It is based on an exact four-dimensional solution for a black hole localized on a brane in AdS 4, first discussed some years ago but never fully investigated in this manner. The MTZ black hole, named after Cristian Martinez, Ricardo Troncoso and Jorge Zanelli, is a black hole solution for (3+1)-dimensional gravity with a minimally coupled self-interacting scalar field.. , the authors studied a 3-dimensional noncommutative geometry inspired rotating black hole based on Gaussian smeared mass distribution; in this letter, we introduce the noncommutativity by taking the mass density to be a Lorentzian smeared mass distribution instead of the conventional Dirac delta function to explore the effects of space noncommutativity on the rotating BTZ black hole. Discussion of BTZ black holes via tensor networks in the p-adic AdS/CFT correspondence: Matthew Heydeman, Matilde Marcolli, Sarthak Parikh, Ingmar Saberi, Nonarchimedean Holographic Entropy from Networks of Perfect Tensors (arXiv:1812.04057), Stephen Ebert, Hao-Yu Sun, Meng-Yang Zhang, Probing holography in pp-adic CFT (arXiv:1911.06313). Using (2), the connection Aa corresponding to the metric (13) may be written as: A1 = − cscχ(dθ− i dR R), A2 = icscχdχ, A3 = icotχ(dθ− i dR R). B. Sathiapalan BTZ black-hole and Luttinger Liquids. Therefore this hyperbolic 3-manifold knot complement does not count as a “knot complement with hyperbolic structure” in the sense of Thurston‘s classification of 3-manifolds? 1,3. Unlike the other black holes, the total energy of the exotic BTZ black hole is represented by the angular momentum instead of the mass, which supports a basic point of view that the same geometry should be determined by the same energy in 3D general relativity whose equation of motion can be given either by normal 3D Einstein gravity or by exotic 3D Einstein gravity. B. Zhang, The mass formula for an exotic btz black hole, Ann. The Bañados‐Teitelboim‐Zanelli (BTZ) black hole model corresponds to a solution of (2+1)‐dimensional Einstein gravity with negative cosmological constant, and by a conformal rescaling its metric can be mapped onto the hyperbolic pseudosphere surface (Beltrami trumpet) with negative curvature. Quantum Liouville Theory And Btz Black Hole Entropy. Description. 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]. The Euclidean BTZ black hole is a hyperbolic 3-manifold homeomorphic to (the interior of) the hyperbolic solid torus, hence to the knot complement of the unknot in the 3-sphere. We investigate the effect of noncommutativity and quantum corrections to the temperature and entropy of a BTZ black hole based on a Lorentzian distribution with the generalized uncertainty principle (GUP). The 2+1 black hole -characterized by mass, angular momentum and charge, defined by flux integrals at infinity- is quite similar to its 3+1 counterpart. BTZ Black Hole Central Charge and Conformal Weight. In this section, we study the test particle’s motion in charged BTZ black holes. History. The BTZ black Math. 1h Speaker. We study a holographic construction of quantum rotating BTZ black holes that incorporates the exact backreaction from strongly coupled quantum conformal fields. Through a re-scaling of the BTZ parameters we map this to the more canonical picture of exponential evaporation. In this paper, we investigate the entanglement thermodynamics of scalar elds in the BTZ black holes) A black hole solution for (2+1)- dimensional gravity with a negative cosmological constant . BTZ black hole: | The |BTZ black hole|, named after black hole solution for |(2+1)-dimensional| gravit... World Heritage Encyclopedia, the aggregation of the largest online encyclopedias available, and the most definitive collection ever assembled. Introduction 1+1 dimensions: Luttinger Liquids BTZ black hole Boundary Theory Summary Motivation AdS/CFT Non-Fermi Liquids. The Euclidean BTZ black hole is a hyperbolic 3-manifold homeomorphic to (the interior of) the hyperbolic solid torus, hence to the knot complement of the unknot in the 3-sphere. 7to study the behavior of the specific heat with respect to the horizon radius. In 1992 Bañados, Teitelboim and Zanelli discovered the BTZ black hole solution (Bañados, Teitelboim & Zanelli 1992). Springer, Berlin, Heidelberg (arXiv:gr-qc/9904083, doi:10.1007/3-540-46671-1_6 ), Aritra Ghosh, Chandrasekhar Bhamidipati, Thermodynamic geometry and interacting microstructures of BTZ black holes (arXiv:2001.10510), Roberto Emparan, Antonia Micol Frassino, Benson Way, Quantum BTZ black hole, JHEP11 (2020) 137 (arXiv:2007.15999), Pablo Bueno, Pablo A. Cano, Javier Moreno, Guido van der Velde, Regular black holes in three dimensions (arXiv:2104.10172). Motivated by several pieces of evidence, in order to show that extremal black holes cannot be obtained as limits of non-extremal black holes, in this paper we calculate explicitly quasinormal modes for the Banados, Teitelboim and Zanelli (BTZ) extremal black hole and show that the imaginary part of the frequency is zero. Anti-de Sitter space appears as a negative energy state separated by a mass gap from the continuous black hole … 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. ISI, Google Scholar; 71. 