Derivation of Regularized Field Equations for the Einstein-Gauss-Bonnet Theory in Four Dimensions

We propose a regularization procedure for the novel Einstein-Gauss-Bonnet theory of gravity, which produces a set of field equations that can be written in closed form in four dimensions. Our method consists of introducing a counter term into the action, and does not rely on the embedding or compactification of any higher-dimensional spaces. This counter term is sufficient to cancel the divergence in the action that would otherwise occur, and exactly reproduces the trace of the field equations of the original formulation of the theory. All other field equations display an extra scalar gravitational degree of freedom in the gravitational sector. We discuss issues concerning the equivalence between our new regularized theory and the original.