scholarly journals From the BTZ black hole to JT gravity: geometrizing the island

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Evita Verheijden ◽  
Erik Verlinde
Keyword(s):  
Black Hole ◽  
Finite Temperature ◽  
Three Dimensional ◽  
Point Of View ◽  
Geometric Representation ◽  
Two Dimensional ◽  
Btz Black Hole ◽  
Island Region ◽  
Dimensional Spacetime ◽  
Over Time

Abstract We study the evaporation of two-dimensional black holes in JT gravity from a three-dimensional point of view. A partial dimensional reduction of AdS3 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. Partially reducing the BTZ black hole gives us the finite temperature version. We compute the entropy of the radiation using geodesics in the three-dimensional spacetime. We then focus on the finite temperature case and describe the dynamics by introducing time-dependence into the parameter controlling the reduction. The energy of the black hole decreases linearly as we slowly move the dividing line between black hole and bath. Through a re-scaling of the BTZ parameters we map this to the more canonical picture of exponential evaporation. Finally, studying the entropy of the radiation over time leads to a geometric representation of the Page curve. The appearance of the island region is explained in a natural and intuitive fashion.

Chiral modular bootstrap

2019 ◽  
Vol 34 (28) ◽  
pp. 1950168 ◽  
Author(s):  
M. Ashrafi
Keyword(s):  
Black Hole ◽  
Upper Bound ◽  
Three Dimensional ◽  
Conformal Weight ◽  
Two Dimensional ◽  
Btz Black Hole ◽  
Conformal Field ◽  
Dimensional Gravity ◽  
Large Spin ◽  
Dimension Ratio

Using modular bootstrap we show the lightest primary fields of a unitary compact two-dimensional conformal field theory (with [Formula: see text], [Formula: see text]) has a conformal weight [Formula: see text]. This implies that the upper bound on the dimension of the lightest primary fields depends on their spin. In particular if the set of lightest primary fields includes extremal or near extremal states whose spin to dimension ratio [Formula: see text], the corresponding dimension is [Formula: see text]. From AdS/CFT correspondence, we obtain an upper bound on the spectrum of black hole in three-dimensional gravity. Our results show that if the first primary fields have large spin, the corresponding three-dimensional gravity has extremal or near extremal BTZ black hole.

scholarly journals Page curve for entanglement negativity through geometric evaporation

2022 ◽  
Vol 12 (1) ◽  
Author(s):  
Jaydeep Kumar Basak ◽  
Debarshi Basu ◽  
Vinay Malvimat ◽  
Himanshu Parihar ◽  
Gautam Sengupta
Keyword(s):  
Black Hole ◽  
Random Matrix Theory ◽  
Random Matrix ◽  
Mixed State ◽  
Dimensional Reduction ◽  
Matrix Theory ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Btz Black Hole ◽  
Diagrammatic Technique

We compute the entanglement negativity for various pure and mixed state configurations in a bath coupled to an evaporating two dimensional non-extremal Jackiw-Teitelboim (JT) black hole obtained through the partial dimensional reduction of a three dimensional BTZ black hole. Our results exactly reproduce the analogues of the Page curve for the entanglement negativity which were recently determined through diagrammatic technique developed in the context of random matrix theory.

HYBRID REFLECTIONS IN POST-MODERN GRAPHIC DESIGN POSTERS

ATLAS JOURNAL ◽  
2021 ◽  
Vol 7 (44) ◽  
pp. 2207-2213
Author(s):  
Fatıma TOKGÖZ GÜN ◽  
Mehmet ÖZKARTAL
Keyword(s):  
Graphic Design ◽  
Hybrid Methods ◽  
Three Dimensional ◽  
Point Of View ◽  
Two Dimensional ◽  
Use Of Technology ◽  
Work Area ◽  
Poster Art ◽  
Motion Images ◽  
Over Time

Hybrid works in art have many examples from past to present. Hybridization in poster art has been in question since the first years when posters started to appear. Hybridization in designs can occur in terms of both method and technique. In present study, it is mentioned how graphic design has removed the boundaries between itself and many disciplines since the use of technology in the field of art and how it allows hybrid studies. As it is known, the main purpose of graphic design is to convey an existing idea to the other party in the simplest way. For this reason, graphic design, which updates itself over time, has added motion and sound to its work area and shows itself with effective designs. While technically designs consist of two-dimensional studies for years, they can also be designed in three-dimensional or even four-dimensional forms with hybrid methods. While poster designs are prepared as flat and static, they update themselves with kinetic typography and motion images. Moreover, with hybrid presentations such as augmented reality and virtual reality in current works, designs interact more with people. It is seen that the artists who can think from a hybrid point of view attract more attention and interaction with the hybridity reflected in their designs, and they also reach the intended result in a catchy manner.

Periodicity and area spectrum of the three dimensional BTZ black hole

2012 ◽  
Vol 44 (11) ◽  
pp. 2865-2872 ◽  
Author(s):  
Hui-Ling Li ◽  
Rong Lin ◽  
Li-Ying Cheng
Keyword(s):  
Black Hole ◽  
Three Dimensional ◽  
Area Spectrum ◽  
Btz Black Hole

Three-dimensional static black hole with Λ and nonlinear electromagnetic fields and its thermodynamics

2019 ◽  
Vol 28 (12) ◽  
pp. 1950160
Author(s):  
M. B. Tataryn ◽  
M. M. Stetsko
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Electromagnetic Fields ◽  
Three Dimensional ◽  
Nonlinear Electrodynamics ◽  
Extended Phase Space ◽  
Field Equations ◽  
Extended Phase ◽  
Dimensional Spacetime ◽  
Static Black Hole

Static black hole with the Power Maxwell invariant (PMI), Born–Infeld (BI), logarithmic (LN), exponential (EN) electromagnetic fields in three-dimensional spacetime with cosmological constant was studied. It was shown that the LN and EN fields represent the Born–Infeld type of nonlinear electrodynamics. It the framework of General Relativity the exact solutions of the field equations were obtained, corresponding thermodynamic functions were calculated and the [Formula: see text] criticality of the black holes in the extended phase-space thermodynamics was investigated.