1. We study the evaporation of two-dimensional black holes in JT gravity from a three-dimensional point of view. It was however shown, that this black hole could arise from collapsing matter and we can calculate the energy-moment tensor of BTZ as same as (3+1) black holes. A natural guess is that black hole entropy should be associated with horizon degrees of freedom. [citation needed], A rotating BTZ black hole admits closed timelike curves. The BTZ black hole is a solution of Einstein’s equations in 2+1d which has two asymptotic regions which are causally separated from each other by an event horizon. The arrows leading to “quantum states” come into play when you use the BTZ black hole as a toy model for thinking about quantum gravity. In ref. The three-dimensional black hole solution was reported in [1] (BTZ solution here after). However, the corrected entropy is an increasing function for large BTZ black holes (for which the horizon radius is larger than this critical value). Quantum Analysis of BTZ Black Hole Formation Due to the Collapse of a Dust Shell . Phys. (e.g Gukov 03, appendix A, Kraus 06, around Fig. a black hole is obtained from a boosted black string by dimensional reduction, the near-horizon geometry of the latter contains a BTZ black hole. 1,2, Artem Starodubtsev. By choosing standard boundary conditions appropriate to the stability problem, we demonstrate the absence of modes which grow in time, for all values of the Chern-Simons coupling. In 1992 Bañados, Teitelboim and Zanelli discovered the BTZ black hole solution (Bañados Teitelboim). 40: 638-657, 2010 (arXiv:0907.1559), (relation to holographic entanglement entropy), Ingmar Saberi, around Figure 4.3 of: Knots, Trees, and Fields: Common Ground Between Physics and Mathematics (doi:10.7907/Z9VX0DHZ, pdf), (with generalization to p-adic string theory), Zhen-Ming Xu, Bin Wu, Wen-Li Yang, Thermodynamic curvature and isoperimetric inequality for the charged BTZ black hole (arXiv:2002.00117). 367 (2016) 280–287. There are two notebooks, a Mathematica one written in Wolfram Language and a Jupyter one, written in Python. are the black hole radii and The original BTZ black hole with trivial internal topology is due to: Máximo Bañados, Claudio Teitelboim, Jorge Zanelli, The Black Hole in Three Dimensional Space Time, Phys. Numerical analyses of "Comments on the anti-Hawking effect on a BTZ black hole spacetime" regarding an Unruh-deWitt detector on Rindler-AdS spacetime and on a static BTZ black hole. History. The event horizon is a surface of constant negative curvature, and the spacetime is asymptotically locally Anti-de-Sitter.. See also. Department of High Energy and Elementary Particles Physics, Saint Petersburg State … Yasser Elmahalawy. {\displaystyle r_{+},~r_{-}} We consider Gedanken experiments to destroy an extremal or near-extremal Banados-Teitelboim-Zanelli (BTZ) black hole by throwing matter into the horizon. Grav. We investigate the effect of noncommutativity and quantum corrections to the temperature and entropy of a BTZ black hole based on a Lorentzian distribution with the generalized uncertainty principle (GUP). More mathematically: ((x,r) are bulk coordinates and r = ∞ is the boundary, with boundary coordinates being x) … For the (2 + 1)-dimensional BTZ black hole solution, one can try to follow the same procedure as used for the cosmic string, by uplifting the In section 3, we show that the entropy counting of these black holes is reduced to that of the corresponding BTZ black holes under appropriate conditions. There are several attempts to understand the microscopic origin of black hole entropy and its relation with horizon area [2{14]. Download full Quantum Liouville Theory And Btz Black Hole Entropy Book or read online anytime anywhere, Available in PDF, ePub and Kindle. In order to obtain the. 16 (1999) 363-382 (arXiv:gr-qc/9805028), Dieter Brill, Black Holes and Wormholes in 2+1 Dimensions, In: Cotsakis S., Gibbons G.W. (2.10), (2.11). r Einstein-Hilbert action, Einstein's equations, general relativity, first-order formulation of gravity, D'Auria-Fre formulation of supergravity, gravity as a BF-theory, Plebanski formulation of gravity, teleparallel gravity, black holes in 3d gravity with negative cosmological constant. Rev. 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. 1,* and . AdS/CFT. BTZ black hole: | The |BTZ black hole|, named after black hole solution for |(2+1)-dimensional| gravit... World Heritage Encyclopedia, the aggregation of the largest online encyclopedias available, and the most definitive collection ever assembled. BTZ black hole can be used as a laboratory to study the quantum aspects of black holes. BTZ black holes provide excellent frameworks for studying theories that are at the interface of classical and quantum gravity. The BTZ solution is related to the Anti-deSitter/Conformal Field Theory (AdS/CFT) correspondence [6] and became a tool to understand black hole entropy [7]. 20 (2003) 2235-2250 (arXiv:gr-qc/0302073), Sergei Gukov, Appendix A of: Three-Dimensional Quantum Gravity, Chern-Simons Theory, and the A-Polynomial, Commun. version of BTZ black hole solution in 3-dim. D 93, 045003 (2016) (arXiv:1511.08662), Wout Merbis, Max Riegler, Geometric actions and flat space holography (arXiv:1912.08207). The linearized perturbation equations can be solved exactly in this case. A partial dimensional reduction of AdS$_3$ in Poincaré coordinates leads to an extremal 2D black hole in JT gravity coupled to a 'bath': the holographic dual of the remainder of the 3D spacetime. Hole solutions using the Wentzel-Kramers-Brillouin ( WKB ) approach hole boundary Theory Summary Motivation AdS/CFT Liquids! 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