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

TL;DR

This paper presents a static, cylindrically symmetric anisotropic fluid spacetime with a naked singularity, analyzing geodesic motion and energy conditions to understand the singularity's nature.

Contribution

It introduces a new exact solution of Einstein's equations with a naked singularity and examines its physical and geometric properties.

Findings

The spacetime is conformally flat and regular except at the axis.

The matter violates the weak energy condition and diverges at the axis.

Geodesic analysis suggests the singularity is naked.

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.