On boundary conditions in three-dimensional AdS gravity

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.

12 pages; a reference added

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• Topological regularization and self-duality in four-dimensional anti-de Sitter gravity
• Regularization of odd-dimensional AdS gravity: Kounterterms
• Universal regularization prescription for Lovelock AdS gravity
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• BTZ Black Hole with Gravitational Chern-Simons: Thermodynamics and Statistical Entropy
• Counterterms in Dimensionally Continued AdS Gravity
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• Asymptotic symmetries of three-dimensional Chern-Simons gravity for the Maxwell algebra
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• Holography in 3D AdS gravity with torsion
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• Sliding Surface Charges on AdS${}_3$
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• General solutions in Chern-Simons gravity and $T\bar{T}$-deformations
• Aspects of Higher Spin Theories, Conformal Field Theories and Holography