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Research Accomplished

In our treatment the nonlinear equations describing the steady, inviscid, rotational, axisymmetric flow in the Kerr metric, have been tailored to form a first-order autonomous dynamical system. The critical points of the phase trajectories of the flow have been identified first, following which, a linearized study in the neighbourhood of these critical points has been carried out. As a consequence of this exercise, a complete and rigorous mathematical classification scheme for the nature of the critical points has been derived, and it has been argued that the critical points can admissibly be only saddle points and centre-type points for the kind of conserved, axisymmetric and rotational flow under study here. While all of these are principally the attributes of the hydrodynamical process itself, the influence of the black hole (the agent external to the fluid, but driving its flow nonetheless) has also been noteworthy to the extent that its intrinsic rotational parameter affects the character of multitransonicity in general and the properties of an individual critical point in particular. This is an important result to have emerged from the study.

In a stationary, general relativistic, axisymmetric, inviscid and rotational accretion flow, described within the Kerr geometric framework, transonicity has been examined by setting up the governing equations of the flow as a first-order autonomous dynamical system. The consequent linearized analysis of the critical points of the flow leads to a comprehensive mathematical prescription for classifying these points, showing that the only possibilities are saddle points and centre-type points for all ranges of values of the fixed flow parameters. The spin parameter of the black hole influences the multi-transonic character of the flow, as well as some of its specific critical properties. The special case of a flow in the space-time of a non-rotating black hole, characterized by the Schwarzschild metric, has also been studied for comparison and the conclusions are compatible with what has been seen for the Kerr geometric case.

Using post-Newtonian formalism, 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 flows, is invariant under the choice of any particular pseudo-potential. Under generically true outer boundary conditions, the inviscid flow has been shown to be stable under an adiabatic and radially propagating perturbation. The perturbation equation has also served the dual purpose of enabling and understanding the acoustic geometry for inviscid and rotational flows.
next up previous
Next: Ongoing/Future Project Up: Astrophysical Fluid as an Previous: Introduction
Tapas Kumar Das 2009-01-17