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

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.

8 pages, no figures

References in corpus (8)

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• Apparent shape of super-spinning black holes
• Shape and position of the shadow in the $\delta =2$ Tomimatsu-Sato space-time
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• Magnification relations for Kerr lensing and testing Cosmic Censorship
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Cited by in corpus (8)

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• Cylindrically symmetric, Asymptotically flat, Petrov Type D spacetime with a Naked Curvature Singularity and Matter Collapse
• Cylindrical symmetric, non-rotating and non-static or static black hole solutions and the naked singularities
• Black holes/naked singularities in four-dimensional non-static space-time and the energy-momentum distributions
• Axial symmetry cosmological constant vacuum solution of field equations with a curvature singularity, closed time-like curves and deviation of geodesics
• A 1+5-dimensional gravitational-wave solution: curvature singularity and spacetime singularity