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

We present arguments for the existence of charged, rotating black holes in d = 2N + 1 dimensions, with d >= 5 with a positive cosmological constant. These solutions possess both a regular horizon and a cosmological horizon of spherical topology and have N equal- magnitude angular momenta. They approach asymptotically the de Sitter- spacetime background. The counterpart equations for d = 2N + 2 are investigated, by assuming that the fields are independent of the extra dimension y, leading to black string solutions. These solutions are regular at the event horizon. The asymptotic form of the metric is not of the de Sitter- type and exhibits a naked singularity at finite proper distance.