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On taking the D → 4 limit of Gauss-Bonnet gravity: theory and solutions

Robie A. HennigarDepartment of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, Newfoundland and Labrador, A1C 5S7, CanadaDavid KubizňákDepartment of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, N2L 3G1, CanadaRobert B. MannDepartment of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, N2L 3G1, CanadaChristopher PollackDepartment of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada

2020en

ABI

Annotatsiya

A bstract 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 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 D = 4 is not well defined and contrast the resultant metrics with the actual solutions of the new theory.

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Identifikatorlar

DOI: 10.1007/jhep07(2020)027

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