Axially Symmetric Null dust Spacetime, Naked Singularity and Cosmic Time Machine

Abstract

In this article, we present a gravitational collapse null dust solution of the Einstein field equations. The spacetime is regular everywhere except on the symmetry axis where it possesses a naked curvature singularity, and admits one parameter isometry group, a generator of axial symmetry along the cylinder which has closed orbits. The space- time admits closed timelike curves (CTCs) which develop at some particular moment in a causally well-behaved manner and may represent a Cosmic Time Machine. The radial geodesics near to the singularity, and the gravitational Lensing (GL) will be discussed. The physical interpretation of this solution, based on the study of the equation of the geodesic deviation, will be presented. It was demonstrated that, this solution depends on the local gravitational field consisting of two components with amplitude ${\Psi }_2$, ${\Psi }_4$.

arXiv comment19 pages ; accepted for publication in Adv. high energy phys

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Cited by in corpus (6)

• Geodesics motion of test particles around Schwarzschild-Klinkhamer wormhole with topological defects and gravitational lensing
• A cylindrically symmetric, static anisotropic fluid spacetime and the naked singularity
• Gravitational lensing in a space-time with cosmic string within the Eddington-inspired Born-Infeld gravity
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• Axial symmetry cosmological constant vacuum solution of field equations with a curvature singularity, closed time-like curves and deviation of geodesics
• Black holes/naked singularities in four-dimensional non-static space-time and the energy-momentum distributions