In four-dimensional spacetime, when the two-sphere of black hole event horizons is replaced by a two-dimensional hypersurface with zero or negative constant curvature, the black hole is referred to as a topological black hole. In this paper we present some exact topological black hole solutions in the Einstein-Maxwell dilaton theory with a Liouville-type dilaton potential.
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Cai et al. (1998) studied this question.
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