Evolution of transonicity in an accretion disc

Abstract

For inviscid, rotational accretion ows driven by a general pseudo Newtonian potential on to a Schwarzschild black hole, the only possible xed points are saddle points and centre-type points. For the speci c choice of the Newtonian potential, the ow has only two critical points, of which the outer one is a saddle point while the inner one is a centre-type point. A restrictive upper bound is imposed on the admissible range of values of the angular momentum of sub-Keplerian ows through a saddle point. These ows are very unstable to any deviation from a necessarily precise boundary condition. The di culties against the physical realisability of a solution passing through the saddle point have been addressed through a temporal evolution of the ow, which gives a non-perturbative mechanism for selecting a transonic solution passing through the saddle point. An equation of motion for a real-time perturbation about the stationary ows reveals a very close correspondence with the metric of an acoustic black hole, which is also an indication of the primacy of transonicity