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A solution to an Einstein--Maxwell--dilaton-type theory with $M$ Liouvillepotentials and $N$ gauge fields is presented, where $M$ and $N$ are arbitraryintegers. This exact solution interpolates between the Lifshitz black hole andthe topological dilaton black hole. The thermodynamic behaviour of the solutionis found to be similar to that of the Lifshitz black hole, where a phasetransition may occur for sufficiently small charge in the canonical ensemble,or sufficiently small potential in the grand canonical ensemble.

Charged dilaton black hole with multiple Liouville potentials and gauge fields