The covariant action of higher spin black holes in three dimensions

Abstract

We propose a set of boundary terms for higher spin theories in AdS${}_3$ that lead to a well-defined variational principle compatible with Dirichlet boundary conditions for the metric and higher spin fields. These boundary terms are valid for higher spin theories in the Fefferman-Graham gauge and they allow us to compute the canonical free energy of higher spin black holes directly from the Euclidean, covariant, on-shell action. Using these results we reproduce the thermodynamics of the higher spin black hole of Ammon, Gutperle, Kraus, and Perlmutter and comment on the corresponding theory of induced $\mathcal{W}$-gravity at the boundary.

20 pages; v2: clarified the origin of the boundary term at the horizon, matches published version

References in corpus (6)

• Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields
• Nonlinear W(infinity) Algebra as Asymptotic Symmetry of Three-Dimensional Higher Spin Anti-de Sitter Gravity
• Setting the boundary free in AdS/CFT
• Generalized Black Holes in Three-dimensional Spacetime
• Some aspects of holographic W-gravity
• Strings from 3D gravity: asymptotic dynamics of AdS${}_3$ gravity with free boundary conditions

Cited by in corpus (4)

• Higher Spin Black Holes with Soft Hair
• An Action for Matter Coupled Higher Spin Gravity in Three Dimensions
• The sky is the limit: free boundary conditions in AdS${}_3$ Chern-Simons theory
• Aspects of Higher Spin Theories, Conformal Field Theories and Holography