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Chern-Simons gravities are theories with a lagrangian given by a Chern-Simonsform constructed from a space-time gauge group. In previous investigations weshowed that, for some special field configurations that are solutions of thefield equations, the extension from Chern-Simons to Transgression forms aslagrangians, motivated by gauge invariance, automatically yields the boundaryterms required to regularize the theory, giving finite conserved charges andblack hole thermodynamics. Further work by other researchers showed that one ofthe action functionals considered in the above mentioned work yields a welldefined action principle in the metric (zero torsion) case and forasymptotically Anti de Sitter (AdS) space-times. In the present work weconsider several action functionals for Chern-Simons AdS gravity constructedfrom Transgression forms, and show the action principles to be well defined andthe Noether charges and Euclidean action to be finite for field configurationssatisfying only that the gauge field curvature (field strength) for the AdSgauge group is asymptotically finite. For that purpose we consider anasymptotic expansion of the vielbein and spin connection that may be regardedas a perturbation of an AdS space-time, but allowing a non zero torsion. Ourresults are of potential interest for Lovelock gravity theories, as it has beenshown that the boundary terms dictated by the transgressions for Chern-Simonsgravities are also suitable to regularize Lovelock theories.

Action Principles for Transgression and Chern-Simons AdS Gravities