scholarly journals D-dimensional self-gravitating lattice gas in general relativity

2021 ◽  
Author(s):  
Benaoumeur Bakhti
Keyword(s):  
Lattice Gas ◽  
Numerical Solutions ◽  
Dimensional Space ◽  
Space Time ◽  
Compact Objects ◽  
Central Pressure ◽  
Friedmann Equations ◽  
Dimensional Space Time ◽  
The One ◽  
Self Gravity

Using a lattice equation of state combined with the D-dimensional Tolman–Oppenheimer–Volkoff equation and the Friedmann equations, we investigate the possibility of the formation of compact objects as well as the time evolution of the scale factor and the density profile of a self-gravitating material cluster. The numerical results show that in a ([Formula: see text])-dimensional space–time, the mass is independent of the central pressure. Hence, the formation of only compact objects with a finite constant mass similar to the white dwarf is possible. However, in a ([Formula: see text])-dimensional space–time, self-gravity leads to the formation of compact objects with a large gap of mass and the corresponding phase diagram has the same structure as the one for Neutron Star. The results also show that beyond certain critical central pressure, the star is unstable against gravitational collapse, and it may end in a black hole. Analysis of space–times of higher dimensions shows that gravity has the stronger effect in [Formula: see text] dimensions. Numerical solutions of the Friedmann equations show that the effect of the curvature of space–time increases with the increasing temperature, but decreases with the increasing dimensionality beyond [Formula: see text].

ULTRAVIOLET FINITE GAUGE THEORIES IN THE FIVE-DIMENSIONAL SPACE-TIME

1993 ◽  
Vol 08 (35) ◽  
pp. 3345-3348
Author(s):  
V. V. BELOKUROV ◽  
M. Z. IOFA
Keyword(s):  
High Power ◽  
Gauge Theories ◽  
Dimensional Space ◽  
Arbitrary Dimension ◽  
Space Time ◽  
Covariant Derivatives ◽  
Dimensional Space Time ◽  
The One

Ultraviolet divergencies in gauge theories including those with higher powers of covariant derivatives are discussed in a space-time of an arbitrary dimension. In particular, it is noted that in the case d=5 all the one-loop graphs are finite, and theories with sufficiently high power of derivatives are finite in all orders.

scholarly journals The Numerical Solutions of a Two-Dimensional Space-Time Riesz-Caputo Fractional Diffusion Equation

2011 ◽  
Vol 1 (1) ◽  
pp. 17-26 ◽  
Author(s):  
Necati OZDEMIR ◽  
Derya AVCI ◽  
Beyza Billur ISKENDER
Keyword(s):  
Diffusion Equation ◽  
Anomalous Diffusion ◽  
Numerical Solutions ◽  
Fourier Transforms ◽  
Dynamic Properties ◽  
Dimensional Space ◽  
Space Time ◽  
Two Dimensional ◽  
Dimensional Space Time ◽  
Fractional Differential

This paper is concerned with the numerical solutions of a two dimensional space-time fractional differential equation used to model the dynamic properties of complex systems governed by anomalous diffusion. The space-time fractional anomalous diffusion equation is defined by replacing second order space and first order time derivatives with Riesz and Caputo operators, respectively. By using Laplace and Fourier transforms, a general representation of analytical solution is obtained as Mittag-Leffler function. Gr\"{u}nwald-Letnikov (GL) approximation is also used to find numerical solution of the problem. Finally, simulation results for two examples illustrate the comparison of the analytical and numerical solutions and also validity of the GL approach to this problem.

Study on Dynamics Model of Solid Trajectory Analysis and Pneumatics Based on Space-Time Four-Dimensional Data

2014 ◽  
Vol 556-562 ◽  
pp. 3856-3859
Author(s):  
Jun Zhang
Keyword(s):  
Mathematical Model ◽  
Dimensional Space ◽  
Space Time ◽  
Flight Trajectory ◽  
Time Data ◽  
One Dimensional ◽  
Dimensional Space Time ◽  
The One ◽  
Steady State Simulation ◽  
The Mathematical Model

In this paper we use elastic-plastic mechanics and air dynamic to establish the mathematical model of badminton flight trajectory and deformation, and use the ANSYS software to do simulation on badminton flight process, and obtain the flight path and deformation of badminton. In order to analyze the badminton four-dimensional space-time data, we establish the one-dimensional time measurement, and use one-dimensional time transient stress to establish flight trajectory and deformation, and design the four-dimensional space-time steady-state simulation process. Through calculation we eventually get the force of badminton flight process and deformation nephogram. Comparing four times results of numerical simulation results, the mathematical model of this design model meets the design requirements. It provides technical reference for badminton athlete's training and teaching.

