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

中文翻译：

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具有多个刘维尔势和规范场的带电膨胀黑洞

给出了具有 M 个刘维尔势和 N 个规范场的爱因斯坦-麦克斯韦-扩张型理论的解，其中 M 和 N 是任意整数。这个精确解在 Lifshitz 黑洞和拓扑膨胀黑洞之间进行了插值。发现该溶液的热力学行为类似于 Lifshitz 黑洞的热力学行为，其中正则系综中足够小的电荷或大正则系综中足够小的势可能会发生相变。