Astronomy and Astrophysics – Astrophysics – High Energy Astrophysical Phenomena
Scientific paper
2009-07-27
Astronomy and Astrophysics
Astrophysics
High Energy Astrophysical Phenomena
This paper has been withdrawn by the authors due to a major algebraic error recently identified in one of the main equations u
Scientific paper
By applying the theory of algebraic polynomials and the theory of dynamical systems, we construct the generalized Sturm sequences/chains to investigate the transonic properties of hydrodynamic accretion onto non-rotating astrophysical black holes, to demonstrate, completely analytically, how many critical point such an accretion flow can have. Our work is significantly important, because for the first time in the literature, we provide a purely analytical method, by applying certain powerful theorem of algebraic polynomials in pure mathematics, to check whether certain astrophysical hydrodynamic accretion may undergo more than one sonic transitions. Our work can be generalized to analytically calculate the maximal number of equilibrium points certain autonomous dynamical systems can have in general (Abridged).
Agarwal Shilpi
Das Tapas K.
Dey Rukmini
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