For a discussion of string theory black holes and their connection to the btz black hole see for example, 46. This disambiguation page lists articles associated with the title btz. Using the bulkboundary correspondence, we also evaluate the twopoint correlator of operators. Hawking department of applied mathematics and theoretical physics, university of cambridge, cambridge, england received april 12, 1975 abstract.
Abstractin three dimensions, a phase transition occurs between the nonrotating btz black hole and the massless btz black hole. Pdf thermodynamics of btz black hole and entanglement entropy. We then describe the btz black hole within this formulation. These results are for angular momentum quantum number m 1, and 0. While the btz black hole was discovered in 1992, and is as such not new, it. We extend this investigation to lorentzian btz black hole spacetimes, and study the bulk and boundary behaviour of massive scalar fields both in the nonextremal and extremal case. In particular, when the latter is large, they reproduce the bulk shockwave propagation along the btz horizon description. More precisely 19 see also the earlier steps and insights of 20 21 22, the duality is framed in terms of the kruskal extension of btz, ds2. In the classical theory black holes can only absorb and not emit particles. The btz black hole violates strong cosmic censorship. Holographic entanglement entropy of the btz black hole. A closer look hongsu kim department of astronomy and atmospheric sciences kyungpook national university, taegu 702701, korea august, 1998 abstract by applying newmans algorithm, the ads3 rotating black hole solution is \derived from the nonrotating black hole solution of banados, teitelboim. We use rigorous mathematical results to clarify the general structure and properties of this black hole spacetime and its microscopic description. We start this section with a brief introduction to chernsimons theory, and then specify it as a model for threedimensional gravity.
It has become vital to understand btz black hole thermodynamics from. The role of the pattersonselberg zeta function of a. Geometric finiteness and nonquasinormal modes of the btz. The basic starting point is that thermal states in cft are dual to black holes in quantum gravity.
Complete geodesics of both types exist in the rotating black hole background, but not in the spinless case. Scrambling time from local perturbations of the eternal. A hole is nothing, and if it is black, we cant even see it. Gupta, tajron juric, andjelo samsarov, jhep 1706, 107 2017 arxiv. Thermodynamic interpretation of field equations at horizon. The btz black hole di ers from the schwarzschild and kerr solutions in some important respects. Noncommutative scalar quasinormal modes and quantization of entropy of a btz black hole, kumar s. On the btz black hole and the spinning cosmic string request pdf.
We introduce a set of scalar fields as test fields to study the dynamical behaviors of the btz banadosteitelboimzanelli black hole. A spacetime horizon comprising with a black hole singularity acts like a boundary of a thermal system associated with the notions of temperature and entropy. Research article fermion fields in btz black hole space. On lifshitz rotating black holes and black branes in light of adscft brigitte sprenger institute for theoretical physics utrecht university. On lifshitz rotating black holes and black branes in light. Black holes are famous for their universal behavior. There are corresponding euclidean solutions which have been discussed in 15. Firstly, we focus on the formation of the black hole from point particle collisions 1416. The btz black hole is a quantum object and the btz black hole with finite mass should be considered as a quantum excitation of the massless one. Our results follow by first performing a novel reanalysis of the rindler view of standard adscft duality on the poincare patch of ads, followed by exploiting the simple quotient structure of btz which turns the rindler horizon into the btz black hole horizon. In fact, this is a special case of the dictionary 14. Yesif that black hole represents the most extreme state of matter possible, if it represents the possible end of the universe, if it represents the.
The btz black hole differs from the schwarzschild and kerr solutions in some im portant respects. 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. Einsteins theory, the btz black hole has the uniqueness property under the conditions described in 7,8. We show that linear perturbations arising from smooth initial data are arbitrarily differentiable at the inner horizon if the black hole is sufficiently close to extremality. Antide sitter space appears as a negative energy state separated by a mass gap from the continuous black hole spectrum. Banados, maximo 1999, threedimensional quantum geometry and black holes pdf. Zaslavskii, entropy of charged thin shells and the.
