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 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 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 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