Critical properties and stability of stationary solutions in multitransonic pseudo-Schwarzschild accretion

For inviscid, rotational accretion ows, both isothermal and polytropic, a simple dy-namical systems analysis of the critical points has given a very accurate mathematical scheme to understand the nature of these points, for any pseudo-potential by which the ow may be driven on to a Schwarzschild black hole. This allows for a complete classi cation of the critical points for a wide range of ow parameters, and shows that the only possible critical points for this kind of ow are saddle points and centre-type points. A restrictive upper bound on the angular momentum of critical solutions has been established. A time-dependent perturbative study reveals that the form of the perturbation equation, for both isothermal and polytropic ows, is invariant under the choice of any particular pseudo-potential. Under generically true outer boundary con-ditions, the inviscid ow has been shown to be stable under an adiabatic and radially propagating perturbation. The perturbation equation has also served the dual pur-pose of enabling an understanding of the acoustic geometry for inviscid and rotational ows. Key words: accretion, accretion discs { black hole physics { hydrodynamics