标题： 相对论性最小定理，极限紧致性，以及引力坍缩的最终状态 显示英文标题

标题： Relativistic Virial Theorem, Limiting Compactness, and the end state of gravitational collapse

摘要： 值得注意的是，静态有界构型的极限致密性由一个普遍原理刻画：\textit{一个，通过内部和外部的质量均分；另一个，通过内部能量消失。}前者意味着引力能量为质量的一半，导致Buchdahl星的极限致密性$M/R = 4/9$；而对于后者，两者相等，给出黑洞（具有视界）的$M/R = 1/2$。 \emph{这是分别对于有质量粒子和无质量粒子的相对论位力定理。} 值得注意的是，它规定只能存在两种平衡状态，这也定义了该天体的极限致密性。 因此，这得出了一个深刻的预言：引力坍缩的最终产物只能是这两种之一，即Buchdahl星或黑洞。 显示英文摘要

摘要： It is noteworthy that limiting compactness of a static bounded configuration is characterized by a general principle: \textit{one, by equipartition of mass between inside and outside, and the other by vanishing of energy inside.} The former implies gravitational energy being half of mass leading to limiting compactness $M/R = 4/9$ of Buchdahl star while for the latter, the two are equal giving $M/R = 1/2$ of black hole with horizon. \emph{This is the relativistic Virial theorem respectively for massive and massless particles.} It is remarkable that it prescribes that there can exist only two equilibrium states which also define limiting compactness of the object. Consequently, it leads to a profound prediction that the ultimate endproduct of gravitational collapse could only be one of the two, Buchdahl star or black hole.