Inconsistencies in four-dimensional Einstein-Gauss-Bonnet gravity

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 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. * AJC and AD are supported by PhD contracts of the program FPU 2015 with references FPU15/02864 and FPU15/05406 (Spanish Ministry of Economy and Competitiveness), respectively. This work is supported by the Spanish Projects (FIS2017-84440-C2-1-P) (MINECO/FEDER, EU) and FIS2016-78198-P (MINECO), the Project No. H2020-MSCA-RISE-2017 GrantNo. FunFiCO-777740, Project No. SEJI/2017/042 (Generalitat Valenciana), the Consolider Program CPANPHY-1205388, and the Severo Ochoa Grant No. SEV-2014-0398 (Spain). JA acknowledges financial support from the Spanish Government through the project FIS2017-86497-C2-2-P (with FEDER contribution), and from the State Agency for Research of the Spanish MCIU through the "Center of Excellence Severo Ochoa" award to the Instituto de Astrofísica de Andalucía (SEV-2017-0709)