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A finite action principle for Einstein-Gauss-Bonnet AdS gravity is presented.The boundary term, which is different for even and odd dimensions, is afunctional of the boundary metric, intrinsic curvature and extrinsic curvature.For even dimensions, the boundary term corresponds to the maximal Chern form ofthe spacetime, and the asymptotic AdS condition for the curvature suffices forthe well-posedness of this action. For odd dimensions, the action is stationaryunder a boundary condition on the variation of the extrinsic curvature. Thebackground-independent Noether charges associated to asymptotic symmetries arefound and the Euclidean continuation of the action correctly describes theblack hole thermodynamics in the canonical ensemble. In particular, thisprocedure leads to a covariant formula for the vacuum energy in odd-dimensionalasymptotically AdS spacetimes.Comment: RevTex, 5 pages, accepted for publication in PR

Vacuum energy in Einstein-Gauss-Bonnet anti–de Sitter gravity