Global embeddings of btz and schwarzschildads type black holes in a flat space. On lifshitz rotating black holes and black branes in light of adscft brigitte sprenger institute for theoretical physics utrecht university. In fact, based on the properties of the btz black hole as a quotient space, banad os, teitelboim and zanelli where able to prove in 5 that the nonrotating black hole j 0. It has become vital to understand btz black hole thermodynamics from. Banadosteitelboimzanelli btz black holes are constructed by orbifolding ads3 geometry by boost transformations of its o2,2 isometry group. The highly damped quasinormal modes of extremal rn and rn ds black holes ramin g daghigh and michael greenrecent citations photon trajectories on a first order scaledependent static btz black hole mohsen fathi et alanalytical solutions in a. In this paper, we investigate properties of rainbow btz black holes in the scenario with the freefall ff orthonormal frame. In the boundary liouville field theory i investigate the reducible verma modules in the elliptic sector, which correspond to certain irreducible representations of the quantum algebra. Black hole sun is a song by soundgarden from the album superunknown. This means, in particular, that any simplyconnected patch of the btz black hole solution can be endowed with a lorentz connection that is locally pure gauge.
We construct the flat connection and its monodromy matrix which generates the nonlocal charges. The btz black hole di ers from the schwarzschild and kerr solutions in some important respects. The result can be naturally extended to a wider class of black hole geometries and point particles in threedimensional spacetime. Our results hold for any time t in particular, when the latter is large, they reproduce the bulk shockwave propagation along the btz horizon description. The btz black hole allows exceptional analytic control because it is locally isometric to threedimensional antide sitter space ads 3, a maximally symmetric spacetime. From examining the general behaviour of the eigen values of the monodromy matrix we determine the set of integral equations which constrain them. By carefully studying the e ect of this particle on the geometry of the black hole, we will be able to read o the sensitivity of ato the addition of w. The btz black hole, named after maximo banados, claudio teitelboim, and jorge zanelli, is a. Pdf dirac particles tunneling from btz black hole ran. Btz m, where mis a simple manifold, and their entropies and greybody factors can be obtained from the btz black hole directly 419 or by duality 2022. Hawking temperature of the btz black hole stack exchange. Scaledependent rotating btz black hole springerlink.
Finally, we combined the knowledge of these to try to calculate the metric of the rotating lifshitz black hole. We rst look at the btz black hole in which case the black hole horizon and the conical singularity are related to each other. This result shows that the btz black hole can be parametrized by at most two parameters, its. On the btz black hole and the spinning cosmic string. This understanding hinges on the modular properties of partition functions in the cft, which allow a transformation from low to high temperatures which is needed in order to specify the entropy. The lefthand side is the generating functional of the bulk or boundary correlators of the btz black hole discussed above, with any bulk sources being analytic in z. This work presents a generalization of the rotating black hole in two plus one dimensions, in the light of scaledependent gravitational. Thermodynamic curvature of the btz black hole core.
The btz black hole and causal cft 2 correlators tutor. Using the modular transformations of the dual 2d cft, we rst obtain an expression of the holographic entanglement entropy for the euclidean btz black hole, ads 3 vacua and conical. The case of zero cosmological constant corresponding to the interior region of a black hole is analyzed in detail. Pdf quantum liouville theory and btz black hole entropy. The latter aspect has been studied by maldacena and strominger 11, 12, who studied btz black holes, which have an asymptotic local antide sitter geometry1. The righthand side is written in terms of the thermofield state formed by two copies of the outsidehorizon r 1 portion of the schwarzschild view of the btz black hole. These quasinormal frequencies are already published and widely explored in several. Holography of the btz black hole, inside and out inspire. Logarithmic correction to the bekensteinhawking entropy of the btz black hole 2879 where. Pdf thermodynamics of btz black hole and entanglement entropy.
