Cylindrical symmetric, non-rotating and non-static or static black hole solutions and the naked singularities

In this work, a four-dimensional cylindrical symmetric and non-static or static space-times in the backgrounds of anti-de Sitter (AdS) space with perfect stiff fluid, anisotropic fluid and electromagnetic field as the stress-energy tensor, is presented. For suitable parameter conditions in the metric function, the solution represents non-static or static non-rotating black hole solution. In addition, we show for various parameter conditions, the solution represents static and/or non-static models with a naked singularity without an event horizon.