Equivalence of solutions between the four-dimensional novel and regularized EGB theories in a cylindrically symmetric spacetime

Recently, a novel four-dimensional Einstein–Gauss–Bonnet (EGB) theory was presented to bypass the Lovelock’s theorem and to give nontrivial effects on the four-dimensional local gravity. The main mechanism is to introduce a redefinition $$\alpha \rightarrow \alpha /(D-4)$$ and to take the limit $$D\rightarrow 4$$. However, this theory does not have standard four-dimensional field equations. Some regularization procedures are then proposed to address this problem (http://arxiv.org/abs/2003.1155