Horndeski gravity as \(D \rightarrow 4\) limit of Gauss-Bonnet

DOI10.1016/J.PHYSLETB.2020.135717zbMATH Open1473.83005arXiv2003.11552OpenAlexW3013206341MaRDI QIDQ822355

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Publication date: 22 September 2021

Published in: (Search for Journal in Brave)

Abstract: We propose a procedure for the $Dightarrow4$ limit of Einstein-Gauss-Bonnet (EGB) gravity that leads to a well defined action principle in four dimensions. Our construction is based on compactifying $D$-dimensional EGB gravity on a $(D-4)$-dimensional maximally symmetric space followed by redefining the Gauss-Bonnet coupling $alphaightarrowfracalphaD-4$. The resulting model is a special scalar-tensor theory that belongs to the family of Horndeski gravity. Static black hole solutions in the scalar-tensor theory are investigated. Interestingly, the metric profile is independent of the curvature of the internal space and coincides with the $Dightarrow4$ limit of the usual EGB black hole with the unusual Gauss-Bonnet coupling $fracalphaD-4$. The curvature information of the internal space is instead encoded in the profile of the extra scalar field. Our procedure can also be generalized to define further limits of the Gauss-Bonnet combination by compactifying the $D$-dimensional theory on a $(D-p)$-dimensional maximally symmetric space with $pleq3$. These lead to different $Dightarrow4$ limits of EGB gravity as well as its $Dightarrow2,3$ limits.

Full work available at URL: https://arxiv.org/abs/2003.11552

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