On Taking the D→ 4 limit of Gauss-Bonnet Gravity: Theory and Solutions

2020/04/30 by Robie A. Hennigar, David Kubiznak, Robert B. Mann +1 · 3 citations
Physics and Astronomy · #gr-qc #hep-th

paper · pdf · doi:10.1007/jhep07(2020)027

19 pages, no figures v2: added references

arxiv created 2020/05/04 · arxiv updated 2020/08/26

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→ 4 solutions of the higher-dimensional Gauss-Bonnet gravity. We show that a well-defined D→ 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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