论文标题
诱捕多环形球的径向不稳定性
Radial instability of trapping polytropic spheres
论文作者
论文摘要
我们完成了对一般相对论的球形对称多型完美流体球的稳定性研究，将注意力集中在包含捕获无效的大地测量区域的新发现的多型物中。我们比较了基于控制多层的无限径向脉动的方程和相关的sturm-liouville特征值方程的方法来处理动力稳定性的方法，用于控制脉冲的本本元素，以及基于能量考虑的稳定性分析方法。两种方法均应用于确定由多粒子指数N在整个范围0 <N <5中控制的多层稳定性，并受到因果关系极限限制的中央压力和能量密度比给出的相对论参数σ。确定绝热指数的临界值以及相对论参数σ的临界值。对于动态方法，我们实施了一种数值方法，该方法独立于选择试验功能，并将其结果与标准试验函数方法进行比较。我们发现能量和动态方法给出了几乎相同的σ临界值。我们发现，根据这两种方法，所有已捕获的无效测量学的配置都是不稳定的。
We complete the stability study of general relativistic spherically symmetric polytropic perfect fluid spheres, concentrating attention to the newly discovered polytropes containing region of trapped null geodesics. We compare the methods of treating the dynamical stability based on the equation governing infinitesimal radial pulsations of the polytropes and the related Sturm-Liouville eigenvalue equation for the eigenmodes governing the pulsations, to the methods of stability analysis based on the energetic considerations. Both methods are applied to determine the stability of the polytropes governed by the polytropic index n in the whole range 0 < n < 5, and the relativistic parameter σ given by the ratio of the central pressure and energy density, restricted by the causality limit. The critical values of the adiabatic index for stability are determined, together with the critical values of the relativistic parameter σ. For the dynamical approach we implemented a numerical method which is independent on the choice of the trial function, and compare its results with the standard trial function approach. We found that the energetic and dynamic method give nearly the same critical values of σ. We found that all the configurations having trapped null geodesics are unstable according to both methods.
