Three-dimensional Gravity Theories Research Articles

Boundary Heisenberg algebras and their deformations

We investigate the deformations and rigidity of boundary Heisenberg-like algebras. In particular, we focus on the Heisenberg and Heisenberg ⊕ mathfrak{witt} algebras which arise as symmetry algebras in three-dimensional gravity theories. As a result of the deformation procedure we find a large class of algebras. While some of these algebras are new, some of them have already been obtained as asymptotic and boundary symmetry algebras, supporting the idea that symmetry algebras associated to diverse boundary conditions and spacetime loci are algebraically interconnected through deformation of algebras. The deformation/contraction relationships between the new algebras are investigated. In addition, it is also shown that the deformation procedure reaches new algebras inaccessible to the Sugawara construction. As a byproduct of our analysis, we obtain that Heisenberg ⊕ mathfrak{witt} and the asymptotic symmetry algebra Weyl-bms3 are not connected via single deformation but in a more subtle way.

Conservation and integrability in lower-dimensional gravity

We address the questions of conservation and integrability of the charges in two and three-dimensional gravity theories at infinity. The analysis is performed in a framework that allows us to treat simultaneously asymptotically locally AdS and asymptotically locally flat spacetimes. In two dimensions, we start from a general class of models that includes JT and CGHS dilaton gravity theories, while in three dimensions, we work in Einstein gravity. In both cases, we construct the phase space and renormalize the divergences arising in the symplectic structure through a holographic renormalization procedure. We show that the charge expressions are generically finite, not conserved but can be made integrable by a field-dependent redefinition of the asymptotic symmetry parameters.

Limits of three-dimensional gravity and metric kinematical Lie algebras in any dimension

We extend a recent classification of three-dimensional spatially isotropic homogeneous spacetimes to Chern-Simons theories as three-dimensional gravity theories on these spacetimes. By this we find gravitational theories for all carrollian, galilean, and aristotelian counterparts of the lorentzian theories. In order to define a nondegenerate bilinear form for each of the theories, we introduce (not necessarily central) extensions of the original kinematical algebras. Using the structure of so-called double extensions, this can be done systematically. For homogeneous spaces that arise as a limit of (anti-)de Sitter spacetime, we show that it is possible to take the limit on the level of the action, after an appropriate extension. We extend our systematic construction of nondegenerate bilinear forms also to all higher-dimensional kinematical algebras.

General formulae for conserved charges and black hole entropy in Chern-Simons-like theories of gravity

This paper deals with the problem of defining off-shell conserved charges in a set of theories known as Chern-Simons-like theories of gravity (CSLTG). The method is derived in a general way, which may find applications in a wide set of theories, and then specified to the case of Generalized minimal massive gravity (GMMG), where known results of the central charge and black hole entropy are reproduced. The results for the charges are useful to the community and can be applied to all three-dimensional gravity theories within the class of CSLTG which includes almost all of them. The given specific examples show a consistency check of the more general method.

Holography of 3D asymptotically flat black holes

We study the asymptotically flat rotating hairy black hole solution of a three-dimensional gravity theory which is given by taking the flat-space limit (zero cosmological constant limit) of new massive gravity. We propose that the dual field theory of the flat-space limit of new massive gravity can be described by a contracted conformal field theory which is invariant under the action of the BMS$_{3}$ group. Using the flat/contracted conformal field theory correspondence, we construct a stress tensor which yields the conserved charges of the asymptotically flat black hole solution. We check that our expressions of the mass and angular momentum fit with the first law of black hole thermodynamics. Furthermore, by taking the appropriate limit of the Cardy formula in the parent conformal field theory, we find a Cardy-like formula which reproduces the Wald's entropy of the 3D asymptotically flat black hole.

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.

Galilean conformal algebra in two dimensions and cosmological topologically massive gravity

We consider a realization of the Galilean conformal algebra (GCA) in two-dimensional space–time on the AdS boundary of a particular three-dimensional gravity theory, the so-called cosmological topologically massive gravity (CTMG), which includes the gravitational Chern–Simons term and the negative cosmological constant. The infinite-dimensional GCA in two dimensions is obtained from the Virasoro algebra for the relativistic CFT by taking a scaling limit t → t , x → ϵ x with ϵ → 0 . The parent relativistic CFT should have left and right central charges of order O ( 1 / ϵ ) but opposite in sign in the limit ϵ → 0 . On the other hand, by Brown–Henneaux's analysis the Virasoro algebra is realized on the boundary of AdS 3, but the left and right central charges are asymmetric only by the factor of the gravitational Chern–Simons coupling 1 / μ . If μ behaves as of order O ( ϵ ) under the corresponding limit, we have the GCA with non-trivial centers on AdS boundary of the bulk CTMG. Then we present a new entropy formula for the Galilean field theory from the bulk black hole entropy, which is a non-relativistic counterpart of the Cardy formula. It is also discussed whether it can be reproduced by the microstate counting.

Quadratic gravity theories in 2+1 dimensions and the topological Chern-Simons term

It is astonishing that a locally trivial and globally nontrivial Einstein-type gravitational theory can be built only by lowering the dimension of our space-time—which is supposed to be four dimensional—by one unit. In fact, threedimensional general relativity is dynamically trivial: outside sources, spacetime is flat—all effects of the localized sources are on the global geometry, which is fixed by the singularities of the worldlines of the particles @1#. The quantum mechanical analogue of this triviality emerges when the HilbertEinstein action related to this theory is quantized. It is easy to establish that the theory does not possess any propagating degrees of freedom. In other words, there are no gravitons. The preceding considerations lead us to raise the following important question: Is it possible to build a nontrivial generally covariant three-dimensional gravity theory having propagating degrees of freedom? The answer is affirmative. Actually, this can be done at least in two different ways: ~i! Adding a topological nontrivial term to general relativity in ~211!D @2#. Ordinary Einstein gravity which is trivial acquires now a propagating, massive, spin-2 mode. This theory is ghost-free and causal, although of the thirdderivative order. ~ii! Including the four-derivatives terms *R 2 Agd 3 x and