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Static vacuum spacetimes with one compact dimension include black holes withlocalised horizons but also uniform and non-uniform black strings where thehorizon wraps over the compact dimension. We present new numerical solutionsfor these localised black holes in 5 and 6-dimensions. Combined with previous6-d non-uniform string results, these provide evidence that the black hole andnon-uniform string branches join at a topology changing solution.Comment: 4 pages, 7 figures. Minor corrections. Accepted for PR

Connecting Black Holes and Black Strings