Regularization of odd-dimensional AdS gravity: Kounterterms

As an alternative to the Dirichlet counterterms prescription, I introduce theconcept of Kounterterms as the boundary terms with explicit dependence on theextrinsic curvature K_{ij} that regularize the AdS gravity action. Instead of aDirichlet boundary condition on the metric, a suitable choice of the boundaryconditions --compatible with any asymptotically AdS (AAdS) spacetime-- ensuresa finite action principle for all odd dimensions. Background-independentconserved quantities are obtained as Noether charges associated to asymptoticsymmetries and their general expression appears naturally split in two parts. The first one gives the correct mass and angular momentum for AAdS blackholes and vanishes identically for globally AdS spacetimes. Thus, the secondpart is a covariant formula for the vacuum energy in AAdS spacetimes andreproduces the results obtained by the Dirichlet counterterms method in anumber of cases. It is also shown that this Kounterterms series regularizes theEuclidean action and recovers the correct black hole thermodynamics in odddimensions.Comment: 35+6 pages, 8 references and an appendix added, improved discussion on boundary conditions and geometrical origin of Kounterterms. Version accepted in JHE