标题： 局部对称性作为自由下落广延物体运动的约束 显示英文标题

标题： Local symmetries as constraints on the motion of freely-falling extended bodies

摘要： 不同的扩展物体可以以不同的方式下落，这取决于它们的内部结构。 尽管如此，某些运动无论如何都是不可能的。 本文推导了在牛顿引力和广义相对论中对扩展物体运动的普遍约束。 在这两种理论中，我们确定了一种“局部对称性”的弱概念，该概念排除了某些力和力矩的组合。 局部对称性意味着物体的四极矩的某些成分不能影响其运动。 它们还意味着某些力只能与适当的力矩结合出现。 其中许多对称性被证明是由潮汐张量的代数结构决定的。 在广义相对论中，因此我们将扩展物体运动的定性特征与时空的Petrov类型联系起来。 这样做表明局部对称性实际上是普遍存在的。 在广义相对论中，所有代数特殊时空至少有两个。 其中一些由Killing向量生成，另一些由共形Killing-Yano张量生成。 然而，许多局部对称性并不属于这两类中的任何一类。 显示英文摘要

摘要： Different extended objects can fall in different ways, depending on their internal structures. Some motions are nevertheless impossible, regardless of internal structure. This paper derives universal constraints on extended-body motion, both in Newtonian gravity and in general relativity. In both theories, we identify a weak notion of "local symmetry" which precludes certain force and torque combinations. Local symmetries imply that certain components of a body's quadrupole moment cannot affect its motion. They also imply that some forces arise only in combination with appropriate torques. Many of these symmetries are shown to be determined by the algebraic structure of the tidal tensor. In general relativity, we thus relate qualitative features of extended-body motion to the Petrov type of the spacetime. Doing so shows that local symmetries are in fact ubiquitous. In general relativity, there are at least two in all algebraically-special spacetimes. Some of these are generated by Killing vectors and some by conformal Killing-Yano tensors. However, many local symmetries do not fall into either of these classes.