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arXiv · 2004.09472

On Taking the $D\to 4$ limit of Gauss-Bonnet Gravity: Theory and Solutions

Robie A. Hennigar·David Kubiznak·Robert B. Mann·Christopher Pollack
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Abstract

We comment on the recently introduced Gauss-Bonnet gravity in four dimensions. We argue that it does not make sense to consider this theory to be defined by a set of $D\to 4$ solutions of the higher-dimensional Gauss-Bonnet gravity. We show that a well-defined $D\to 4$ limit of Gauss-Bonnet Gravity is obtained generalizing a method employed by Mann and Ross to obtain a limit of the Einstein gravity in $D=2$ dimensions. This is a scalar-tensor theory of the Horndeski type obtained by a dimensional reduction methods. By considering simple spacetimes beyond spherical symmetry (Taub-NUT spaces) we show that the naive limit of the higher-dimensional theory to four dimensions is not well defined and contrast the resultant metrics with the actual solutions of the new theory.

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Robie A. Hennigar, David Kubiznak, Robert B. Mann, Christopher Pollack. 2020-04-20. On Taking the $D\to 4$ limit of Gauss-Bonnet Gravity: Theory and Solutions. https://doi.org/10.1007/jhep07(2020)027

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