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Einstein-Gauss-Bonnet gravity in five-dimensional spacetime provides anexcellent example of a theory that, while including higher-order curvaturecorrections to General Relativity, still shares many of its features, such assecond-order field equations for the metric. We focus on the largely unexploredcase where the coupling constants of the theory are such that noconstant-curvature solution is allowed, leaving open the question of what thevacuum state should then be. We find that even a slight deviation from theanti-de Sitter Chern-Simons theory, where the vacuum state is five-dimensionalAdS spacetime, leads to a complete symmetry breakdown, with the fifth dimensioneither being compactified into a small circle or shrinking away exponentiallywith time. A complete family of solutions, including duality relations amongthem, is uncovered and shown to be unique within a certain class. Thisdynamical dimensional reduction scenario seems particularly attractive as ameans for higher-dimensional theories to make contact with our four-dimensionalworld.

Effectively four-dimensional spacetimes emerging from d=5 Einstein-Gauss-Bonnet Gravity