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

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Gürses M., Sisman T. C., Tekin B.

EUROPEAN PHYSICAL JOURNAL C, vol.80, 2020 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 80
  • Publication Date: 2020
  • Doi Number: 10.1140/epjc/s10052-020-8200-7
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, INSPEC, zbMATH, Directory of Open Access Journals
  • Middle East Technical University Affiliated: Yes


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, in terms of metric only, 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.