标题： 一维相对论自引力系统 显示英文标题

标题： One-Dimensional Relativistic Self-Gravitating Systems

摘要： 物理学中最古老的问题之一是计算在特定相互作用力下$N$粒子的运动：即$N$体问题。 如果指定的力是非相对论性引力，对此问题已有大量了解，并且通过在单个空间维度中考虑该问题已经取得了相当大的进展。 在这里，我回顾关于相对论性引力$N$体问题的已知内容。 简化为一个空间维度具有无引力辐射的特点，从而允许对一维相对论性和非相对论性自引力系统的物理特性进行清晰比较。 在描述如何获得与$N$点粒子耦合的相对论性引力理论之后，我依次讨论了两体问题、三体问题、四体问题和$N$体问题。 对于两体问题，可以得到相当普遍的精确解，这与三维空间中广义相对论的情况不同，在后者中只存在高度特定的解。 三体问题表现出轻微形式的混沌，并为研究相对论性混沌提供了一个最早的理论背景。 对于$N\geq 4$，其他有趣的特性也会出现。 相对论性自引力系统有许多有趣的问题有待进一步研究，为我们探索相对论性多体系统提供了新的前沿领域。 显示英文摘要

摘要： One of the oldest problems in physics is that of calculating the motion of $N$ particles under a specified mutual force: the $N$-body problem. Much is known about this problem if the specified force is non-relativistic gravity, and considerable progress has been made by considering the problem in one spatial dimension. Here, I review what is known about the relativistic gravitational $N$-body problem. Reduction to one spatial dimension has the feature of the absence of gravitational radiation, thereby allowing for a clear comparison between the physics of one-dimensional relativistic and non-relativistic self-gravitating systems. After describing how to obtain a relativistic theory of gravity coupled to $N$ point particles, I discuss in turn the two-body, three-body, four-body, and $N$-body problems. Quite general exact solutions can be obtained for the two-body problem, unlike the situation in general relativity in three spatial dimensions for which only highly specified solutions exist. The three-body problem exhibits mild forms of chaos, and provides one of the first theoretical settings in which relativistic chaos can be studied. For $N\geq 4$, other interesting features emerge. Relativistic self-gravitating systems have a number of interesting problems awaiting further investigation, providing us with a new frontier for exploring relativistic many-body systems.