On boundary conditions in three-dimensional AdS gravity

TL;DR

This paper proposes a new boundary condition for three-dimensional AdS gravity that naturally regularizes the action and charges without extra counterterms, and discusses its consistency and potential extension to higher dimensions.

Contribution

It introduces a boundary condition based on asymptotic extrinsic curvature that simplifies the action principle and charge finiteness in 3D AdS gravity.

Findings

The boundary condition yields a finite Euclidean action and Noether charges.

It is consistent with the Dirichlet problem and Chern-Simons formulation.

Potential applicability to higher odd-dimensional AdS gravities.

Abstract

A finite action principle for three-dimensional gravity with negative cosmological constant, based on a boundary condition for the asymptotic extrinsic curvature, is considered. The bulk action appears naturally supplemented by a boundary term that is one half the Gibbons-Hawking term, that makes the Euclidean action and the Noether charges finite without additional Dirichlet counterterms. The consistency of this boundary condition with the Dirichlet problem in AdS gravity and the Chern-Simons formulation in three dimensions, and its suitability for the higher odd-dimensional case, are also discussed.