Analytic solutions to the accretion of a rotating finite cloud towards a central object - II. Schwarzschild spacetime

TL;DR

This paper presents an analytic general relativistic model for the accretion of a rotating finite cloud onto a Schwarzschild black hole, providing explicit solutions for streamlines, velocity, and density fields useful for benchmarking and parameter exploration.

Contribution

It introduces a novel analytic framework for relativistic accretion flows with explicit solutions, extending previous Newtonian models to Schwarzschild spacetime.

Findings

Analytic expressions for streamlines and velocity fields using Jacobi elliptic functions.

A numerical scheme for calculating the density field in the accretion flow.

The model serves as a benchmark for relativistic hydrodynamical simulations.

Abstract

We construct a general relativistic model for the accretion flow of a rotating finite cloud of non-interacting particles infalling onto a Schwarzschild black hole. The streamlines start at a spherical shell, where boundary conditions are fixed, and are followed down to the point at which they either cross the black hole horizon or become incorporated into an equatorial thin disc. Analytic expressions for the streamlines and the velocity field are given, in terms of Jacobi elliptic functions, under the assumptions of stationarity and ballistic motion. A novel approach allows us to describe all of the possible types of orbit with a single formula. A simple numerical scheme is presented for calculating the density field. This model is the relativistic generalisation of the Newtonian one developed by Mendoza, Tejeda, Nagel, 2009 and, due to its analytic nature, it can be useful in providing a benchmark for general relativistic hydrodynamical codes and for exploring the parameter space in applications involving accretion onto black holes when the approximations of steady state and ballistic motion are reasonable ones.