We determine the black hole quasi-normal mode spectrum for tensor perturbations in topologically massive AdS-gravity. In the special case of chiral gravity quasi-normal modes are absent despite of the presence of a horizon. In the process we uncover a simple algebraic structure in the quasi normal modes spectrum: the tower of QNM's consists of descendents of a "chiral highest weight'' QNM which in turn satisfies a first order equation.
We calculate quasinormal modes of a massive scalar perturbation on the topologically massive black hole (CS-BTZ black hole). The chiral point of $μ\ell=1$ corresponds to a newly extremal black hole. We show that there is no quasinormal modes at this point. Accordingly, we prove the unitarity of the CS-BTZ black hole at the chiral point.
We extend our recent work on the quasilocal formulation of conserved charges to a theory of gravity containing a gravitational Chern-Simons term. As an application of our formulation, we compute the off-shell potential and quasilocal conserved charges of some black holes in three-dimensional topologically massive gravity. Our formulation for conserved charges reproduces very effectively the well-known expressions on conserved charges and the entropy expression of black holes in the topologically massive gravity.
In this paper we obtain conserved charges of spin-3 topologically massive gravity by using a quasi-local formalism. We find a general formula to calculate conserved charge of the spin-3 topologically massive gravity which corresponds to a Killing vector field $ξ$. We show that this general formula reduces to the previous one for the ordinary spin-3 gravity presented in \cite{31} when we take into account only transformation under diffeomorphism, without considering generalized Lorentz gauge transformation (i.e. $λ_ξ =0$), and by taking $\frac{1}μ\rightarrow 0$. Then we obtain a general formula…
Light propagation and quasinormal modes of a topologically charged Schwarzschild-Klinkhamer wormhole
Universidade Federal do Espírito Santo（圣埃斯皮里图联邦大学）；Instituto Federal de Educação Ciência e Tecnologia do Maranhão（马拉尼昂联邦教育、科学和技术学院）；University of Valladolid UVA（巴利亚多利德大学）；Universidade Estadual do Maranhão（马拉尼昂州立大学）；Universidade Federal do Pará（帕拉联邦大学）；Universidade Federal da Paraíba（帕拉伊巴联邦大学）；Universidade Federal de Campina Grande（坎皮纳格兰德联邦大学）
For cosmological topologically massive gravity at the chiral point we calculate momentum space 2- and 3-point correlators of operators in the postulated dual CFT on the cylinder. These operators are sourced by the bulk and boundary gravitons. Our correlators are fully consistent with the proposal that cosmological topologically massive gravity at the chiral point is dual to a logarithmic CFT. In the process we give a complete classification of normalizable and non-normalizeable left, right and logarithmic solutions to the linearized equations of motion in global AdS_3.
We demonstrate that the warped AdS3 black hole solutions of Topologically Massive Gravity are classically stable against massive scalar field perturbations by analysing the quasinormal and bound state modes of the scalar field. In particular, it is found that although classical superradiance is present it does not give rise to superradiant instabilities. The stability is shown to persist even when the black hole is enclosed by a stationary mirror with Dirichlet boundary conditions. This is a surprising result in view of the similarity between the causal structure of the warped AdS3 black hole …
We generalize the one-to one correspondence between quasi normal modes in 3- dimensional anti deSitter black holes and the poles of the retarded correlators in the boundary conformal field theory to include logarithmic operators in the latter. This analysis is carried out explicitly for the logarithmic mode in chiral topologically massive gravity.
We study topologically massive (2+1)-dimensional gravity with a negative cosmological constant. The masses of the linearized curvature excitations about AdS_3 backgrounds are not only shifted from their flat background values but, more surprisingly, split according to chirality. For all finite values of the topological mass, we find a single bulk degree of freedom with positive energy, and exhibit a complete set of normalizable, finite-energy wave packet solutions. This model can also be written as a sum of two higher-derivative SL(2,R) Chern--Simons theories, weighted by the central charges o…
It is shown that the warped black holes geometries discussed recently in 0807.3040 admit an algebra of asymptotic symmetries isomorphic to the semi-direct product of a Virasoro algebra and an algebra of currents. The realization of this asymptotic symmetry by canonical charges allows one to find the central charge of the Virasoro algebra. The right-moving central charge $c_R = \frac{(5\hatν^2+3)l}{G\hatν (\hatν^2+3)}$ is obtained when the Virasoro generators are normalized in order to have a positive zero mode spectrum for the warped black holes. The current algebra is also shown to be central…
We consider the area and entropy spectra of black holes in topologically massive gravity with gravitational Chern-Simons term. The examples we consider are the BTZ black hole and the warped AdS black hole. For the non-rotating BTZ black hole, the area and entropy spectra are equally spaced and independent of the coupling constant $\v$ of the Chern-Simons term. For the rotating BTZ black hole case, the spectra of the inner and outer horizon areas are not equally spaced in general and dependent of the coupling constant $\v$. However the entropy spectrum is equally spaced and independent of the c…
Following the monodromy technique performed by Motl and Neitzke, we consider the analytic determination of the highly damped (asymptotic) quasi-normal modes of small Schwarzschild-de Sitter (SdS) black holes. We comment the result as compared to the recent numerical data of Konoplya and Zhidenko.
