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.

• Received 24 November 1997

DOI:https://doi.org/10.1103/PhysRevD.57.6547