We show that the asymptotic symmetries close to nonextremal black hole horizons are generated by an extension of supertranslations. This group is generated by a semidirect sum of Virasoro and Abelian currents. The charges associated with the asymptotic Killing symmetries satisfy the same algebra. When considering the special case of a stationary black hole, the zero mode charges correspond to the angular momentum and the entropy at the horizon.

The computation of two and three point functions in the Coulomb gas free field approach to string theory in the SL(2,R)/U(1) black hole background is reviewed. An interesting relation arises when comparing the results obtained using two different screening operators. The formalism is then modified to study string theory propagating in AdS 3 which is considered as the direct product of the SL(2)/U(1) coset times a timelike free boson. This representation allows to naturally include the spectral flow symmetry and winding number in vertex operators and correlation functions. Two and three point tachyon amplitudes are computed in this new scenario and the results coincide with previous reports in the literature. Novel expressions are found for processes violating winding number conservation. IntroductionString theory on three dimensional Anti de Sitter space (AdS 3 ) is an interesting model to analyse the AdS/CFT correspondence beyond the field theory approximation. Much progress has been achieved in understanding this theory in recent years (see [1,2]), although there are still important issues to be clarified.Unitarity has been the leading subject in this story during the last decade since, unlike string theory in flat spacetime, the Virasoro constraints seemed unable to annihilate all the negative norm states of the string propagating in AdS 3 . Fortunately a naturally unitary spectrum has been revealed by the spectral flow symmetry disclosed in reference [3]. The new representations obtained by the spectral flow were originally considered in [2] in the context of string theory in the SL(2,R) group manifold. It was shown in reference [3] that they resolve some of the longstanding negative consequences of arbitrarily truncating the spin j (equivalently the mass) of the physical states when the traget space is the universal cover of SL(2,R). This represents an important step in the construction of a consistent model, but the consistency of the theory cannot be completely established until interactions are included and the closure of the operator product expansion is determined. Indeed, regarded as a conformal field theory, string theory in AdS 3 will be completly characterized by the spectrum and the full set of three point functions.In this paper we continue the study of correlation functions of string theory in AdS 3 which was started in reference [4]. Based on the proposal in [3] we consider the theory as the tensor product of the coset space H + 3 /U(1) (the euclidean version of the SL(2,R)/U(1) group manifold) times the state space of a timelike free boson. The vertex operators are constructed and correlation functions are computed extending to the non-compact case a prescription developed for SU(2) in reference [5]. This formalism is suitable to manifestly include the spectral flow parameter or winding number ω. We explicitly construct two and three point functions of physical states using the modified Coulomb gas formalism developed in [4], and we then compare the expressions obtained with results re...

We show that three-dimensional massive gravity admits Lifshitz metrics with generic values of the dynamical exponent z as exact solutions. At the point z = 3, exact black hole solutions which are asymptotically Lifshitz arise. These spacetimes are three-dimensional analogues of those that were recently proposed as gravity duals for anisotropic scale invariant fixed points.The enormous success of gauge-gravity duality [1] has triggered the interest in generalizing the holographic techniques to other areas of physics. Recently, the attempts to generalize AdS/CFT correspondence to nonrelativistic condensed matter physics have received considerable attention. Besides being an active line of research, this has given raise to very interesting new ideas; see Ref.[2] and references therein for a review.Recently, candidates to be gravity duals for nonrelativistic scale invariant theories, both exhibiting Galilean invariance or not, have been proposed. In Refs. [3,4], spacetimes whose isometry group is the so-called Schrödinger group were proposed to be gravity duals for Galilean and scale invariant systems. In Ref.[5], the scale invariant fixed points that do not exhibit Galilean symmetry were also analyzed, and the metric of the corresponding gravity duals were introduced (see Eq.(2) below). These metrics manifestly exhibit the anisotropic scale invariance

We prove that non-extremal black holes in four-dimensional general relativity exhibit an infinite-dimensional symmetry in their near horizon region. By prescribing a physically sensible set of boundary conditions at the horizon, we derive the algebra of asymptotic Killing vectors, which is shown to be infinite-dimensional and includes, in particular, two sets of supertranslations and two mutually commuting copies of the Witt algebra. We define the surface charges associated to the asymptotic diffeomorphisms that preserve the boundary conditions and discuss the subtleties of this definition, such as the integrability conditions and the correct definition of the Dirac brackets. When evaluated on the stationary solutions, the only non-vanishing charges are the zero-modes. One of them reproduces the Bekenstein-Hawking entropy of Kerr black holes. We also study the extremal limit, recovering the NHEK geometry. In this singular case, where the algebra of charges and the integrability conditions get modified, we find that the computation of the zero-modes correctly reproduces the black hole entropy. Furthermore, we analyze the case of three spacetime dimensions, in which the integrability conditions notably simplify and the field equations can be solved analytically to produce a family of exact solutions that realize the boundary conditions explicitly. We examine other features, such as the form of the algebra in the extremal limit and the relation to other works in the literature.