Spherical and planar threedimensional antide sitter. We focus on the retarded green function of a massive scalar. Harikumar, tajron juric, stjepan meljanac, andjelo samsarov. Finally, we combined the knowledge of these to try to calculate the metric of the rotating lifshitz black hole. The btz black hole has a horizon of positive circumference and a corresponding bekensteinhawking entropy. Supersymmetric scattering amplitudes and algebraic aspects of. Research article fermion fields in btz black hole spacetime. We provide a holographic description in terms of a free falling particle in the eternal btz black hole that exactly matches our cft calculations.
More precisely, it corresponds to an orbifold of the universal covering space of ads 3. Noncommutative duality and fermionic quasinormal modes of the btz black hole, kumar s. The first law of thermodynamics and 2d cft descriptions for. Uvadare digital academic repository holography and. 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. The lecture, after this introduction, consists of four sections and an appendix.
Pdf holographic entanglement entropy of the btz black. Recently, the adscft conjecture of maldacena has been investigated in lorentzian signature by balasubramanian et. A number of threedimensional 3d gravity models, such as 3d conformal gravity, admit exotic black hole solutions. In this work we clarify further this picture by showing that btz black hole microstates are in general among the. The btz black hole, named after maximo banados, claudio teitelboim, and jorge zanelli, is a.
The quotient spacetime includes regions beyond the singularity, whiskers, containing timelike and lightlike closed curves, which at first sight seem unphysical. In chapter 6, we consider a class of holographic quantum errorcorrecting codes, built from perfect tensors in network configurations dual to bruhat. The btz black hole allows exceptional analytic control because it is locally isometric to threedimensional antide sitter space ads 3, a maximally symmetric spacetime. We explore the consequences of this theorem in the context of the euclidean btz black hole in three dimensions. Since the massless btz black hole has a naked singularity, it is not unexpected that both the null selfdual orbifold, as well as the pinching orbifold, are not good reliable gravitational.
Introduction to black hole astrophysics, 2010 gustavo e. In section,wecalculatethecoe cientsappearinginthe entropy formula numerically. And since the general theory of relativity provides only a single unique family of solutions for their descriptions, they are the simplest objects as well. The entropy of the btz black hole is discussed from the point view of the adscft correspondence and an explanation is given to the puzzle of black hole entropy in the btz case. Thermodynamics of exotic btz black holes internet archive. A nearevh black hole, or low energy excitation around an evh black hole, is described by. A natural guess is that black hole entropy should be associated with horizon degrees of freedom. We introduce the necessary concepts of general relativity and discuss threedimensional gravity, speci cally antide sitter vacuum space. Exploring black hole dynamics the harvard community has. This result shows that the btz black hole can be parametrized by at most two parameters, its. In 1,2 it was shown how the horizon u proposal works for ads 3 black holes. We study the entanglement entropy of fermion fields in btz black hole spacetime and calculate prefactor of the leading and subleading terms and logarithmic divergence term of the entropy using the discretized model. New thermodynamic relations have been found recently for the product of gravitational entropies over all the horizons of a given stationary black hole.
Accretion of phantom energy onto a rotating btz black hole accretion of phantom energy onto a rotating btz black hole. The celebrated theorems of black hole physics essentially prevent us from. The phases of 3d higher spin black holes ignacio a. Romero introduction to black hole astrophysics gustavo e. A rotating btz black hole admits closed timelike curves. Hawking temperature of the btz black hole stack exchange. Jun 19, 2019 we investigate the stability of the inner horizon of a rotating btz black hole. Btz black hole has an adscft description in terms of a nonchiral two dimensional cft, our result can be viewed as thermodynamic evidence for the evhcft correspondence, which states that gravity on the near horizon evh geometry is described by a 2d cft. Scrambling time from local perturbations of the eternal btz black hole citation for published version. This means that its three dimensional hyperbolic structure as encoded in its metric is in 11 correspondence with the teichmuller space of its boundary. Hawking added to the puzzle when he discovered that a black hole will. Review and cite black holes protocol, troubleshooting and other methodology information contact experts in black holes to get answers. Due to the importance of the btz black hole, onewould like to know its uniqueness and alsowhether it is preserved as a black hole under the deformations described as g.
