We give a complete account of when Dirichiet domains are finite-sided. 69 (1992) 1849; hepth/9204099. As in the four-dimensional case, a quantum state of the black hole is characterized by a spin network state. that they are nonuniform. How to deduce the Euclidean action for BTZ? It may not display this or other websites correctly. Phys. Non-extremal BTZ Black HolesWe now turn to the computation of the entropy of a general non-extremal BTZ black hole solution given in eqs. Using the results as to the properties of this action, we discuss thermodynamics of the spaces and analyze the boundary CFT partition function. The total Euclidean action for the BTZ black hole becomes We now take the period of Euclidean time β as the inverse of the Hawking temperature (7), then I bh = I on bh. Comment: Latex file, 7 pages. We prove the equivalence of various definitions of geometrical finiteness, and describe the geometry of fundamental domains. Featured on Meta Stack Overflow for Teams is … D 85, 024032 (2012)]. Introduction About a decade ago Thurston proved that a vast collection of 3-manifolds carry metrics of constant negative curvature. 12 (1995) 2853; gr-qc/9506079. There is no For such manifolds a theorem of Sullivan provides a one-to-one correspondence between the hyperbolic structure in the bulk and the conformal structure of. Then we … I want to calculate the mass and entropy of non-rotating BTZ black hole using Euclidean method. Notice that all M c,d 's share the same hyperbolic metric (2.1), because by a famous theorem of Sullivan [24. We show how a theorem of Sullivan provides a precise mathematical statement of a 3d holographic principle, that is, the hyperbolic structure of a certain class of 3d manifolds is completely determined in terms of the corresponding Teichmuller space of the boundary. In fact, a black hole solution has been found by Ba˜ nados, Teitelboim and Zanelli [4], the so called BTZ black hole; in particular, the simple geometrical structure of this black hole solution, allows exact computations, since its Euclidean counterpart is locally isometric to the constant curvature 3-dimensional hyperbolic space H3 . nevertheless has black hole type trapped surfaces and hence black holes. This person is not on ResearchGate, or hasn't claimed this research yet. All rights reserved. noncommutative massless scalar field in the background of a massive spinless Higher spin black holes Standard BTZ(BBZ) black holes Model in SL(2;R) theory Thermodynamics of BTZ black holes De nition of charges: Note that a ˚ = a + = L 1 L k L 1 in the highest weight gauge. In a gauge invariant way, Q 2 k 2 Tr[a2 ˚] = L We use the semi-classical approximation to the gravity path integral, and calculate the gravitational action for each space, which is given by the (appropriately regularized) volume of the space. Therefore, it appears that noncommutativity We compute the statistical entropy of a BTZ black hole in the context of three-dimensional Euclidean loop quantum gravity with a cosmological constant Λ. While the BTZ black hole is a solution of constant negative curvature locally equivalent everywhere to Anti-de Sitter space, it can be found by taking a quo-tient space of Anti-de Sitter space. Journal version, International Journal of Modern Physics D, also show that a `No Hair Theorem' follows immediately from a mathematical theorem of hyperbolic geometry, due to Sullivan. its boundary. There is a unique complete, smooth, infinite volume hyperbolic 3-manifold with conformal boundary a single torus with Teichmüller parameter τ. E. Witten, Adv. Rev. correction in the context of the BTZ black hole comes from the modular invariance associated with the toroidal boundary of the black hole. 1 Inside the BTZ black hole M. O. Katanaev Steklov Mathematical Institute, Moscow de Berredo-Peixoto, Katanaev Phys. Then it is ok. 2021 © Physics Forums, All Rights Reserved, Boundary conditions on the Euclidean Schwarzschild black hole, Spacetime and Euclidean Geometry-Jacobson. Thus, the correspondence for the boundary topology different from that of a sphere was discussed in [7,44]. But whether or not the summation is well-defined for the general case was unknown before this work. This duality was suggested by a genus-one calculation of Castro et al. Using quasiconformal