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In this paper, a Banados-Teitelboim-Zanelli (BTZ) black hole [Phys. Rev. Lett. 69, 1849 (1992)] is constructed from an exact solution of the Einstein field equations in a (2 + 1)--dimensional anti--de Sitter spacetime in the context of noncommutative geometry. The BTZ black hole turns out to have either two horizons, no horizon, or a single horizon corresponding to a minimal mass. Certain thermodynamical properties are investigated, including Hawking temperature, entropy, and heat capacity. Also discussed is the geodesic structure of BTZ black holes for both massless and massive particles. In particular, it is shown that bound orbits for test particles are possible. [ABSTRACT FROM AUTHOR]

Noncommutative geometry, an off shoot of string theory, replaces pointlike structures with smeared objects and has recently been extended to higher dimensions. The purpose of this paper is to obtain wormhole solutions with this extended noncommutative geometry as a background. It is found through this investigation that wormhole solutions exist in the usual four, as well as in five dimensions, but they do not exist in higher-dimensional spacetimes. [ABSTRACT FROM AUTHOR]