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In this work, a four-dimensional cylindrical symmetric and non-static orstatic space-times in the backgrounds of anti-de Sitter (AdS) space withperfect stiff fluid, anisotropic fluid and electromagnetic field as thestress-energy tensor, is presented. For suitable parameter conditions in themetric function, the solution represents non-static or static non-rotatingblack hole solution. In addition, we show for various parameter conditions, thesolution represents static and/or non-static models with a naked singularitywithout an event horizon.

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