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arXiv 0807.4728gr-qc
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关于反向旋转粒子薄壳的动力学

On the dynamics of thin shells of counter rotating particles

Reinaldo J. Gleiser, Marcos A. Ramirez

摘要:

本文研究了自引力球对称反旋粒子薄壳的动力学。我们考虑所有可能的粒子的速度分布,并表明,运动方程本身并不约束这种分布。因此,我们考虑几种可能的过程下产生的配置的动力学稳定性。这包括作为一个整体的静态配置的稳定性,在那里我们找到一个下界的壳的紧凑性。我们还分析了单粒子轨道的稳定性,并找到了“单粒子蒸发”的条件。最后,在壳的粒子的角动量被限制为两个值的情况下,我们考虑分裂成两个单独的壳的稳定性条件。这种分析导致的结论是,在某些条件下,这是明确给出的,一个不断发展的壳可能会分裂成一个或多个单独的壳。我们提供明确的例子来说明这一现象。我们还包括推导的厚壳到薄壳极限的爱因斯坦壳,表明角动量的极限分布是唯一的,连续覆盖有限范围的值。

英文摘要:

In this paper we study the dynamics of self gravitating spherically symmetric thin shells of counter rotating particles. We consider all possible velocity distributions for the particles, and show that the equations of motion by themselves do not constrain this distribution. We therefore consider the dynamical stability of the resulting configurations under several possible processes. This include the stability of static configurations as a whole, where we find a lower bound for the compactness of the shells. We analyze also the stability of the single particle orbits, and find conditions for "single particle evaporation". Finally, in the case of a shell with particles whose angular momenta are restricted to two values, we consider the conditions for stability under splitting into two separate shells. This analysis leads to the conclusion that under certain conditions, that are given explicitly, an evolving shell may split into one or more separate shells. We provide explicit examples to illustrate this phenomenon. We also include a derivation of the thick to thin shell limit for an Einstein shell that shows that the limiting distribution of angular momenta is unique, covering continuously a finite range of values.

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