标题： 轴对称爱因斯坦-维拉索夫系统的定态解：现状和开放问题 显示英文标题

标题： Stationary solutions of the axially symmetric Einstein-Vlasov system: present status and open problems

摘要： 本工作的目的是回顾轴对称爱因斯坦-福克方程组的定态解的现状，重点关注分析和数值方面的开放问题。 对于后者，我们强调用于在\cite{Ames2016,Ames2019}中构建定态解的代码是开源的，参见\cite{Ames2023joss}。 在分析框架中，开放问题包括建立证明轴对称定态解存在的方法，这些解远离球对称，既包括一般情况，也包括文中指出的某些特殊解类。 在数值框架中，高度相对论性解具有一些引人注目的性质，需要进一步关注，例如这样的定态解序列是否可以接近克尔黑洞，或者它们是否必然接近类似于宇宙弦的薄环极限。 定态解是否包含像许多星系中看到的薄盘状形态的状态的问题也是开放的。 最后，有将此研究扩展到新领域的机遇，例如无质量粒子的情况以及耦合黑洞-物质系统的情况。 我们认为这里突出的一些开放问题是理解自然的核心重要问题。 显示英文摘要

摘要： The purpose of this work is to review the status about stationary solutions of the axially symmetric Einstein-Vlasov system with a focus on open problems of both analytical and numerical nature. For the latter we emphasize that the code used to construct stationary solutions in \cite{Ames2016,Ames2019} is open source, see \cite{Ames2023joss}. In the analytical setting the open problems include establishing methods for proving existence of axisymmetric stationary solutions which are far from spherically symmetric, both in the general case and for certain special classes of solutions pointed out in the text. In the numerical setting there are intriguing properties of highly relativistic solutions that demand further attention, such as whether a sequence of such stationary solutions can approach a Kerr black hole, or if they necessarily approach the thin ring limit reminiscent of cosmic strings. The question of whether stationary solutions include states with thin-disk like morphologies as seen in many galaxies is also open. Finally, there are opportunities to extend this research to new settings such as the case of massless particles and coupled black hole-matter systems. We believe that some of the open problems highlighted here are of central importance for the understanding of nature.