Charged dilaton black holes with a cosmological constant

The properties of static spherically symmetric black holes, which are either electrically or magnetically charged, and which are coupled to the dilaton in the presence of a cosmological constant, are considered. It is shown that such solutions do not exist if >0 (in arbitrary spacetime dimensions 4). However, asymptotically anti--de Sitter black hole solutions with a single horizon do exist if 0. These solutions are studied numerically in four dimensions and the thermodynamic properties of the solutions are derived. The extreme solutions are found to have zero entropy and infinite temperature for all nonzero values of the dilaton coupling constant.