English

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

General Relativity and Quantum Cosmology 2020-12-04 v3 High Energy Physics - Theory

Abstract

No! We show that the field equations of Einstein-Gauss-Bonnet theory defined in generic D>4D>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=4D=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>4D>4 dimensional. As there is no canonical choice of 4 spacetime dimensions out of DD dimensions for generic metrics, the theory is not well defined in four dimensions.

Cite

@article{arxiv.2004.03390,
  title  = {Is there a novel Einstein-Gauss-Bonnet theory in four dimensions?},
  author = {Metin Gurses and Tahsin Cagri Sisman and Bayram Tekin},
  journal= {arXiv preprint arXiv:2004.03390},
  year   = {2020}
}

Comments

8 pages, typos corrected, discussions expanded

R2 v1 2026-06-23T14:42:50.980Z