Is there a novel Einstein-Gauss-Bonnet theory in four dimensions?

Abstract

No! We show that the field equations of Einstein-Gauss-Bonnet theory defined in generic $D>4$ dimensions split into two parts one of which always remains higher dimensional, and hence the theory does not have a non-trivial limit to $D=4$. Therefore, the recently introduced four-dimensional, novel, Einstein-Gauss-Bonnet theory does not admit an intrinsically four-dimensional definition as such it does not exist in four dimensions. The solutions (the spacetime, the metric) always remain $D>4$ dimensional. As there is no canonical choice of 4 spacetime dimensions out of $D$ dimensions for generic metrics, the theory is not well defined in four dimensions.

8 pages, typos corrected, discussions expanded

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• Gravitational Energy in Quadratic Curvature Gravities
• Super-energy tensors
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