Regular Article - Theoretical Physics
Is there a novel Einstein–Gauss–Bonnet theory in four dimensions?
Department of Mathematics, Faculty of Sciences, Bilkent University, 06800, Ankara, Turkey
2 Department of Astronautical Engineering, University of Turkish Aeronautical Association, 06790, Ankara, Turkey
3 Department of Physics, Middle East Technical University, 06800, Ankara, Turkey
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Accepted: 2 July 2020
Published online: 20 July 2020
No! We show that the field equations of Einstein–Gauss–Bonnet theory defined in generic dimensions split into two parts one of which always remains higher dimensional, and hence the theory does not have a non-trivial limit to . 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 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.
© The Author(s), 2020