黑洞的稳定临界吸积：自引力和音速点特征
Steady critical accretion onto black holes: selfgravity and sonic point characteristics
摘要：
多变理想流体在黑洞上的球对称稳定吸积是能够证明反作用（自引力）效应的最简单的流动模型。16年前就已经发现，在适当的条件下，反反应不会影响声波点的某些（“密集”）特性。在这里，我们考虑更广泛的状态方程，多方指数在范围（1，2]，并建立详细的边界条件，允许证明这一事实。我们还发现数值例子显示我们的分析标准的限制-如果不满足合适的分析条件，那么自重影响所有的特性的声波点。这一事实限制了鲍姆加特和夏皮罗最近提出的估计致密恒星物体内黑洞寿命的建议的适用性。
英文摘要：
The spherically symmetric steady accretion of polytropic perfect fluids onto a black hole is the simplest flow model that can demonstrate effects of backreaction (selfgravity). It has been discovered 16 years ago that backreaction does not influence some ("intensive") characteristics of sonic points, under suitable conditions. Herein we consider a wider class of equations of state, with polytropic indices in the range (1,2], and establish detailed boundary conditions that allow one to prove this fact. We find also numerical examples showing limits of our analytic criteria - if suitable analytic conditions are not satisfied, then selfgravity influences all characteristics of sonic points. That fact constrains the applicability of the recent proposal of Baumgarte and Shapiro to estimate the lifetime of black holes within compact stellar objects.
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