论文标题
爱因斯坦 - 维拉索夫系统的数值稳定性分析
A numerical stability analysis for the Einstein-Vlasov system
论文作者
论文摘要
我们在Schwarzschild，Maximal Areal和Eddington-Finkelstein坐标中数字上的球形对称爱因斯坦 - Vlasov系统的稳态问题进行了稳定问题。在所有坐标系中，我们确认了沿稳态的一个参数家族的第一个结合能的最大值表示不稳定性的发作。除了这种最大扰动的溶液之外，要么塌陷到黑洞，形成杂斜轨道，或者最终完全分散。与较早的研究相反，我们发现负结合能不一定与完全分散的解决方案相对应。我们还从数值结果的角度评论了所谓的转折点原理。通过在三个不同的坐标系统中获得一致的结果以及系统地使用动态可访问的扰动，可以增强后者的物理可靠性。
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.
