Abstract

An axially symmetric nonvacuum solution of the Einstein field equations, regular everywhere and free from curvature divergence is presented. The matter-energy content is a the pure radiation field satisfying the energy conditions, and the metric is of type N in the Petrov classification scheme. The space-time develops circular closed timelike curves everywhere outside a finite region of space i.e., beyond a null curve. Furthermore, the physical interpretation of the solution based on the study of the equations of geodesic deviation is presented. Finally, the von Zeipel cylinders with respect to the Zero Angular Momentum Observers (ZAMOs) is discussed. In addition, circular null and timelike geodesic of pace-time are also presented.

中文翻译：

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具有因果关系违反曲线和von Zeipel圆柱体的轴对称N型时空

摘要

提出了一个爱因斯坦场方程的轴对称非真空解，该解在各处都规则且没有曲率发散。物质能量含量是满足能量条件的纯辐射场，度量标准是彼得罗夫分类方案中的N型。时空在有限的空间区域外（即超出零曲线）处到处都形成圆形的闭合时态曲线。此外，基于对测地线偏离方程的研究，给出了对解的物理解释。最后，讨论了关于零角动量观测器（ZAMO）的von Zeipel圆柱体。此外，还介绍了起步时间的圆形空值和类似时间的测地线。