NO-BOUNDARY WAVE FUNCTION IN A HIGHER-DIMENSIONAL SPHERICALLY SYMMETRIC MICROSUPERSPACE MODEL

1992 ◽  
Vol 07 (08) ◽  
pp. 653-658 ◽  
Author(s):  
SUBENOY CHAKRABORTY
Keyword(s):  
Wave Function ◽  
Dimensional Space ◽  
Space Time ◽  
Functional Integral ◽  
Steepest Descent ◽  
Spherically Symmetric ◽  
Higher Dimensional ◽  
Dimensional Space Time ◽  
Method Of Steepest Descent

The wave function following the Hartle-Hawking (HH) no-boundary proposal is evaluated in five-dimensional space-time with topology of the four space S1×S3, generalizing the concept of microsuperspace. The functional integral in the expression for the wave function is simplified to an ordinary integration of one variable and is evaluated by the method of steepest-descent.

NATURE OF THE SINGULARITIES IN HIGHER-DIMENSIONAL HUSAIN SPACE–TIME

2006 ◽  
Vol 15 (09) ◽  
pp. 1359-1371 ◽  
Author(s):  
K. D. PATIL ◽  
S. S. ZADE
Keyword(s):  
Gravitational Collapse ◽  
Dimensional Space ◽  
Higher Dimensions ◽  
Cosmic Censorship ◽  
Space Time ◽  
Spherically Symmetric ◽  
Naked Singularities ◽  
Higher Dimensional ◽  
Dimensional Space Time ◽  
Cosmic Censorship Hypothesis

We generalize the earlier studies on the spherically symmetric gravitational collapse in four-dimensional space–time to higher dimensions. It is found that the central singularities may be naked in higher dimensions but depend sensitively on the choices of the parameters. These naked singularities are found to be gravitationally strong that violate the cosmic censorship hypothesis.

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.

scholarly journals Visualising higher-dimensional space-time and space-scale objects as projections to ℝ3

2017 ◽  
Vol 3 ◽  
pp. e123 ◽  
Author(s):  
Ken Arroyo Ohori ◽  
Hugo Ledoux ◽  
Jantien Stoter
Keyword(s):  
Dimensional Space ◽  
Space Time ◽  
Three Dimensions ◽  
Time And Space ◽  
3D Objects ◽  
Levels Of Detail ◽  
Higher Dimensional Space Time ◽  
Space Scale ◽  
Higher Dimensional ◽  
Dimensional Space Time

Objects of more than three dimensions can be used to model geographic phenomena that occur in space, time and scale. For instance, a single 4D object can be used to represent the changes in a 3D object’s shape across time or all its optimal representations at various levels of detail. In this paper, we look at how such higher-dimensional space-time and space-scale objects can be visualised as projections from ℝ4to ℝ3. We present three projections that we believe are particularly intuitive for this purpose: (i) a simple ‘long axis’ projection that puts 3D objects side by side; (ii) the well-known orthographic and perspective projections; and (iii) a projection to a 3-sphere (S3) followed by a stereographic projection to ℝ3, which results in an inwards-outwards fourth axis. Our focus is in using these projections from ℝ4to ℝ3, but they are formulated from ℝnto ℝn−1so as to be easily extensible and to incorporate other non-spatial characteristics. We present a prototype interactive visualiser that applies these projections from 4D to 3D in real-time using the programmable pipeline and compute shaders of the Metal graphics API.

scholarly journals First Integral Technique for Finding Exact Solutions of Higher Dimensional Mathematical Physics Models

Symmetry ◽  
2019 ◽  
Vol 11 (6) ◽  
pp. 783 ◽  
Author(s):  
Shumaila Javeed ◽  
Sidra Riaz ◽  
Khurram Saleem Alimgeer ◽  
M. Atif ◽  
Atif Hanif ◽  
...  
Keyword(s):  
Exact Solutions ◽  
Dimensional Space ◽  
Nonlinear Partial Differential Equations ◽  
First Integral ◽  
Mathematical Physics ◽  
Space Time ◽  
Mathematical Tool ◽  
Long Wave ◽  
Higher Dimensional ◽  
Dimensional Space Time

In this work, we establish the exact solutions of some mathematical physics models. The first integral method (FIM) is extended to find the explicit exact solutions of high-dimensional nonlinear partial differential equations (PDEs). The considered models are: the space-time modified regularized long wave (mRLW) equation, the (1+2) dimensional space-time potential Kadomtsev Petviashvili (pKP) equation and the (1+2) dimensional space-time coupled dispersive long wave (DLW) system. FIM is a powerful mathematical tool that can be used to obtain the exact solutions of many non-linear PDEs.

scholarly journals Gravitational Theory Without the Cosmological Constant Problem

1997 ◽  
Vol 12 (32) ◽  
pp. 2421-2424 ◽  
Author(s):  
E. I. Guendelman ◽  
A. B. Kaganovich
Keyword(s):  
Cosmological Constant ◽  
Degrees Of Freedom ◽  
Vacuum Energy ◽  
Dimensional Space ◽  
Realistic Model ◽  
Gravitational Theory ◽  
Space Time ◽  
Higher Dimensional Space Time ◽  
Higher Dimensional ◽  
Dimensional Space Time

We develop a gravitational theory where the measure of integration in the action principle is not necessarily [Formula: see text] but it is determined dynamically through additional degrees of freedom. This theory is based on the demand that such measure respects the principle of "non-gravitating vacuum energy" which states that the Lagrangian density L can be changed to L + const. without affecting the dynamics. Formulating the theory in the first-order formalism we get as a consequence of the variational principle a constraint that enforces the vanishing of the cosmological constant. The most realistic model that implements these ideas is realized in a six or higher dimensional space–time. The compactification of extra dimensions into a sphere gives the possibility of generating scalar masses and potentials, gauge fields and fermionic masses. It turns out that the remaining four-dimensional space–time must have effective zero cosmological constant.

scholarly journals Space–times over normed division algebras, revisited

2020 ◽  
Vol 35 (10) ◽  
pp. 2050055
Author(s):  
R. Vilela Mendes
Keyword(s):  
Homogeneous Spaces ◽  
Dimensional Space ◽  
Internal Symmetry ◽  
Space Time ◽  
Mathematical Framework ◽  
The Real ◽  
Higher Dimensional ◽  
Dimensional Space Time ◽  
Symmetry Transformations ◽  
Extended Group

Normed division and Clifford algebras have been extensively used in the past as a mathematical framework to accommodate the structures of the Standard Model and grand unified theories. Less discussed has been the question of why such algebraic structures appear in Nature. One possibility could be an intrinsic complex, quaternionic or octonionic nature of the space–time manifold. Then, an obvious question is why space–time appears nevertheless to be simply parametrized by the real numbers. How the real slices of an higher-dimensional space–time manifold might be almost independent from each other is discussed here. This comes about as a result of the different nature of the representations of the real kinematical groups and those of the extended spaces. Some of the internal symmetry transformations might however appear as representations on homogeneous spaces of the extended group transformations that cannot be implemented on the elementary states.

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