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

Understand

Einstein-Gauss-Bonnet gravity in five-dimensional spacetime provides an excellent example of a theory that, while including higher-order curvature corrections to General Relativity, still shares many of its features, such as second-order field equations for the metric.

• We focus on the largely unexplored case where the coupling constants of the theory are such that no constant-curvature solution is allowed, leaving open the question of what the vacuum state should then be.
• We find that even a slight deviation from the anti-de Sitter Chern-Simons theory, where the vacuum state is five-dimensional AdS spacetime, leads to a complete symmetry breakdown, with the fifth dimension either being compactified into a small circle or shrinking away exponentially with time.
• A complete family of solutions, including duality relations among them, is uncovered and shown to be unique within a certain class.