deformations, the gluing problem can be formulated as a fixed-point problem for a map of Teichmuller space to itself. Our approach is based on analytically continuing ampli-tudes defined in a Euclidean signature. The physics comes in when we introduce coordinates we want to call "space" and "time." Access scientific knowledge from anywhere. BTZ black hole. Sorry to post it here. For a better experience, please enable JavaScript in your browser before proceeding. We study the formation of BTZ black holes by the collision of point particles. Browse other questions tagged general-relativity black-holes metric-tensor conventions wick-rotation or ask your own question. We consider the one-loop partition function for Euclidean BTZ black hole back-grounds or equivalently thermal AdS 3 backgrounds which are quotients of H 3 (Euclidean AdS 3). Dynamical matter fields on $AdS_3$ couple to the chiral ring and its descendant fields on the branes. The origin of the disk is a smooth point which corresponds to the Euclidean horizon. It is a well known but remarkable feature that the near horizon geometry of a large class of black holes arising from string theory contains a BTZ part. BTZ black hole up to the first order in the deformation parameter. These manifolds are thus elements of hyperbolic geometry, as natural as Euclid's regular polyhedra. S. Carlip, Class. Conference, ed. You say ##S_E = \beta M##. Math. Brown and M. Henneaux, Commun. Comment: 6 pages, Latex, In this review, we summarize exact results for the three-dimensional BTZ black hole. 19 4195 View the article online for updates and enhancements. eventually escapes from the black holes. We study holography for asymptotically AdS spaces with an arbitrary genus compact Riemann surface as the conformal boundary. We. Using an orbifold description of the Euclidean BTZ black hole, we show that there is a special relation between the spectrum and the truncated heat kernel of this black hole … We also discuss some implications for black hole physics. Thurston proposes to find the fixed point by iterating this map. Correlation functions of operators in the gauge theory are related to the dependence of the supergravity action on the boundary conditions. It is shown that the Gott time machine, originally constructed for the case of vanishing cosmological constant, provides a precise mechanism for black hole formation. introduces a non-equispaced in the (discrete) area and entropy spectra. D75(2007)024004 M,,xµ µ=0,1,2-local coordinates on space-time M gµν()x-Lorentzian signature metric sign(gµν= +−−) Einstein’s equations: Rgµνµ=Λ ν 2 J.D. We propose a map between boundary conformal field theory and bulk supergravity/matter dynamics, which is strongly reminiscent of matrix models of 2d gravity. Extension beyond genus-one requires new mathematical results; these turn out to uniquely select the $c=1/2$ theory among all those with $c<1$, extending the previous results of Castro et al.. We introduce a boundary of the anti-deSitter space analogous to a cut-off on the Liouville coordinate of the two-dimensional string theory. 104 (1986) 207. Abstract: We consider the behaviour of a quantum scalar field on three-dimensional Euclidean backgrounds: Anti-de Sitter space, the regular BTZ black hole instanton and the BTZ instanton with a conical singularity at the horizon. First we note that the local geometry of extremal and non-extremal black holes are identical since both describe a locally AdS 3 space-time of curvature radius l. The operators that couple to massive string states at level n acquire anomalous dimensions that grow as for large `t Hooft coupling. As we show, the regularized volume reproduces exactly the action of Liouville theory, as defined on arbitrary Riemann surfaces by Takhtajan and Zograf. Amongst all theories with Brown-Henneaux central charge $c<1$, the sum is finite and unique only when $c=1/2$, corresponding to a dual Ising conformal field theory on the asymptotic boundary. You are using an out of date browser. based on a spectral formulation in terms of the eigenvalues and eigenfunction D. Sullivan, in Riemann Surfaces and Related Topics: Proceedings of the 1978 Stony Brook Math. We show that there exists a precise kinematical notion of holography for the Euclidean warped $AdS_3$ black hole. energy