论文标题
关于空间的等效性，cartan-karlhede算法
On the Equivalence of Spacetimes, the Cartan-Karlhede Algorithm
论文作者
论文摘要
众所周知，在一般相对论理论中，指标与坐标转换相关的两个空间在物理上是等效的。但是，给定两个行元素，几乎不可能实现最通用的坐标转换以检查空间的等效性。在本文中，我们介绍了所谓的Cartan-Karlhede算法，该算法提供了有限的步骤来决定两个指标是否等效。本说明的目的是通过几个简单的示例来说明该方法，以便读者可以在实践中学习算法的基本原理和细节。
It is well known that in general relativity theory two spacetimes whose metrics are related by a coordinate transformation are physically equivalent. However, given two line elements, it is virtually impossible to implement the most general coordinate transformation in order to check the equivalence of the spacetimes. In this paper we present the so-called Cartan-Karlhede algorithm, which provides a finite sequence of steps to decide whether or not two metrics are equivalent. The point of this note is to illustrate the method through several simple examples, so that the reader can learn the fundamentals and details of the algorithm in practice.
