Black p-branes and their Vertical Dimensional Reduction

We construct multi-center solutions for charged, dilatonic, non-extremal black holes in D=4. When an infinite array of such non-extremal black holes are aligned periodically along an axis, the configuration becomes independent of this coordinate, which can therefore be used for Kaluza-Klein compactification. This generalises the vertical dimensional reduction procedure to include {\it non-extremal} black holes. We then extend the construction to multi-center non-extremal $(D-4)$-branes in $D$ dimensions, and discuss their vertical dimensional reduction.