A Dynamical Systems Analysis of Axisymmetric Accretion in a   Schwarzschild Black Hole
  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. 
Shamreen Iram
gr-qc