David Tempo

Higher spin gravity in 3D: Black holes, global charges and thermodynamics

Abstract Global charges and thermodynamic properties of three-dimensional higher spin black holes that have been recently found in the literature are revisited. Since these solutions possess a relaxed asymptotically AdS behavior, following the canonical approach, it is shown that the global charges, and in particular the energy, acquire explicit nontrivial contributions given by nonlinear terms in the deviations with respect to the reference background. It is also found that there are cases for which the first law of thermodynamics can be readily worked out in the canonical ensemble, i.e., without work terms associated to the presence of higher spin fields, and remarkably, the semiclassical higher spin black hole entropy is exactly reproduced from Cardy formula.

Generalized Black Holes in Three-dimensional Spacetime

A bstractThree-dimensional spacetime with a negative cosmological constant has proven to be a remarkably fertile ground for the study of gravity and higher spin fields. The theory is topological and, since there are no propagating field degrees of freedom, the asymptotic symmetries become all the more crucial. For pure (2 + 1) gravity they consist of two copies of the Virasoro algebra. There exists a black hole which may be endowed with all the corresponding charges. The pure (2 + 1) gravity theory may be reformulated in terms of two Chern-Simons connections for sl (2,

Higher spin black hole entropy in three dimensions

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Chemical potentials in three-dimensional higher spin anti-de Sitter gravity

). This permits an immediate generalization which may be interpreted as containing gravity and a finite number of higher spin fields. The generalization is achieved by replacing sl (2,

Field theories with anisotropic scaling in 2D, solitons and the microscopic entropy of asymptotically Lifshitz black holes

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Higher spin black holes with soft hair

) by sl (3,

Static spherically symmetric solutions for conformal gravity in three dimensions

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Higher spin extension of cosmological spacetimes in 3D: asymptotically flat behaviour with chemical potentials and thermodynamics

) or, more generally, by sl (N,

Boundary conditions for General Relativity on AdS3 and the KdV hierarchy

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Gravitational solitons, hairy black holes and phase transitions in BHT massive gravity

). The asymptotic symmetries are then two copies of the so-called WN algebra, which contains the Virasoro algebra as a subalgebra. The question then arises as to whether there exists a generalization of the standard pure gravity (2 + 1) black hole which would be endowed with all the WN charges. Since the generalized Chern-Simons theory does not admit a direct metric interpretation, one must define the black hole in Euclidean spacetime through its thermal properties, and then continue to Lorentzian spacetime. The original pioneering proposal of a black hole along this line for N = 3 turns out, as shown in this paper, to actually belong to the so called “diagonal embedding” of sl (2,