A simple accretion model of a rotating gas sphere onto a Schwarzschild black hole

TL;DR

This paper develops an analytic general relativistic model of rotating gas accretion onto a Schwarzschild black hole, extending Newtonian models and predicting an unbounded growth of the accretion disc radius with angular momentum.

Contribution

It introduces a simple, analytic relativistic accretion model using Jacobi elliptic functions, generalizing Newtonian accretion to the relativistic regime.

Findings

Analytic solutions for relativistic accretion flows are derived.

The model predicts an infinitely increasing disc radius with angular momentum.

It extends classical accretion models into the relativistic domain.

Abstract

We construct a simple accretion model of a rotating pressureless gas sphere onto a Schwarzschild black hole. We show how to build analytic solutions in terms of Jacobi elliptic functions. This construction represents a general relativistic generalisation of the Newtonian accretion model first proposed by Ulrich (1976). In exactly the same form as it occurs for the Newtonian case, the flow naturally predicts the existence of an equatorial rotating accretion disc about the hole. However, the radius of the disc increases monotonically without limit as the flow reaches its maximum allowed angular momentum.