A novel method, based on superpotentials is proposed for obtaining the quasi-normal modes of anti-de Sitter black holes. This is inspired by the case of the three-dimensional BTZ black hole, where the quasi-normal modes can be obtained exactly and are proportional to the surface gravity. Using this approach, the quasi-normal modes of the five dimensional Schwarzschild anti-deSitter black hole are computed numerically. The modes again seem to be proportional to the surface gravity for very small and very large black holes. They reflect the well-known instability of small black holes in anti-deS…
We derive the partition function of an $\mathcal N=2$ chiral multiplet on topologically twisted $H^2\times S^1$. The chiral multiplet is coupled to a background vector multiplet encoding a real mass deformation. We consider an $ H^2\times S^1$ metric containing two parameters: one is the $S^1$ radius, while the other gives a fugacity $q$ for the angular momentum on $H^2$. The computation is carried out by means of supersymmetric localization, which provides a finite answer written in terms of $q$-Pochammer symbols and multiple Zeta functions. Especially, the partition function of normalizable …
We study the spectrum of tensor perturbations on extremal BTZ black holes in topologically massive gravity for arbitrary values of the coefficient of the Chern-Simons term, $μ$. Imposing proper boundary conditions at the boundary of the space and at the horizon, we find that the spectrum contains quasi-normal modes.
We calculate the quasinormal modes and associated frequencies of the Banados, Zanelli and Teitelboim (BTZ) non-rotating black hole. This black hole lives in 2+1-dimensions in an asymptotically anti-de Sitter spacetime. We obtain exact results for the wavefunction and quasi normal frequencies of scalar, electromagnetic and Weyl (neutrino) perturbations.
We obtain exact expressions for the quasi-normal modes of various spin for the BTZ black hole. These modes determine the relaxation time of black hole perturbations. Exact agreement is found between the quasi-normal frequencies and the location of the poles of the retarded correlation function of the corresponding perturbations in the dual conformal field theory. This then provides a new quantitative test of the AdS/CFT correspondence.
We discuss three mathematical structures which arise in topologically massive abelian gauge theory. First, the euclidean topologically massive abelian gauge theory defines a contact structure on a manifold. We briefly discuss three solutions and the related contact structures on the flat 3-torus, the AdS space, the 3-sphere which respectively correspond to Bianchi type I, VIII, IX spaces. We also present solutions on Bianchi type II, VI and VII spaces. Secondly, we discuss a family of complex (anti-)self-dual solutions of the euclidean theory in cartesian coordinates on R3 which are given by (…
We obtain the quasi-normal mode frequencies of scalar perturbation on new type black holes in three dimensional new massive gravity. In some special cases, the exact quasi-normal mode frequencies are obtained by solving scalar field equations exactly. On some parameter regions, the highly damped quasi-normal mode frequencies are obtained in an analytic form by the so-called Stokes line method. This study on quasi-normal modes shed some light on the mysterious nature of these black holes. We also comment about AdS/CFT correspondence and the entropy/area spectrum for new type black holes.
We study quasi-normal modes for a higher dimensional black hole with Lifshitz scaling, as these quasi-normal modes can be used to test Lifshitz models with large extra dimensions. Furthermore, as the effective Planck scale is brought down in many models with large extra dimensions, we study these quasi-normal modes for a UV completion action. Thus, we analyze quasi-normal modes for higher dimensional dilaton-Lifshitz black hole solutions coupled to a non-linear Born-Infeld action. We will analyze the charged perturbations for such a black hole solution. We will first analyze the general condit…
We calculate analytically quasi-normal modes of AdS Schwarzschild black holes including first-order corrections. We consider massive scalar, gravitational and electromagnetic perturbations. Our results are in good agreement with numerical calculations. In the case of electromagnetic perturbations, ours is the first calculation to provide an analytic expression for quasi-normal frequencies, because the effective potential vanishes at zeroth order. We show that the first-order correction is logarithmic.
In this paper, we construct the quasi-normal modes of three-dimensional extremal black holes in an algebraic way. We show that the infinite towers of the quasi-normal modes of scalar, vector and tensor could be constructed as the descendents of the highest weight modes. Our investigation shows that the hidden conformal symmetry suggested in arXiv:1007.4269 is an intrinsic property of the extremal black hole. Moreover, we notice that we need to fix the freedom in defining the local vector fields and find the right hidden conformal symmetry to obtain the physical quasi-normal modes.
We calculate analytically low frequency quasi-normal modes of gravitational perturbations of AdS Schwarzschild black holes in $d$ dimensions. We arrive at analytic expressions which are in agreement with their counterparts from linearized hydrodynamics in $S^{d-2}\times \mathbb{R}$, in accordance with the AdS/CFT correspondence. Our results are also in good agreement with results of numerical calculations.
