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.
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Barceló et al. (2003) studied this question.
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