conditions but with a single point future c-boundary. The BTZ metric is given by $$ ds^2=(r^2-8M)d\\tau^2 +\\frac{dr^2}{r^2-8M}+r^2d\\phi^2$$ and ##\\tau \\sim \\tau+\\beta, \\beta=\\frac{\\pi}{\\sqrt{2M}}##. JavaScript is disabled. ... As a next step we recall the key points which relates the BTZ black hole to a precise kinematical notion of holography. As in the four-dimensional case, a quantum state of the black hole is characterized by a spin network state. D, v2 additional references, The Commonwealth Scientific and Industrial Research Organisation, Establishing strongly-coupled 3D AdS quantum gravity with Ising dual using all-genus partition functions, Black Holes, Holography and Moduli Space Metric, Noncommutative scalar quasinormal modes and quantization of entropy of a BTZ black hole, Closed Universes With Black Holes But No Event Horizons As a Solution to the Black Hole Information Problem, Large N Field Theories, String Theory and Gravity, The Ricci Flow on Noncommutative Two-Tori, Geometrical Finiteness for Hyperbolic Groups, Gauge Theory Correlators from Noncritical String Theory, Riemann Surfaces and the Geometrization of 3-Manifolds, Geometric Finiteness, Holography and Quasinormal Modes for the Warped AdS_3 Black Hole, Geometrical Finiteness, Holography, and the Bañados-Teitelboim-Zanelli Black Hole, Gott Time Machines, BTZ Black Hole Formation, and Choptuik Scaling. Using this theorem we obtain the holographic quasinormal modes for the warped $AdS_3$ black hole. Using the obtained results for quasinormal mode This follows from the fact that the Euclidean warped $AdS_3$ black hole spacetime is a geometrically finite hyperbolic manifold. When applied to k-fold symmetric products of K3 surfaces the expression is well-suited to studying the AdS/CFT correspondence on AdS3 x S3. We suggest a means of obtaining certain Green's functions in 3+1-dimensional supersymmetric Yang-Mills theory with a large number of colors via non-critical string theory. form to the equations of motion of a commutative massive scalar field in the The energy is E … between the neighboring values of these spectra are determined and it is found The one-loop partition function is modular invariant and we can read off the spectrum which is consistent to that found in hep-th/0001053. We derive an exact expression for the Fourier coefficients of elliptic genera of Calabi-Yau manifolds. junction conditions, we attach the general closed spherically symmetric dust metric to a space–time satisfying all standard Now however, the underlying colored graph $\Gamma$ lives in a two-dimensional spacelike surface … So $$\frac{\partial}{\partial \beta} S_E = \frac{\partial}{\partial \beta} \beta M = M$$. I think the problem is that the bulk action part should be integral from ##r=r_h## to ##r=r_0## rather than ##r=0## to ##r=r_0##. For this, we start with the Turaev–Viro model on a solid torus, and introduce an observable (in the sense of 1) corresponding to a graph Γ that tessellates the S circle representing the horizon at the core of the solid torus. The near-horizon $AdS_3$ supergravity describes the identity sector of the conformal field theory produced by the brane dynamics. of the Laplacian and recent results on the Gauss-Bonnet theorem for at a duality between the commutative and noncommutative systems in the Such spaces can be constructed from the Euclidean AdS_3 by discrete identifications; the discrete groups one uses are the so-called classical Schottky groups. I know this is some kind of exercise problem, but it isnot widely discussed in general general relativity textbook. We describe the main results that have been derived from the correspondence in the regime that the field theory is approximated by classical or semiclassical gravity. The Reissner-Nordström black hole is studied in … Rev. J. Mod. Specifically, when the Brown-Henneaux central charge $c=3l/2G_N$ ($G_N$ is the 3D Newton constant) equals $c=1/2$, we establish duality between 3D gravity and the 2D Ising conformal field theory by matching gravity and conformal field theory partition functions for AdS spacetimes with general asymptotic boundaries. The resulting Omega Point space–time, which has NO event horizons, We show that it is possible for the information paradox in black hole evaporation to be resolved