A Dynamical Systems Analysis of Axisymmetric Accretion in a Schwarzschild Black Hole

TL;DR

This paper analyzes the behavior of axisymmetric accretion flows onto Schwarzschild black holes using dynamical systems theory, identifying the nature of critical points and flow geometries in a relativistic framework.

Contribution

It provides a comprehensive dynamical systems analysis of transonic accretion flows in general relativity, classifying critical points for different flow geometries and conditions.

Findings

Only saddle and centre points are physically possible for transonic flows.

Critical points depend on flow geometry and thermodynamic conditions.

Flow stability is characterized by eigenvalue analysis of the dynamical system.

Abstract

Stationary, inviscid, axi-symmetric, rotating, transonic accretion flow has been studied in a general relativistic framework, in the Schwarzschild metric; for three different flow geometries - under both polytropic and isothermal conditions. The equilibrium points of the underlying fluid system have been located and an eigenvalue based linear dynamical systems analysis of these critical points has been carried out, to obtain a taxonomic scheme of the critical points. It has hence been shown that only saddle and centre type points can arise for real, physical transonic flow.