A cylindrically symmetric, static anisotropic fluid spacetime and the naked singularity

Abstract: In this article, a cylindrical symmetry and static solution of the Einstein's field equations, was presented. The space-time is conformally flat, regular everywhere except on the symmetry axis where it possesses a naked curvature singularity. The matter-energy source anisotropic fluids violates the weak energy condition (WEC), diverge on the symmetry axis. We discuss geodesics motion of free test-particles near to the singularity, and geodesic expansion in the metric to understand the nature of singularity which is naked or covered, and finally the C-energy of the space-time.