We present a Petrov type II general space–time which violates causality in the sense that it allows for the formation of closed timelike curves that appear after a definite instant of time. The metric, which is axially symmetric, admits an expansion-free, twist-free and shear-free null geodesic congruence. From the general metric, we obtain two particular type II metrics. One is a vacuum solution while the other represents a Ricci flat solution with a negative cosmological constant.

中文翻译：

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轴对称 Petrov II 型一般时空曲线和闭合类时曲线

我们提出了一个彼得罗夫 II 型一般时空，它违反了因果关系，因为它允许形成在特定时刻之后出现的闭合类时曲线。该度量标准是轴对称的，允许无膨胀、无扭曲和无剪切的零测地线全等。从一般指标中，我们获得了两个特定的 II 类指标。一种是真空解，另一种是具有负宇宙学常数的里奇平面解。