A Zeta Function for the BTZ Black Hole

2003 ◽  
Vol 18 (12) ◽  
pp. 2205-2209 ◽  
Author(s):  
F. L. Williams
Keyword(s):  
Black Hole ◽  
Zeta Function ◽  
Three Dimensional ◽  
Thermodynamic Quantities ◽  
Btz Black Hole ◽  
Special Values

For the three-dimensional BTZ black hole we consider a Selberg type zeta function. We indicate how special values of its logarithm correspond to certain thermodynamic quantities associated with the black hole.

scholarly journals Coherent structures and chaotic advection in three dimensions

2010 ◽  
Vol 654 ◽  
pp. 1-4 ◽  
Author(s):  
STEPHEN WIGGINS
Keyword(s):  
Dynamical Systems ◽  
Fluid Mechanics ◽  
Coherent Structures ◽  
Three Dimensional ◽  
Point Of View ◽  
Three Dimensions ◽  
Chaotic Advection ◽  
Periodic Flow ◽  
Two Dimensional ◽  
Time Periodic

In the 1980s the incorporation of ideas from dynamical systems theory into theoretical fluid mechanics, reinforced by elegant experiments, fundamentally changed the way in which we view and analyse Lagrangian transport. The majority of work along these lines was restricted to two-dimensional flows and the generalization of the dynamical systems point of view to fully three-dimensional flows has seen less progress. This situation may now change with the work of Pouransari et al. (J. Fluid Mech., this issue, vol. 654, 2010, pp. 5–34) who study transport in a three-dimensional time-periodic flow and show that completely new types of dynamical systems structures and consequently, coherent structures, form a geometrical template governing transport.

scholarly journals Using of Parallel Coordinates in Finding Minimum Distance in Time-Space

2019 ◽  
Vol 21 (3) ◽  
pp. 3-7
Author(s):  
Olga Blazekova ◽  
Maria Vojtekova
Keyword(s):  
Coordinate System ◽  
Minimum Distance ◽  
Three Dimensional ◽  
Multidimensional Data ◽  
Fourth Dimension ◽  
Geometric Representation ◽  
Two Dimensional ◽  
Parallel Coordinates ◽  
Time Space ◽  
Cartesian Coordinate

Airspace domain may be represented by a time-space consisting of a three-dimensional Cartesian coordinate system and time as the fourth dimension. A coordinate system provides a scheme for locating points given its coordinates and vice versa. The choice of coordinate system is important, as it transforms data to geometric representation. Visualization of the three and more dimensional data on the two-dimensional drawing - computer monitor is usually done by projection, which often can restrict the amount of information presented at a time. Using the parallel coordinate system is one of possibilities to present multidimensional data. The aim of this article is to describe basics of parallel coordinate system and to investigate lines and their characteristics in time-space.

scholarly journals Modeling in AUTOCAD for bachelors

2021 ◽  
pp. 25-28
Author(s):  
Л.В. Карпюк ◽  
Н.О. Давіденко
Keyword(s):  
3D Model ◽  
Three Dimensional ◽  
Model Space ◽  
Educational Process ◽  
Point Of View ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Three Dimensional Objects ◽  
Graphic Editor

The article discusses the methods of using the AutoCad graphic editor for creating three-dimensional objects. The possibilities of three-dimensional modeling in the AutoCad graphic editor for optimizing the educational process of bachelors of technical specialties are also considered. The article analyzes the best ways to create mechanical engineering drawings.The most developed software tool for the production of design documentation is AutoCAD - a universal graphic design system. Creating models of any complexity in space by using this graphic editor, the user will be able to see their relative position, estimate the distance between them. The model can be freely moved in space, viewing many options. The ability to control the point of view allows to conveniently select the view of the 3D model that is being developed. Zooming, panning in real time with the ability to freely rotate the camera around the model provide the ability to quickly view objects from any point of view. The article provides examples of choosing the most optimal option for creating a three-dimensional model. The traditional way to create a 3D model drawing is to make 2D views of the model. When creating a flat drawing, there is a possibility of error when making projections, since they are created independently from each other and consist of several images. It is rather difficult to represent an object in space from a flat drawing. At present, modern software graphic editors are aimed at creating three-dimensional models that allow to create realistic models and, on their basis, get two-dimensional projections. Graphic editor AutoCad allows to create three-dimensional objects based on standard commands, in the form of a cylinder, cone, box, torus, etc., when editing which you can get the desired shapes. After creating a three-dimensional model, the user can get its two-dimensional projections not only on the main planes, but also on any plane at will. The 3D modeling method allows you to create a complex drawing with any number of images based on a 3D model. There are ways to create 2D plane drawings from a 3D model and the ability to edit ready-made designs that can be inserted from model space into paper space. Editing takes place by changing the parameters of a 3D object in model space, and these changes are automatically reflected in paper space. This method allows us to use the tools to quickly create a system of 3-4 linked views for a 3D AutoCad model.

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