The Chern-Simons modification to general relativity in four dimensions consists of adding to the Einstein-Hilbert term a scalar field that couples to the first class Pontryagin density. In this theory, which has attracted considerable attention recently, the Schwarzschild metric persists as an exact solution, and this is why this model resists several observational constraints. In contrast, the spinning black hole solution of the theory is not given by the Kerr metric but by a modification of it, so far only known for slow rotation and small coupling constant. In the present paper, we show that, in this approximation, the null geodesic equation can be integrated, and this allows us to investigate the shadow cast by a black hole. We discuss how, in addition to the angular momentum of the solution, the coupling to the Chern-Simons term deforms the shape of the shadow.

Lovelock theory is a natural extension of Einstein theory of gravity to higher dimensions, and it is of great interest in theoretical physics as it describes a wide class of models. In particular, it describes string theory inspired ultraviolet corrections to Einstein-Hilbert action, while admits the Einstein general relativiy and the so called Chern-Simons theories of gravity as particular cases. Recently, five-dimensional Lovelock theory has been considered in the literature as a working example to illustrate the effects of including higher-curvature terms in the context of AdS/CFT correspondence.Here, we give an introduction to the black hole solutions of Lovelock theory and analyze their most important properties. These solutions can be regarded as generalizations of the Boulware-Deser solution of Einstein-Gauss-Bonnet gravity, which we discuss in detail here. We briefly discuss some recent progress in understading these and other solutions, like topological black holes that represent black branes of the theory, and vacuum thinshell wormhole-like geometries that connect two different asymptotically de-Sitter spaces. We also make some comments on solutions with time-like naked singularities.2 The eleven-dimensional Newton constant is given by the Planck scale G (11D) = 2π 4 l 9 P . 3 Actually, while second-order terms of heterotic string theory expressed in a particular frame agree with the second-order term of the Lovelock theory, the fourth-order terms of Type IIA and IIB string theories (and M-theory) do not agree with the fourth-order term of the Lovelock theory.4 Compactifying to four dimensions gives raise to the higher-curvature correctionSee [10] for a recent discussion on these quartic terms in four dimensions.

We study AdS-waves in the three-dimensional new theory of massive gravity recently proposed by Bergshoeff, Hohm, and Townsend. The general configuration of this type is derived and shown to exhibit different branches, with different asymptotic behaviors. In particular, for the special fine tuning m 2 = ±1/(2l 2 ), solutions with logarithmic fall-off arise, while in the range m 2 > −1/(2l 2 ), spacetimes with Schrödinger isometry group are admitted as solutions. Spacetimes that are asymptotically AdS3, both for the Brown-Henneaux and for the weakened boundary conditions, are also identified. The metric function that characterizes the profile of the AdS-wave behaves as a massive excitation on the spacetime, with an effective mass given by m 2 eff = m 2 − 1/(2l 2 ). For the critical value m 2 = −1/(2l 2 ), the value of the effective mass precisely saturates the Breitenlohner-Freedman bound for the AdS3 space where the wave is propagating on. The analogies with the AdS-wave solutions of topologically massive gravity are also discussed. Besides, we consider the coupling of both massive deformations to Einstein gravity and find the exact configurations for the complete theory, discussing all the different branches exhaustively. One of the effects of introducing the Chern-Simons gravitational term is that of breaking the degeneracy in the effective mass of the generic modes of pure New Massive Gravity, producing a fine structure due to parity violation. Another effect is that the zoo of exact logarithmic specimens becomes considerably enlarged. PACS numbers:1 See Ref.[15] for a preliminary derivation of the no-logarithmic branch, where it was argued that in order to be supersymmetric the solutions should not depend on the retarded time. See also Ref. [16], where the interpretation as AdS-waves was first given to the final forms of the metric originally derived in Ref. [13].

Abstract:We generalize the four-dimensional R 2 -corrected z = 3/2 Lifshitz black hole to a two-parameter family of black hole solutions for any dynamical exponent z and for any dimension D. For a particular relation between the parameters, we find the first example of an extremal Lifshitz black hole. An asymptotically Lifshitz black hole with a logarithmic decay is also exhibited for a specific critical exponent depending on the dimension. We extend this analysis to the more general quadratic curvature corrections for which we present three new families of higher-dimensional D ≥ 5 analytic Lifshitz black holes for generic z. One of these higher-dimensional families contains as critical limits the z = 3 three-dimensional Lifshitz black hole and a new z = 6 four-dimensional black hole. The variety of analytic solutions presented here encourages to explore these gravity models within the context of non-relativistic holographic correspondence.