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We propose a regularization procedure for the novel Einstein-Gauss-Bonnettheory of gravity, which produces a set of field equations that can be writtenin closed form in four dimensions. Our method consists of introducing a counterterm into the action, and does not rely on the embedding or compactification ofany higher-dimensional spaces. This counterterm is sufficient to cancel thedivergence in the action that would otherwise occur, and exactly reproduces thetrace of the field equations of the original formulation of the theory. Allother field equations display an extra scalar gravitational degree of freedomin the gravitational sector, in keeping with the requirements of Lovelock'stheorem. We discuss issues concerning the equivalence between our newregularized theory and the original.

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