标题： 关于刚性准局部框架的存在性和效用 显示英文标题

标题： On the Existence and Utility of Rigid Quasilocal Frames

摘要： 刚性准局域框架（RQF）的概念为广义相对论中定义一个系统提供了一种几何上自然的方式，并为分析运动问题提供了新方法。 一个RQF被定义为由有限空间体积的历史边界（拓扑结构为R×S²）组成的一组两参数族的时间世界线，其刚性条件是世界线的会聚不能有膨胀和剪切。 换句话说，系统的大小和形状不会改变。 在之前的工作中，已经证明了闵可夫斯基空间中的此类系统具有我们熟悉的牛顿时空中的刚体运动的六个自由度，且没有任何限制，从而绕过了赫格洛茨和诺特的一个世纪老定理。 这是由于任意形状的二维球面总是精确地具有六个保形Killing矢量场的事实，这些矢量场在球面上生成了洛伦兹群的作用。 在这里，我们回顾了平坦时空中的先前工作，并从三个方面扩展了它：（1）利用费米法坐标的方法，我们显式构造了在一般弯曲时空中的RQF刚性方程的一般解，直到面积半径的幂级数的前几项，并表明由此产生的RQF与平坦时空中的具有完全相同的六个运动自由度；（2）我们讨论了RQF如何提供了一个理解系统内外能量、动量和角动量流动的自然背景；特别是，我们导出了一个简单而精确的表达式，用以操作上定义的几何量表示引力能量（引力的Poynting矢量类比）在边界上的通量；（3）我们使用这种新的引力（或“几何”）能量通量来解决另一个明显的悖论，这个悖论涉及平坦时空中的电磁学，这是我们在这项工作中发现的。 显示英文摘要

摘要： The notion of a rigid quasilocal frame (RQF) provides a geometrically natural way to define a system in general relativity, and a new way to analyze the problem of motion. An RQF is defined as a two-parameter family of timelike worldlines comprising the boundary (topologically R x S^2) of the history of a finite spatial volume, with the rigidity conditions that the congruence of worldlines be expansion- and shear-free. In other words, the size and shape of the system do not change. In previous work, such systems in Minkowski space were shown to admit precisely the same six degrees of freedom of rigid body motion that we are familiar with in Newtonian space-time, without any constraints, circumventing a century-old theorem due to Herglotz and Noether. This is a consequence of the fact that a two-sphere of any shape always admits precisely six conformal Killing vector fields, which generate an action of the Lorentz group on the sphere. Here we review the previous work in flat spacetime and extend it in three directions: (1) Using a Fermi normal coordinates approach, we explicitly construct, to the first few orders in powers of areal radius, the general solution to the RQF rigidity equations in a generic curved spacetime, and show that the resulting RQFs possess exactly the same six motional degrees of freedom as in flat spacetime; (2) We discuss how RQFs provide a natural context in which to understand the flow of energy, momentum and angular momentum into and out of a system; in particular, we derive a simple, exact expression for the flux of gravitational energy (a gravitational analogue of the Poynting vector) in terms of operationally-defined geometrical quantities on the boundary; (3) We use this new gravitational (or "geometrical") energy flux to resolve another apparent paradox, this one involving electromagnetism in flat spacetime, which we discovered in the course of this work.