黑洞吸积过程中的跨音性--广义Sturm链的数学研究
Transonicity in black hole accretion -- A mathematical study using the generalized Sturm chains
摘要：
利用代数多项式理论和动力系统理论，构造了广义Sturm序列/链，研究了非旋转天体物理黑洞的流体动力吸积流的跨音速性质，完全解析地证明了这种吸积流可以有多少个临界点.我们的工作是非常重要的，因为第一次在文献中，我们提供了一个纯粹的分析方法，通过应用某些强大的代数多项式定理在纯数学，检查是否某些天体物理流体动力吸积可能会经历一个以上的音速转变。我们的工作可以推广到解析计算某些自治动力系统的平衡点的最大数量可以在一般情况下（节略）。
英文摘要：
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).
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