We investigate stability issues for steady states of the spherically symmetric Einstein-Vlasov system numerically in Schwarzschild, maximal areal, and Eddington-Finkelstein coordinates. Across all coordinate systems we confirm the conjecture that the first binding energy maximum along a one-parameter family of steady states signals the onset of instability. Beyond this maximum perturbed solutions either collapse to a black hole, form heteroclinic orbits, or eventually fully disperse. Contrary to earlier research, we find that a negative binding energy does not necessarily correspond to fully dispersing solutions. We also comment on the so-called turning point principle from the viewpoint of our numerical results. The physical reliability of the latter is strengthened by obtaining consistent results in the three different coordinate systems and by the systematic use of dynamically accessible perturbations.

中文翻译：

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爱因斯坦-弗拉索夫系统的数值稳定性分析

我们在 Schwarzschild、最大面积和 Eddington-Finkelstein 坐标中以数值方式研究球对称爱因斯坦-弗拉索夫系统稳态的稳定性问题。在所有坐标系中，我们确认了这样一个猜想，即沿单参数稳态族的第一个结合能最大值标志着不稳定的开始。超过这个最大扰动解要么坍缩成黑洞，形成异宿轨道，要么最终完全分散。与早期的研究相反，我们发现负结合能并不一定对应于完全分散的溶液。我们还从我们的数值结果的角度评论了所谓的转折点原理。