Stacking a 4D geometry into an Einstein-Gauss-Bonnet bulk

TL;DR

This paper investigates the extension of a stacking procedure from Einstein gravity to Einstein-Gauss-Bonnet gravity, revealing it is limited to metrics with constant Krestschmann scalar and excluding certain solutions like black strings.

Contribution

It demonstrates the constraints of stacking methods in Einstein-Gauss-Bonnet gravity, highlighting the necessity of constant Krestschmann scalar for such constructions.

Findings

Stacking procedure only applies to metrics with constant Krestschmann scalar.

Black-string solutions are not compatible with Einstein-Gauss-Bonnet stacking.

The method's limitations differ from Einstein gravity, affecting solution construction.

Abstract

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 only be applied to metrics with a constant Krestschmann scalar. For instance, we show that solutions of the black-string type are not allowed in this framework.