The light rays and wave fronts in a linear class of the Gödel-type metric are examined to reveal the causality-violating features of the space-time. Noncausal features demonstrated by the development of unusual wave front singularities are shown to be related to the nonmonotonic advance of time along the light rays, as measured by a system of observers at rest with respect to one another with synchronized clocks.

中文翻译：

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违反因果关系的哥德尔型度量中的波阵面

对Gödel型度量的线性类别中的光线和波阵面进行了检查，以揭示时空违反因果关系的特征。异常波阵面奇异点的发展所证明的非因果特征与沿光线的时间的非单调提前有关，这是由一组静止的观察者相对于彼此同步的时钟系统所测量的。