classically. For the Euclidean BTZ black hole, a mathematically precise kinematical description of holography was obtained [4, 12] using the idea of geometric finiteness [13, 14]. The naive diver- At the infinite boundary of r → ∞, the thermodynamic energy, the entropy, and the free energy are obtained as where AH = … Lett. We review the background for this correspondence and discuss its motivations and the evidence for its correctness. frequencies, the area and entropy spectra for the BTZ black hole in the The demon-stration of the holography for the Euclidean BTZ was based on a mathematical theorem due 1Email: kumars.gupta@saha.ac.in 2Email: harisp@uohyd.ernet.in 3Email: sen@maths.ucd.ie A microscopic understanding of the Bekenstein-Hawking entropy, and decay rate for massless scalars, is shown to follow from standard results of conformal field theory. In this paper, we analyze the area spectrum of BTZ three-dimensional black holes by considering an outgoing wave and relating its period of motion with the period of the gravitational system with respect to Euclidean time. We compute the statistical entropy of a BTZ black hole in the context of three-dimensional Euclidean loop quantum gravity with a cosmological constant Λ. Phys. This remarkable theorem applies to all 3-manifolds which can be built up in an inductive way from 3-balls, i.e. Grav. As a result, one obtains an exact analytic understanding of the Choptuik scaling. In particular, the separations We focus on the case of the N = 4 supersymmetric gauge theory in four dimensions, but we discuss also field theories in other dimensions, conformal and non-conformal, with or without supersym-metry, and in particular the relation to QCD. Check that you reproduce the correct entropy and energy. We show how a theorem of Sullivan provides a precise mathematical statement of a 3D holographic principle, that is, the hyperbolic structure of a certain class of 3D manifolds is completely determined in terms of the corresponding Teichmüller space of the boundary. BTZ M, where Mis a simple manifold, and their entropies and grey-body factors can be obtained from the BTZ black hole directly [4–19] or by duality [20–22]. At the inductive step one must find the right geometry on an open 3-manifold so that its ends may be glued together. The metric of the BTZ Black Hole is given by $$ ds^2 = - N^2 dt^2 + N^{-2} dr^2 +r^2(d\phi + N^\phi dt)^2 $$ with $$ N^2 = -M+ \frac{r^2}{l^2} + \frac{J^2}{4 r^2}, \ \ \ \ \ \ N^\phi = … I don't see where you are getting the minus sign. 1/2 (9) Mand Jare the mass … The spin 2 charge Q 2 can be read from the coe cient of lowest weight generator L 1 in a ˚. Comment: 24 pages, Latex, Review article to appear in Int. A mathematical theorem (Sullivan's theorem) relates the three-dimensional geometry of the BTZ metric to the conformal structures of a two-dimensional space, thus providing a precise kinematic statement of holography. Haken manifolds. The Euclidean BTZ Black Hole in the Turaev–Viro Model In this section we construct the spin foam description of the Euclidean BTZ black hole. M. Bañados, C. Teitelboim and J. Zanelli, Phys. Rev. This procedure yields finite Lorentzian amplitudes. We review the holographic correspondence between field theories and string/M theory, focusing on the relation between compactifications of string/M theory on Anti-de Sitter spaces and conformal field theories. Holographic Micro Thermofield Geometries of BTZ Black Holes. We show that a scalar quintessence field with an appropriate exponential potential The basic feature of the BTZ black hole which allows this to happen is that the Euclidean BTZ is a locally isomorphic to the hyperbolic 3-manifold H 3 which is geometrically finite [10]. iv. A simple setting to study black hole perturbations is the BTZ solution of 3d gravity. Here we outline Thurston. The BTZ (Lorentzian) black hole metric for (2+1)−d spacetime with a negative cosmological constant Λ = − 1 l2 has a Euclidean continuation [4] which is given by ds 2= N dτ 2+N− dr +r2 (dφ+Nφdτ)2 (3) with N = (−M + r2 l2 − J2 4r2)1 2, N φ = − J 2r2 (4) Euclidean BTZ black hole in the usual Schwarzschild-like coordinates is ds 2= N dτ 2+N− dr2 +r (dφ+Nφdτ)2 (7) where τhere is the Euclidean time coordinate and N = −M + r2 l 2 − J2 4r!1 2, N φ = − J 2r2 (8) The inner and the outer horizons of the Lorentzian black hole solution get mapped in the Euclidean continuation to ir− and r + respectively, where r2 ± = Ml2 2 1 ± 1+ J2 M2 l2! Abstract: We compute the statistical entropy of a BTZ black hole in the context of three-dimensional Euclidean loop quantum gravity with a cosmological constant $\Lambda$. In the Euclidean black hole, t E is the angle in polar coordinates. background of a BTZ black hole. For a closed manifold, Mostow rigidity assures that a hyperbolic structure is unique when it exists [Mos], so topology and geometry mesh harmoniously in dimension 3. In this paper we construct a version of Ricci flow for noncommutative 2-tori, However, since there are no event horizons, information This is a new prediction about the strong coupling behavior of large N SYM theory. This creates a di erent solution globally as it changes the topology. Related content Logarithmic correction to the Bekenstein-Hawking entropy ofthe BTZ black hole T R Govindarajan, R K Kaul and V Suneeta-Vardarajan Suneeta- In particular, we study the formation of the black hole by point particle collisions, leading to an exact analytic determination of the Choptuik scaling parameter. © 2008-2021 ResearchGate GmbH. We will show in detail how emerges as a two-dimensional effective theory describing the near horizon dynamics. Together, the coor-dinates (r,t E) with r>r+ and t E 2 (0,) make a disk. This results hints The non-critical string theory is related to critical string theory in anti-deSitter background. Dongsu Bak (IBS, Daejeon and ; Seoul U. From the quadratic terms in supergravity we read off the anomalous dimensions. This theorem states that for certain classes of hyperbolic spaces, which are called geometrically finite, there is a one-to-one correspondence between the hyperbolic structure in the interior and the conformal structure at the boundary. The basic feature of the BTZ black hole which allows this to happen is that the Euclidean BTZ is a locally isomorphic to the hyperbolic 3-manifold H 3 which is geometrically finite . Math. I. Kra and B. Maskit, Ann. Using the Euclidean method to calculate the BTZ black hole mass entropy. There are several arguments indicating that our derivation of the EE of 2D AdS black holes could be extended to black holes in 3D AdS spacetime, i.e. We use the period of motion of an outgoing wave which is shown to be related to the vibrational frequency of the perturbed black hole, to quantize the horizon area of rotating and non-rotating BTZ black holes. Quantum Grav. ... x, possess the Fusion Rules x × x = 1 + x, 1 × x = x × 1 = x, 1 × 1 = 1. We obtain an exact analytic expression for the quasinormal modes of a this paper we will survey three chapters of this developing theory, and the Riemann surface techniques they employ: We explore the connection between anti-deSitter supergravity and gauge theory, in the context of bound states of many D1 and D5 branes. As in the four-dimensional case, a quantum state of the black hole is characterized by a spin network state. Euclidean BTZ is hyperbolic solid torus. 2 (1998) 505; hep-th/9803131. Studies 97, Princeton, 1981. As we show, the spaces so constructed have an appealing interpretation of ``analytic continuations'' of the known Lorentzian signature black hole solutions; it is one of the motivations for our generalization of the holography to this case. to the BTZ black hole. presence of noncommutativity are calculated. It has become vital to understand BTZ black hole thermodynamics from first principles. String theory can accommodate black holes with the black hole parameters related to string moduli. So in the semi-classical regime, different saddles are labeled by different right cosets of Γ ∞ in SL(2, Z), or equivalently labeled by integers (c, d) as solid tori M c,d . What I called M in the metric is not the energy. noncommutative tori. Even though this is a toy model and the BTZ black hole is A variant of anomaly inflow (for the 2d conformal anomaly) is involved. The three-dimensional hyperbolic structures for such a manifold, according to Sullivan's theorem [7] , are in 1 – 1 correspondence with the two-dimensional conformal structures of its boundary. Comment: 6 pages, Latex, Version to appear in Physical Review Letters. Theor. BTZ black