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Inconsistencies in four-dimensional Einstein-Gauss-Bonnet gravity

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arxiv 2004.12998 v2 pith:VLMLHLWN submitted 2020-04-27 gr-qc

Julio Arrechea , Adrià Delhom , Alejandro Jiménez-Cano This is my paper
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keywords aroundeinstein-gauss-bonnetequationsfour-dimensionalgravityill-definedperturbationssolutions
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We attempt to clarify several aspects concerning the recently presented four-dimensional Einstein-Gauss-Bonnet gravity. We argue that the limiting procedure outlined in [Phys. Rev. Lett. 124, 081301 (2020)] generally involves ill-defined terms in the four dimensional field equations. Potential ways to circumvent this issue are discussed, alongside some remarks regarding specific solutions of the theory. We prove that, although linear perturbations are well behaved around maximally symmetric backgrounds, the equations for second-order perturbations are ill-defined even around a Minkowskian background. Additionally, we perform a detailed analysis of the spherically symmetric solutions, and find that the central curvature singularity can be reached within a finite proper time.

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Cited by 3 Pith papers

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