Axially Symmetric, Asymptotically Flat Vacuum Metric with a Naked Singularity and Closed Timelike Curves

Abstract EN

We present an axially symmetric, asymptotically flat empty space solution of the Einstein field equations containing a naked singularity.

The space-time is regular everywhere except on the symmetry axis where it possesses a true curvature singularity.

The space-time is of type D in the Petrov classification scheme and is locally isometric to the metrics of case IV in the Kinnersley classification of type D vacuum metrics.

Additionally, the space-time also shows the evolution of closed timelike curves (CTCs) from an initial hypersurface free from CTCs.