Remarks on Definitions of Perturbation in General Relativity

有在一般相关性的框架的物理数量的不安的二种定义：一个人是直接的，其它是几何的。相应地，有与这二个定义联系的计量器转变的二种类型。被动途径基于一般协变性的性质，并且活跃的通过谎言衍生物的行动。尽管在一种合适的并列选择下面，二条途径似乎同意对方，他们在自然是不同的。为计量器转变的相对论的不安和活跃途径的几何定义在在物理解释糊涂的数学和更少是更严密的。然而，直接定义似乎在物理意思与困难被折磨，并且被动途径是更尴尬的使用，特别为高顺序的计量器转变。

There are two kinds of definitions of perturbation of physical quantities in the framework of general relativity： one is direct, the other is geometrical. Correspondingly, there are two types of gauge transformation related with these two definitions. The passive approach is based on the property of general covariance, and the active one is through the action of Lie-derivative. Although under a proper coordinate choice, the two approaches seem to agree with each other, they are different in nature. The geometrical definition of relativistic perturbation and the active approach for gauge transformation are more rigorous in mathematics and less confusing in physical explanation. The direct definition, however, seems to be plagued with difficulties in physical meaning, and the passive approach is more awkward to use, especially for high-order gauge transformations.