Yet another comment on four-dimensional Einstein-Gauss-Bonnet gravity

Abstract

In this comment we clarify several aspects concerning four-dimensional Einstein-Gauss-Bonnet gravity. We argue that the limiting procedure outlined in [Phys. Rev. Lett. 124, 081301 (2020)] is not well defined as it generally produces divergent 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.