes.

## Abstract

We present a novel analytic model of relativistic wind accretion on to a Schwarzschild black hole. This model constitutes a general relativistic extension of the classical model of wind accretion by Bondi, Hoyle, and Lyttleton (BHL). As in BHL, this model is based on the assumptions of steady state, axisymmetry, and ballistic motion. Analytic expressions are provided for the wind streamlines while simple numerical schemes are presented for calculating the corresponding accretion rate and density field. The resulting accretion rate is greater in the relativistic model when compared to the Newtonian BHL one. Indeed, it is two times greater for asymptotic wind speeds $v_\infty \ge 0.4\,\mathrm{c}$ and more than an order of magnitude greater for $v_\infty \ge 0.8\,\mathrm{c}$. We have compared this full relativistic model versus numerical simulations performed with the free GNU Public Licensed hydrodynamics code AZTEKAS and found a good agreement for the streamlines in the upstream region of the flow and also, to within 10 per cent, for the corresponding accretion rates.