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We propose a boundary term to the Einstein-Gauss-Bonnet action for gravity,which is constructed as the dimensional continuation of the Chern-Weil theorem,and such that the extremization of the full action yields the equations ofmotion when Dirichlet boundary conditions are imposed. When translated intotensorial language, this boundary term is the generalization to this theory ofthe Katz boundary term and vector for general relativity. The constructionallows to deal with a general background and includes the Gibbons-Hawking-Myersboundary term as a special case, when the background is taken to be a productmanifold. As a first application we show that this Einstein Gauss-Bonnet Katzaction yields, without any extra ingredients or regularization, the expectedmass of the Boulware-Deser black hole.

Einstein-Gauss-Bonnet theory of gravity: The Gauss-Bonnet-Katz boundary term