Axially symmetric, asymptotically flat vacuum metric with a naked singularity and closed timelike curves

TL;DR

This paper introduces a new axially symmetric vacuum solution to Einstein's equations featuring a naked singularity and evolving closed timelike curves, expanding understanding of possible spacetime geometries.

Contribution

It presents a novel exact solution with a naked singularity and CTC evolution, enriching the catalog of known vacuum solutions in general relativity.

Findings

Contains a naked singularity on the symmetry axis

Exhibits evolution of closed timelike curves from CTC-free initial hypersurface

Is of Petrov type D, isometric to Kinnersley's case IV

Abstract

We present an axially symmetric, asymptotically flat empty space solution of the Einstein field equations containing a naked singularity. The spacetime is regular everywhere except on the symmetry axis where it possess a true curvature singularity. The spacetime 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 spacetime also shows the evolution of closed timelike curves (CTCs) from an initial hypersurface free from CTCs.