Classical central extension for asymptotic symmetries at null infinity in three spacetime dimensions

The symmetry algebra of asymptotically flat spacetimes at null infinity in three dimensions is the semi-direct sum of the infinitesimal diffeomorphisms on the circle with an abelian ideal of supertranslations. The associated charge algebra is shown to admit a non trivial classical central extension of Virasoro type closely related to that of the anti-de Sitter case.Comment: 4 sign mistakes due to a change of conventions are corrected in section 2, none of the conclusions are affected, takes precedence over published version, including corrigendu

Orientifolded Locally AdS3 Geometries

Continuing the analysis of [arXiv:1003.4089[hep-th]], we classify all locally AdS3 stationary axi-symmetric unorientable solutions to AdS3 Einstein gravity and show that they are obtained by applying certain orientifold projection on AdS3, BTZ or AdS3 self-dual orbifold, respectively O-AdS3, O-BTZ and O-SDO geometries. Depending on the orientifold fixed surface, the O-surface, which is either a space-like 2D plane or cylinder, or a light-like 2D plane or cylinder one can distinguish four distinct cases. For the space-like orientifold plane or cylinder cases these geometries solve AdS3 Einstein equations and are hence locally AdS3 everywhere except at the O-surface, where there is a delta-function source. For the light-like cases the geometry is a solution to Einstein equations even at the O-surface. We discuss the causal structure for static, extremal and general rotating O-BTZ and O-SDO cases as well as the geodesic motion on these geometries. We also discuss orientifolding Poincare patch AdS3 and AdS2 geometries as a way to geodesic completion of these spaces and comment on the 2D CFT dual to the O-geometries.Comment: 26 page, 4 .eps figure

Holography in Three-dimensional Kerr-de Sitter Space with a Gravitational Chern-Simons Term

The holographic description of the three-dimensional Kerr-de Sitter space with a gravitational Chern-Simons term is studied, in the context of dS/CFT correspondence. The space has only one (cosmological) event horizon and its mass and angular momentum are identified from the holographic energy-momentum tensor at the asymptotic infinity. The thermodynamic entropy of the cosmological horizon is computed directly from the first law of thermodynamics, with the usual Hawking temperature, and it is found that the usual Gibbons-Hawking entropy is modified. It is remarked that, due to the gravitational Chern-Simons term, (a) the results go beyond analytic continuation from AdS, (b) the maximum-mass/N-bound conjecture may be violated, and (c) the three-dimensional cosmology is chiral. A statistical mechanical computation of the entropy, from a Cardy-like formula for a dual CFT at the asymptotic boundary, is discussed. Some technical difference in the Chern-Simons energy-momentum tensor, from literatures is remarked also.Comment: Typos corrected; Accepted in CQ

Isolated horizons in higher-dimensional Einstein-Gauss-Bonnet gravity

The isolated horizon framework was introduced in order to provide a local description of black holes that are in equilibrium with their (possibly dynamic) environment. Over the past several years, the framework has been extended to include matter fields (dilaton, Yang-Mills etc) in D=4 dimensions and cosmological constant in $D\geq3$ dimensions. In this article we present a further extension of the framework that includes black holes in higher-dimensional Einstein-Gauss-Bonnet (EGB) gravity. In particular, we construct a covariant phase space for EGB gravity in arbitrary dimensions which allows us to derive the first law. We find that the entropy of a weakly isolated and non-rotating horizon is given by $\mathcal{S}=(1/4G_{D})\oint_{S^{D-2}}\bm{\tilde{\epsilon}}(1+2\alpha\mathcal{R})$. In this expression $S^{D-2}$ is the $(D-2)$-dimensional cross section of the horizon with area form $\bm{\tilde{\epsilon}}$ and Ricci scalar $\mathcal{R}$, $G_{D}$ is the $D$-dimensional Newton constant and $\alpha$ is the Gauss-Bonnet parameter. This expression for the horizon entropy is in agreement with those predicted by the Euclidean and Noether charge methods. Thus we extend the isolated horizon framework beyond Einstein gravity.Comment: 18 pages; 1 figure; v2: 19 pages; 2 references added; v3: 19 pages; minor corrections; 1 reference added; to appear in Classical and Quantum Gravit

Stochastic Quantization of Scalar Fields in de Sitter Spacetime

We consider the stochastic quantization method for scalar fields defined in a curved manifold. The two-point function associated to a massive self-interacting scalar field is evaluated, up to the first order level in the coupling constant $\lambda$, for the case of de Sitter Euclidean metric. Its value for the asymptotic limit of the Markov parameter $\tau\to\infty$ is exhibited. We discuss in detail the covariant stochastic regularization to render the one-loop two-point function finite in the de Sitter Euclidean metric

The Asymptotic Dynamics of de Sitter Gravity in three Dimensions

We show that the asymptotic dynamics of three-dimensional gravity with positive cosmological constant is described by Euclidean Liouville theory. This provides an explicit example of a correspondence between de Sitter gravity and conformal field theories. In the case at hand, this correspondence is established by formulating Einstein gravity with positive cosmological constant in three dimensions as an SL(2,C) Chern-Simons theory. The de Sitter boundary conditions on the connection are divided into two parts. The first part reduces the CS action to a nonchiral SL(2,C) WZNW model, whereas the second provides the constraints for a further reduction to Liouville theory, which lives on the past boundary of dS_3.Comment: 12 pages, LaTeX, no figures, v2: Minor changes, references adde

Aspects of Quantum Gravity in de Sitter Spaces

In these lectures we give a review of recent attempts to understand quantum gravity on de Sitter spaces. In particular, we discuss the holographic correspondence between de Sitter gravity and conformal field theories proposed by Hull and by Strominger, and how this may be reconciled with the finite-dimensional Hilbert space proposal by Banks and Fischler. Furthermore we review the no-go theorems that forbid an embedding of de Sitter spaces in string theory, and discuss how they can be circumvented. Finally, some curious issues concerning the thermal nature of de Sitter space are elucidated.Comment: 36+1 pages, 5 Postscript figures, introduction and section 6 extended, further references, final version to appear in JCA