In this paper, we present a type D, nonvanishing cosmological constant, vacuum solution of Einstein’s field equations, extension of an axially symmetric, asymptotically flat vacuum metric with a curvature singularity. The space-time admits closed time-like curves (CTCs) that appear after a certain instant of time from an initial space-like hypersurface, indicating it represents a time-machine space-time. We wish to discuss the physical properties and show that this solution can be interpreted as gravitational waves of Coulomb-type propagate on anti-de Sitter space backgrounds. Our treatment focuses on the analysis of the equation of geodesic deviations.

中文翻译：

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具有曲率奇异性，闭合时间样曲线和测地线偏差的场方程的轴对称宇宙学常数真空解

在本文中，我们提出了D型，爱因斯坦场方程的不变的宇宙常数，真空解，带有曲率奇点的轴向对称，渐近平坦真空度量的扩展。时空允许闭合的类似时间的曲线（CTC），这些曲线出现在从初始类似空间的超曲面的某个特定时间之后，表明它代表了一个时空时空。我们希望讨论其物理性质，并证明该解可以解释为库仑型引力波在反德西特空间背景上的传播。我们的处理重点是测地线偏差方程的分析。