Black strings with a negative cosmological constant: inclusion of electric charge and rotation

We generalize the vacuum static black string solutions of Einstein's equations with negative cosmological constant recently discussed in literature, by including an electromagnetic field. These higher- dimensional configurations have no dependence on the 'compact' extra dimension, while their boundary topology is the product of time and Sd-3 x S-1 or Hd-3 x S-1. Rotating generalizations of the even dimensional black string configurations are considered as well. Different from the static, neutral case, no regular limit is found for a vanishing event horizon radius. We explore numerically the general properties of such classical solutions and, using a counterterm prescription, we compute their conserved charges and discuss their thermodynamics. We find that the thermodynamics of the black strings follows the pattern of the corresponding black hole solutions in AdS backgrounds.