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We present arguments for the existence of charged, rotating black holes in$d=2N+1$ dimensions, with $d\geq 5$ with a positive cosmological constant.These solutions posses both, a regular horizon and a cosmological horizon ofspherical topology and have $N$ equal-magnitude angular momenta. They approachasymptotically the de Sitter spacetime background. The counterpart equationsfor $d=2N+2$ are investigated, by assuming that the fields are independant ofthe extra dimension $y$, leading to black strings solutions. These solutionsare regular at the event horizon. The asymptotic form of the metric is not thede Sitter form and exhibit a naked singularity at finite proper distance.Comment: 21 pages, 9 figure

Charged–rotating black holes and black strings in higher dimensional Einstein–Maxwell theory with a positive cosmological constant