ON THE PHYSICAL PROPERTIES RELATED TO THE ALGEBRAIC STRUCTURE OF THE DIRAC EQUATION IN THREE-DIMENSIONAL SPACE–TIME

1998 ◽  
Vol 13 (09) ◽  
pp. 1523-1542
Author(s):  
C. A. LINHARES ◽  
JUAN A. MIGNACO
Keyword(s):  
Dirac Equation ◽  
Algebraic Structure ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Space Time ◽  
Four Dimensions ◽  
Dimensional Space Time ◽  
The One ◽  
Physical Consequences ◽  
Three Dimensional Space

We look for the physical consequences resulting from the SU(2) ⊗ SU(2) algebraic structure of the Dirac equation in three-dimensional space–time. We show how this is obtained from the general result we have proven relating the matrices of the Clifford–Dirac ring and the Lie algebra of unitary groups. It allows the introduction of a notion of chirality closely analogous to the one used in four dimensions. The irreducible representations for the Dirac matrices may be labelled with different chirality eigenvalues, and they are related through inversion of any single coordinate axis. We analyze the different discrete transformations for the space of solutions. Finally, we show that the spinor propagator is a direct sum of components with different chirality; the photon propagator receive separate contributions for both chiralities, and the result is that there is no generation of a topological mass at one-loop level. In the case of a charged particle in a constant "magnetic" field we have a good example where chirality plays a determinant role for the degeneracy of states.

Topology knots and hierarchy problem

2019 ◽  
Author(s):  
Vitaly Kuyukov
Keyword(s):  
Quantum Theory ◽  
String Theory ◽  
Quantum Gravity ◽  
Dimensional Space ◽  
Space Time ◽  
Elementary Particles ◽  
Hierarchy Problem ◽  
Topological Quantum ◽  
Dimensional Space Time ◽  
New Formula

Many approaches to quantum gravity consider the revision of the space-time geometry and the structure of elementary particles. One of the main candidates is string theory. It is possible that this theory will be able to describe the problem of hierarchy, provided that there is an appropriate Calabi-Yau geometry. In this paper we will proceed from the traditional view on the structure of elementary particles in the usual four-dimensional space-time. The only condition is that quarks and leptons should have a common emerging structure. When a new formula for the mass of the hierarchy is obtained, this structure arises from topological quantum theory and a suitable choice of dimensional units.

Electromagnetic Casimir effect of concentric cylinders in (D + 1)-dimensional space–time

2019 ◽  
Vol 34 (08) ◽  
pp. 1950035
Author(s):  
Chun Yong Chew ◽  
Yong Kheng Goh
Keyword(s):  
Boundary Condition ◽  
Interaction Energy ◽  
Casimir Effect ◽  
Dimensional Space ◽  
Order Term ◽  
Perturbation Technique ◽  
Space Time ◽  
Concentric Cylinders ◽  
Dimensional Minkowski Space ◽  
Dimensional Space Time

We study the electromagnetic Casimir interaction energy between two parallel concentric cylinders in [Formula: see text]-dimensional Minkowski space–time for different combinations of perfectly conducting boundary condition and infinitely permeable boundary condition. We consider two cases where one cylinder is outside each other and where one is inside the other. By solving the equation of motion and computing the TGTG formulas, explicit formulas for the Casimir interaction energy can be derived and asymptotic behavior of the Casimir interaction energy in the nanoregime is calculated by using perturbation technique. We computed the interaction energy analytically up to next-to-leading order term.

scholarly journals TRAVERSABLE WORMHOLES IN A STRING CLOUD

2008 ◽  
Vol 17 (08) ◽  
pp. 1179-1196 ◽  
Author(s):  
MARTÍN G. RICHARTE ◽  
CLAUDIO SIMEONE
Keyword(s):  
Thin Shell ◽  
Dimensional Space ◽  
Space Time ◽  
Exotic Matter ◽  
Spherically Symmetric ◽  
Related Model ◽  
Traversable Wormholes ◽  
Dimensional Space Time ◽  
Thin Shell Wormholes ◽  
The Stability

We study spherically symmetric thin shell wormholes in a string cloud background in (3 + 1)-dimensional space–time. The amount of exotic matter required for the construction, the traversability and the stability of such wormholes under radial perturbations are analyzed as functions of the parameters of the model. In addition, in the appendices a nonperturbative approach to the dynamics and a possible extension of the analysis to a related model are briefly discussed.

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