本论文由两部分组成。第一部分主要介绍了两类参考系。众所周知，时空中所有时钟可同步的参考系都是超曲面正交的，而赵峥教授首先提出了较弱的时钟同步条件[Z.Zhao,Science In China,34(7),835(1991)]。在本文中，我们对此进行了详细的讨论。赵文的另一个结论是:“钟速同步的可传递性”等价于“热平衡的可传递性”。对此结论本文进行了更为详细的分析与推导(包括热平衡及其可传递性在广义相对论中的精确定义)，得出了与赵氏结论相近而不完全相同的结果。本文的第二部分介绍了用外尔算符本征值作为广义相对论可观测量的理论，计算了3球宇宙模型中外尔算符的本征值谱。

This thesis consists of two parts. In the first part, we mainly introduce two kinds of reference frames. It is well known that all reference frames that are clock synchronizable are hypersurface orthogonal. A weaker requirement for clock synchronization was first suggested by Zhao [Z. Zhao, Science In China, 34(7), 835 (1991)] and is investigated in detail in this paper. Zhao's paper also raised another suggestion claiming the equivalence of “transitivity of clock rate synchronizability”and “transitivity of thermal equilibrium”.A more transparent treatment (including precise definitions for thermal equilibrium and its transitivity in general relativity) as well as a more precise conclusion are given in this paper. Somehow unlike Zhao's assertion, the equivalence is valid only provided certain condition is satisfied. The second part introduces the theory on eigenvalues of the Weyl operator as observables of general relativity and we calculated the eigenvalues of theWeyl operator in the 3-sphere cosmological model.