Gravitational collapse in a cylindrical symmetric vacuum space-time and the naked singularity

Abstract

We construct a cylindrical symmetry vacuum solution of the Einstein field equations, regular everywhere except on the symmetry axis where it possesses a naked curvature singularity. The geodesics motion of free test particles near the singularity, geodesic expansion to understand the nature of singularity, and the C-energy of the vacuum metric, will be discussed. Finally, the physical interpretation of this solution, based on the study of the equation of the geodesics deviation, will be presented.