Global embeddings of btz and schwarzschildads type black holes. Quantum fields on btz black holes white rose university. We use rigorous mathematical results to clarify the general structure and properties of this black hole spacetime and its microscopic description. Far from the extremal point, the effective dimension becomes less than one, which leads to one possible speculation on the underlying structure for the corresponding statistical model. Following on from this, we invoke a precise mathematical theorem of hyperbolic geometry, due to sullivan 19, 20, to establish a no hair theorem for the btz black hole 21. Dynamical black holes in topologically massive gravity. Hadamard states and tunnelling e ects for a btz black hole. Aspects of the relation between the black hole entropy and the. Complete geodesics of both types exist in the rotating black hole background, but not in the spinless case. Black holes and bps solutions in sixdimensional supergravity. Btz black hole perturbed by a massless conformal scalar eld, and their dependence on p m where m is the mass of the black hole. Btz quasinormal frequencies as poles of greens function.
Lectures on quantum gravity and black holes thomas hartman cornell university please email corrections and suggestions to. The basic starting point is that thermal states in cft are dual to black holes in quantum gravity. In three spacetime dimensions the graviton does not have any polarization modes, and hence the concept of gravity is we know it form. Maximo 1999, three dimensional quantum geometry and black holes pdf, arxiv. The effective spatial dimension of the statistical system corresponding to the nearextremal btz black holes is one. Complete geodesics of both types exist in the rotating blackhole background. Luttinger liquids 3 btz black hole 4 boundary theory 5 summary collaborators. The btz black hole in schwarzschild coordinates is described by the metric. On lifshitz rotating black holes and black branes in light. The hawking temperature of a black hole is such that the wien wave length corresponds to the radius of the black hole itself. We introduce a set of scalar fields as test fields to study the dynamical behaviors of the btz banadosteitelboimzanelli black hole. We consider static circularly symmetric solution of threedimensional einsteins equations with negative cosmological constant the btz black hole. We derive on physical grounds three basic mass scales that are relevant to characterize these limitations. If an internal link led you here, you may wish to change the link to point directly to the intended article.
In fact, this is a special case of the dictionary 14. Pv criticality of a modified btz black hole was recently studied by kubeka and sadeghi in 1. Probing the btz black hole with test fields internet archive. Thebtz black hole is constructed from the ads space by periodic identi. They introduced some anstaz that gives a modified btz black hole and then showed that this modified btz black hole is satisfied by the equation of state of liquidgas phase transition.
On the thermal description of the btz black holes core. 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 with the patterson. Logarithmic correction to the bekensteinhawking entropy. A natural guess is that black hole entropy should be associated with horizon degrees of freedom. As we will see in chapter 2black holes and the butter y e ectchapter. The microscopic derivation of the bekensteinhawking entropy of a string theory black hole is perhaps the most notable 1. At the classical level we are led to a finitedimensional system by imposing on a general threedimensional line element the two manifest local isometries of the btz black hole.
Btz black hole backgrounds francesco belgiorno, sergio l cacciatori, francesco dalla piazza et al. Carlip 1995 section 3 black holes and gravitational collapse. Schwarzschild black hole obtained in the four dimensional canonical gravity formalism and also in a lorentzian computation of btz black hole entropy. Holography of the btz black hole, inside and out pdf. Hawking added to the puzzle when he discovered that a black hole will. We provide a holographic description in terms of a free falling particle in the eternal btz black hole that exactly matches our cft calculations. Zaslavskii, entropy of charged thin shells and the. Btz black hole spacetime and construct the entanglement thermodynamics for. Classical integrability in the btz black hole inspirehep. This disambiguation page lists articles associated with the title btz. Exploring black hole dynamics the harvard community has. Permanently erasing a file can an ios app that has access to photos get all my photos.
These results are for angular momentum quantum number m 1, and 0. Boundary contributions to the btz black hole hamiltonian. Abstractwe investigate the limitations on the thermal description of threedimensional btz black holes. Scrambling time from local perturbations of the eternal. We focus on the retarded green function of a massive scalar.
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