# Cylindrically symmetric, Asymptotically flat, Petrov Type D spacetime with a Naked Curvature Singularity and Matter Collapse

## TL;DR

This paper introduces a new cylindrically symmetric spacetime solution of Einstein's equations that features a naked singularity, anisotropic matter, and the potential for closed timelike curves, contributing to understanding cosmic time machines.

## Contribution

It presents a novel exact solution with specific symmetry and matter properties, including a naked singularity and the ability to generate rotating spacetimes with closed timelike curves.

## Key findings

- Spacetime has a naked curvature singularity on the axis.
- The solution involves anisotropic fluid satisfying energy conditions.
- It can generate rotating spacetimes with closed timelike curves.

## Abstract

We present a cylindrically symmetric, Petrov type D, nonexpanding, shear free and vorticity free solution of Einstein's field equations. The spacetime is asymptotically flat radially and regular everywhere except on the symmetry axis where it possesses a naked curvature singularity. The energy momentum tensor of the spacetime is that for an anisotropic fluid which satisfies the different energy conditions. This spacetime is used to generate a rotating spacetime which admits closed timelike curves and may represent a Cosmic Time Machine.