Abstract
We present a gravitational collapse null dust solution of the Einstein field equations. The space-time 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 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 amplitudes Ψ2 and Ψ4.
Highlights
For algebraically special metrics, the Petrov classification is a way to characterize the space-time by the number of times a principal null direction (PND) admits
The possibility that a naked curvature singularity gives rise to a Cosmic Time Machine has been discussed by Clarke and de Felice [66]
We presented an axially symmetric time-dependent solution of the field equations which possesses a naked curvature singularity on the symmetry axis
Summary
The Petrov classification is a way to characterize the space-time by the number of times a principal null direction (PND) admits. An earliest model that admits both naked and covered singularities is the Lemaitre-Tolman-Bondi (LTB) [14,15,16] solutions, a spherically symmetric inhomogeneous collapse of dust fluid. Papapetrou [17] pointed out the formation of naked singularities in Vaidya [18] radiating solution, a null dust fluid space-time generated from Schwarzschild vacuum solution. The theoretical existence of naked singularities would mean that the gravitational collapse may be observable from the rest of the space-time. Nakao and Morisawa [36] studied the high-speed collapse of cylindrically symmetric thick shell composed of dust and perfect fluid with nonvanishing pressure [37]. Where ρ is the energy density of null dust (pure radiation field) and kμ is the null vector
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