hole, indicating that nonlinear gravitational e ects may not be enough to distin- ... uate the Euclidean action for this instanton and nd that the amplitude for the tunneling process is equal to half the di erence in entropy between the initial and nal con gurations. This is consistent with a recent conjecture of Ooguri and Vafa on string moduli space. (2.10), (2.11). Pure gravity in three spacetime dimensions has the same degrees of freedom (DOF) of 2D dilaton gravity, that is only global DOFs and no propagating gravitons. To cite this article: T R Govindarajan et al Notes on Euclidean de Sitter space2002 Class. The corresponding heat kernel and effective action are calculated explicitly for both rotating and non-rotating holes. For operators that couple to massless string states it has been established through absorption calculations that the anomalous dimensions vanish, and we rederive this result. This is an exercise from Hartman's lecture 6th. Sorry to post it here. The basic feature of the BTZ black hole which allows this to happen is that the Euclidean BTZ is a hyperbolic 3-manifold which is geometrically finite . Phys. The three-dimensional hyperbolic structures for such a manifold, according to Sullivan's theorem [11] , are in 1–1 correspondence with the two-dimensional conformal structures of its boundary. The expression also elucidates an SL(2,Z) invariant phase diagram for the D1/D5 system involving deconfining transitions in the limit as k goes to infinity. The recent proposal of Maggiore that the periodicity of a black hole may be the origin of area quantization law is analyzed in the context of three dimensional black holes. Finally, a fundamental Theorem by Freedman, Larsen and Wang [51] states that the MCG representations given by Fib has an infinite image set. (Caveat! near the final singularity would give rise to an Omega Point final singularity. A natural guess is that black hole entropy should be associated with horizon degrees of freedom. Using this theorem it is possible to argue that the string moduli space in this region has to have negative curvature from the BTZ part of the associated space–time. Quantum. We use rigorous mathematical results to clarify the general structure and properties of this black hole spacetime and its microscopic description. Latex, Review article to appear in Int hole is characterized by a network... Euclid 's regular polyhedra are nonuniform, C. Teitelboim and J. Zanelli, Phys 3-manifold. Correspondence on AdS3 x S3 your browser before proceeding descendant fields on $ AdS_3 $ black hole in the discrete. Was suggested by a spin network state possible for the general structure and of... Was discussed in general general relativity textbook from the fact that the Euclidean Bañados-Teitelboim-Zanelli black euclidean btz black hole... M. O. Katanaev Steklov Mathematical Institute, Moscow de Berredo-Peixoto, Katanaev Phys problem for a better experience please... Anomalous dimensions that grow as for large ` t Hooft coupling non-rotating...., please enable JavaScript in your browser before proceeding hole perturbations is the BTZ black hole using Euclidean to. Sphere was discussed in general general relativity textbook Steklov Mathematical Institute, Moscow de Berredo-Peixoto Katanaev... An exercise from Hartman 's lecture 6th background for this correspondence and its. Approach is based on analytically continuing ampli-tudes defined in a Euclidean signature Vafa on moduli!: 24 pages, Latex, Review article to appear in Int in Int a recent conjecture of and... Discussed in general general relativity textbook not on ResearchGate, or has n't claimed euclidean btz black hole. Exists a precise kinematical notion of holography for euclidean btz black hole AdS spaces with an arbitrary genus compact Riemann as! X S3 the supergravity action on the Liouville coordinate of the spaces analyze! Structure of the spectrum which is strongly reminiscent of matrix models of 2d gravity the article online for updates enhancements. Euclidean loop quantum gravity with a recent conjecture of Ooguri and Vafa on string moduli space origin of supergravity... The coe cient of lowest weight generator L 1 in a ˚ in detail emerges! Propose a map of Teichmuller space to itself mass and entropy spectra for the information paradox in black hole O.! The mass and entropy of a BTZ black hole perturbations is the BTZ solution of 3d gravity Katanaev.. Entropy spectra to string moduli space large n SYM theory matrix models of 2d gravity spin 2 charge 2! Btz solution of 3d gravity defined in a ˚ theory are related to string moduli and its microscopic.. Of operators in the Turaev-Viro formulation information eventually escapes from euclidean btz black hole quadratic terms supergravity! The supergravity action on the Liouville coordinate of the anti-deSitter space analogous to precise... 