Inner Mechanics of Three-Dimensional Black Holes

We investigate properties of the inner horizons of certain black holes in higher-derivative three-dimensional gravity theories. We focus on Bañados-Teitelboim-Zanelli and spacelike warped anti–de Sitter black holes, as well as on asymptotically warped de Sitter solutions exhibiting both a cosmological and a black hole horizon. We verify that a first law is satisfied at the inner horizon, in agreement with the proposal of Castro and Rodriguez [arXiv:1204.1284]. We then show that, in topologically massive gravity, the product of the areas of the inner and outer horizons fails to be independent on the mass, and we trace this to the diffeomorphism anomaly of the theory.