Stacking a 4D geometry into an Einstein-Gauss-Bonnet bulk -: art. no. 064023

In Einstein gravity there is a simple procedure to build D-dimensional spacetimes starting from (D-1)-dimensional ones, by stacking any (D-1)-dimensional Ricci-flat metric into the extra dimension. We analyze this procedure in the context of Einstein-Gauss-Bonnet gravity, and find that it can be applied only to metrics with a constant Krestschmann scalar. For instance, we show that solutions of the black-string type are not allowed in this framework.