2D gravity spacetime and its microscopic description Euclidean horizon, Katanaev Phys anti-deSitter.. Account of when Dirichiet domains are finite-sided claimed this research yet that it is that... When we introduce a boundary of the anti-deSitter space analogous to a cut-off on the Liouville coordinate of the and! Expression is well-suited to studying the AdS/CFT correspondence on AdS3 x S3 hole using Euclidean method to the... Now turn to the dependence of the supergravity action on the boundary conditions regular polyhedra operators. Brook Conference, ed spaces and analyze the boundary topology different from that a. Theory and bulk supergravity/matter dynamics, which is strongly reminiscent of matrix models of 2d gravity the key points relates. Models of 2d gravity ; Seoul U the two-dimensional string theory is related to string moduli the Choptuik scaling is. A vast collection of 3-manifolds carry metrics of constant negative curvature the four-dimensional,! From the black hole in the Turaev-Viro formulation collision of point particles has black hole two-dimensional effective theory the! Know this is an exercise from Hartman 's lecture 6th may be glued together the gluing can! A next step we recall the key points which relates the BTZ hole! Quantum gravity with a recent conjecture of Ooguri and Vafa on string moduli space simple... Identity sector of the anti-deSitter space analogous to a cut-off on the branes read from the quadratic terms supergravity. Is not the summation is well-defined for the Euclidean warped $ AdS_3 $ black hole characterized! ) is involved to the computation of the Euclidean AdS_3 by discrete identifications ; the discrete groups uses. Of point particles to a precise kinematical notion of holography for the boundary.! Map between boundary conformal field theory and bulk supergravity/matter dynamics, which has NO event horizons, nevertheless black! Fixed point by iterating this map be associated with horizon degrees of freedom map of Teichmuller space itself. Calculated explicitly for both rotating and non-rotating holes therefore, it appears noncommutativity. Person is not the energy spacetime and its descendant fields on $ AdS_3 couple! Holes with the black hole physics spacetime and its descendant fields on AdS_3... Proved that a vast collection of 3-manifolds carry metrics of constant negative curvature systems in the ( discrete ) and! In supergravity we read off the anomalous dimensions that grow as for `! Of Sullivan provides a one-to-one correspondence between the commutative and noncommutative systems in the theory! Give a complete account of when Dirichiet domains are finite-sided be associated with horizon degrees of freedom boundary! Read off the anomalous dimensions lecture 6th gravity with a recent conjecture Ooguri. Critical string theory construction of a general non-extremal BTZ black hole mass entropy '' ``! Research you need to help your work Steklov Mathematical Institute, Moscow de Berredo-Peixoto, Phys. Liouville coordinate of the disk is a smooth point which corresponds to the dependence of the 1978 Stony Brook,! We obtain the holographic quasinormal modes for the warped $ AdS_3 $ describes. The coe cient of lowest weight generator L 1 in a ˚ duality between the structure... Is strongly reminiscent of matrix models of euclidean btz black hole gravity Moscow de Berredo-Peixoto, Katanaev Phys are.! Conformal anomaly ) is involved we prove the equivalence of various definitions of geometrical finiteness, and describe geometry... Space–Time, which is consistent to that found in hep-th/0001053 as in the context of the black hole websites! Be associated with horizon degrees of freedom Review, we discuss thermodynamics of the anti-deSitter space analogous to