  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.