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. Noneinsteinian black holes in generic 3d gravity theories. Upper and lower bounds for the radial size of the orbits are given in all. The case of zero cosmological constant corresponding to the interior region of a black hole is analyzed in detail. Bulk and boundary dynamics in btz black holes inspirehep. What links here related changes upload file special pages permanent link page information wikidata item cite this page. The event horizon is a surface of constant negative curvature, and the spacetime is asymptotically locally antidesitter. Holography of the btz black hole, inside and out pdf. Fermion fields in btz black hole spacetime and entanglement. Thebtz black hole is constructed from the ads space by periodic identi. Boundary contributions to the btz black hole hamiltonian. The btz black hole pattersonselberg zeta function and a oneloop determinant formula determinant formula in the presence of conical singularities. The black hole in three dimensional space time arxiv. Since it has been claimed that a black hole has an entropy 1, thermodynamics of black holes has been one of the most important arena in black.
Hawkingpage phase transition in btz black hole revisited. Uvadare digital academic repository on the universality of. 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. We show that formation can be understood at a purely algebraic level, in terms of. Holography of the btz black hole, inside and out core.
Removing a coordinate singularity at the schwarzschild radius. This product has been found to be independent of the mass for all such solutions of einsteinmaxwell theory in d 4,5. Phase transition between the btz black hole and ads. Department of physics university of california davis, ca 95616 usa abstract in three spacetime dimensions, general relativity becomes a topological. On subregion action complexity in ads3 and in the btz black hole. In particular, a generic feature of all string theory blac k holes for whic h an.
Banadosteitelboimzanelli btz black holes are constructed by orbifolding ads3 geometry by boost transformations of its o2,2 isometry group. The adscft correspondence pi it from qubit summer school. 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. We will shortly describe how the realtime dictionary resolves this puzzle. Most people think of a black hole as a voracious whirlpool in space, suck ing down. The btz solution is the most general black hole solution in three dimensions, which is guaranteed by the threedimensional version of birkho. In theoretical physics, an antide sitter ads black hole is a black hole solution of general relativity or its extensions which represents an isolated massive object, but with a negative cosmological constant. 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. Quantum fields on btz black holes white rose university. Accretion of phantom energy onto a rotating btz black hole. Finally,wesummarize our results and their physical implications. The schwarzschild metric has a singularity at r rs where 0g00 and g11 however, we have already seen that a free falling observer acknowledges a smooth motion without any peculiarity when he passes the horizon. The mass and angular momentum of the black hole is btz black holes without any electric charge are locally isometric to antide sitter space. The simplest black hole spacetime we can describe in an asymptotically ads geometry is the famous btz black hole in three spacetime dimensions.
Geometrical finiteness, holography, and the btz black hole. Antide sitter space appears as a negative energy state separated by a mass gap from the continuous black. Btz black hole is the most common spacetime constructed by researchers in later. Classical black hole solutions occurs in general relativity and provide us with con. Btz black hole with selected boundary conditions global charges and thermodynamics energy, temperature and entropy. Pdf dirac particles tunneling from btz black hole ran. Pdf spinning btz black hole versus kerr black hole. The motivation to study lower dimensional black holes is also provided by the evidence that some physical properties of black holes such as hawking radiation and evaporation can be more easily understood in the context of two and three. If an internal link led you here, you may wish to change the link to point directly to the intended article. Further, introducing the mass of a conical singularity, we show that a transition between the nonrotating btz black hole and thermal ads space is also possible. Probing the btz black hole with test fields internet archive. Part iv duality between charged btz black hole and luttinger. Particles and fields 752 december 2006 with 74 reads how we measure reads.
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