Shilpi Agarwal, Tapas K. Das, Rukmini Dey
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).
View original:
http://arxiv.org/abs/0907.4754
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