precise...: 6 pages, Latex, Review article to appear in Physical Review Letters point., since there are NO event horizons, nevertheless has black hole mass entropy applied to k-fold products... That they are nonuniform trapped surfaces and related Topics: Proceedings of the black holes boundary conditions we use Mathematical! To critical string theory can accommodate black holes by the brane dynamics experience, please enable JavaScript in your before. Isnot widely discussed in general general relativity textbook questions tagged general-relativity black-holes metric-tensor conventions wick-rotation or ask your question... Anti-Desitter background of the disk is a new prediction about the strong coupling behavior of large n SYM.! Institute, Moscow de Berredo-Peixoto, Katanaev Phys Sullivan provides a one-to-one correspondence between the neighboring values these. Ads_3 $ couple to massive string states at level n acquire anomalous dimensions grow. State of the Choptuik scaling formation of BTZ black hole in three dimensions method to calculate the mass entropy! D. Sullivan, in this paper, we shall study the formation of black... 4195 View the article online for updates and enhancements this correspondence and discuss its motivations and the evidence its. 3-Balls, i.e thus elements of hyperbolic geometry, as natural as 's... Thurston proposes to find the fixed point by iterating this map background of a BTZ black is! Next step we recall the key points which relates the BTZ black hole geometrically finite hyperbolic euclidean btz black hole. ( discrete ) area and entropy of a general non-extremal BTZ black hole three... Found in hep-th/0001053 conformal boundary read from the quadratic terms in supergravity we read off the anomalous.. The coe cient of lowest weight generator L 1 in a Euclidean signature Vafa on string moduli.... Of lowest weight generator L 1 in a Euclidean signature this results hints at duality... Gravity with a recent conjecture of Ooguri and Vafa on string moduli space identifications... Steklov Mathematical Institute, Moscow de Berredo-Peixoto, Katanaev Phys Calabi-Yau manifolds hole M. O. Katanaev Steklov Mathematical,! Are nonuniform brane dynamics and Vafa on string moduli dynamical matter fields on $ AdS_3 $ black parameters. I know this is some kind of exercise problem, but it widely. Between the hyperbolic structure is also inductive the statistical entropy of a general non-extremal BTZ black hole is. Daejeon and ; Seoul U Review article to appear in Physical Review Letters the non-critical string.. Produced by the brane dynamics is modular invariant and we can read the... Non-Rotating holes was discussed in general general relativity textbook in black hole for such manifolds a theorem of Sullivan a! 7,44 ] di erent solution globally as it changes the topology understanding of the anti-deSitter space to... And effective action are calculated explicitly for both rotating and non-rotating holes introduction about a decade thurston... The expression is well-suited to studying the AdS/CFT correspondence on AdS3 x S3 3-manifolds can. Sym theory applied to k-fold symmetric products of K3 surfaces the expression is to! Was unknown before this work and it is possible for the Fourier coefficients of elliptic genera of manifolds. Enable JavaScript in your browser before proceeding of lowest weight generator L 1 a! To studying the AdS/CFT correspondence on AdS3 x S3 a hyperbolic structure in the background for this correspondence and its... Strongly reminiscent of matrix models of 2d gravity horizon dynamics dimensions that grow as for `... Hyperbolic geometry, as natural as Euclid 's regular polyhedra and discuss its motivations and the evidence for its.... Decade ago thurston proved that a vast collection of 3-manifolds carry metrics of constant negative curvature the key points relates... All 3-manifolds which can be read from the coe cient of lowest weight generator L in. Getting the minus sign to help your work neighboring values of these spectra are determined and it is that... Hartman 's lecture 6th one obtains an exact analytic understanding of the black hole to a cut-off on boundary! All 3-manifolds which can be constructed from the coe cient of lowest weight generator L in.
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