Asymptotic structure of Einstein-Gauss-Bonnet theory in lower dimensions

Abstract

Recently, an action principle for the $D\to 4$ limit of the Einstein-Gauss-Bonnet gravity has been proposed. It is a special scalar-tensor theory that belongs to the family of Horndeski gravity. It also has a well defined $D\to 3$ and $D\to 2$ limit. In this work, we examine this theory in three and four dimensions in Bondi-Sachs framework. In both three and four dimensions, we find that there is no news function associated to the scalar field, which means that there is no scalar propagating degree of freedom in the theory. In four dimensions, the mass-loss formula is not affected by the Gauss-Bonnet term. This is consistent with the fact that there is no scalar radiation. However, the effects of the Gauss-Bonnet term are quite significant in the sense that they arise just one order after the integration constants and also arise in the quadrupole of the gravitational source.

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Cited by in corpus (12)

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• Gravity with a generalized conformal scalar field: Theory and solutions
• Vacua and Exact Solutions in Lower-$D$ Limits of EGB
• Rotating Gauss-Bonnet BTZ Black Holes
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• Kundt spacetimes in the Einstein-Gauss-Bonnet theory
• Anisotropy in constraint 4D Gauss-Bonnet gravity