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

By M. Gürses, Tahsin Cagri Sisman, B. Tekin. The European Physical Journal C, 2020

234 citations recorded by the source corpus.

No! We show that the field equations of Einstein–Gauss–Bonnet theory defined in generic D>4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$D>4$$\end{document} 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\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$D=4$$\end{document}. 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\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$D>4$$\end{document} 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.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/a134cd8b621588f1af5a201db570e4242ead34b9

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Citations in the corpus

The 4D Einstein–Gauss–Bonnet theory of gravity: a review (2022, background): “To see why, one can re-cast equation (19) in terms of space–time indices and take the Hodge dual of the (D − 1)-form obtaining (see reference [167] for details) ενα = 2 (D − 4)!Hνα = 0, (41)”
Gravitational lensing by black holes in the 4D Einstein-Gauss-Bonnet gravity (2020, background): “Interestingly, neither of the critics [34, 36, 38] disprove dimensional regularization procedure of [10] at least for the case of spherically symmetric spacetimes.”