标题： 外尔张量的解释 显示英文标题

标题： Interpretation of the Weyl Tensor

摘要： 根据广义相对论的民间说法，Weyl张量可以分解为对应于牛顿类似、入射和出射波状场分量的部分。 在这里表明，这种解释不能应用于具有圆柱对称性的时空几何。 这是通过研究一些具有全圆柱对称性的爱因斯坦场方程的著名精确解来完成的，这些解的物理解释非常明确，但标准的Weyl解释会对它们产生矛盾的结果。 然而，对于平面或球形几何，标准解释适用于静态和动态时空。 认为圆柱情况失败的一个原因是，对于在两个空间维度上传播的波，在线性水平上就没有局部准则来区分入射波和出射波。 结果表明， Thorne的局部能量概念，在某些限定条件下，提供了一种有效的诊断工具，以提取圆柱配置情况下时空几何的正确物理解释。 显示英文摘要

摘要： According to folklore in general relativity, the Weyl tensor can be decomposed into parts corresponding to Newton-like, incoming- and outgoing wave-like field components. It is shown here that this interpretation cannot be applied to space-time geometries with cylindrical isometries. This is done by investigating some well-known exact solutions of Einstein's field equations with whole-cylindrical symmetry, for which the physical interpretation is very clear, but for which the standard Weyl interpretation would give contradictory results. For planar or spherical geometries, however, the standard interpretation works for both, static and dynamical space-times. It is argued that one reason for the failure in the cylindrical case is that for waves spreading in two spatial dimensions there is no local criterion to distinguish incoming and outgoing waves already at the linear level. It turns out that Thorne's local energy notion, subject to certain qualifications, provides an efficient diagnostic tool to extract the proper physical interpretation of the space-time geometry in the case of cylindrical configurations.