广义相对论中测量和传输定域角动量的规定
Prescriptions for measuring and transporting local angular momenta in general relativity
摘要：
对于弯曲时空中的观测者，从观测者的切空间到自身的线性化庞加莱变换的对偶空间的元素可以自然地解释为局部线性和角动量。我们提出了一个操作程序，通过它，观察者可以测量这些量只使用有关的时空曲率在他们的位置。当观察者在静止、真空、渐近平坦的时空中，在类空或零无穷远附近应用时，有一种意义，即这个过程产生了时空的明确定义的线性动量和角动量。我们还描述了一个一般的方法，通过该方法，观察者可以将局部线动量和角动量从一个点传输到另一个点，这改进了以前的处方。这种输运一般不是路径无关的，但在相同的限制范围内，对于测量的动量，这种输运变得与路径无关。输运公式是用微分方程来定义的，但它也可以被解释为在一个特定的直和矢量束中的平行输运。利用这个丛上联络的曲率，我们计算并讨论了输运律的完整性。我们预计，这些测量和输运定义最终可能会被证明对于澄清渐进平坦时空的邦迪-梅茨纳-萨克斯荷的物理解释有用。
英文摘要：
For observers in curved spacetimes, elements of the dual space of the set of linearized Poincaré transformations from an observer's tangent space to itself can be naturally interpreted as local linear and angular momenta. We present an operational procedure by which observers can measure such quantities using only information about the spacetime curvature at their location. When applied by observers near spacelike or null infinity in stationary, vacuum, asymptotically flat spacetimes, there is a sense in which the procedure yields the well-defined linear and angular momenta of the spacetime. We also describe a general method by which observers can transport local linear and angular momenta from one point to another, which improves previous prescriptions. This transport is not path independent in general, but becomes path independent for the measured momenta in the same limiting regime. The transport prescription is defined in terms of differential equations, but it can also be interpreted as parallel transport in a particular direct-sum vector bundle. Using the curvature of the connection on this bundle, we compute and discuss the holonomy of the transport law. We anticipate that these measurement and transport definitions may ultimately prove useful for clarifying the physical interpretation of the Bondi-Metzner-Sachs charges of asymptotically flat spacetimes.
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