scholarly journals COLLAPSING SHELLS OF RADIATION IN HIGHER DIMENSIONAL SPACE–TIME AND COSMIC CENSORSHIP CONJECTURE

2001 ◽  
Vol 16 (27) ◽  
pp. 4481-4488 ◽  
Author(s):  
S. G. GHOSH ◽  
R. V. SARAYKAR ◽  
A. BEESHAM
Keyword(s):  
Dimensional Space ◽  
Cosmic Censorship ◽  
Space Time ◽  
Naked Singularities ◽  
Higher Dimensional ◽  
Dimensional Space Time ◽  
Self Similar ◽  
Strong Curvature ◽  
Special Case ◽  
Cosmic Censorship Conjecture

Gravitational collapse of radiation shells in a non-self-similar higher dimensional spherically symmetric space–time is studied. Strong curvature naked singularities form a highly inhomogeneous collapse, violating the cosmic censorship conjecture. As a special case, self similar models can be constructed.

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 GRAVITATIONAL COLLAPSE OF PERFECT FLUID IN SELF-SIMILAR HIGHER DIMENSIONAL SPACE–TIMES

2003 ◽  
Vol 12 (05) ◽  
pp. 913-924 ◽  
Author(s):  
S. G. GHOSH ◽  
D. W. DESHKAR
Keyword(s):  
Perfect Fluid ◽  
Gravitational Collapse ◽  
Dimensional Space ◽  
Energy Condition ◽  
Cosmic Censorship ◽  
Naked Singularities ◽  
Four Dimensions ◽  
Higher Dimensional ◽  
Self Similar ◽  
Strong Curvature

We investigate the occurrence and nature of naked singularities in the gravitational collapse of an adiabatic perfect fluid in self-similar higher dimensional space–times. It is shown that strong curvature naked singularities could occur if the weak energy condition holds. Its implication for cosmic censorship conjecture is discussed. Known results of analogous studies in four dimensions can be recovered.

scholarly journals NON-MARGINALLY BOUND INHOMOGENEOUS DUST COLLAPSE IN HIGHER DIMENSIONAL SPACE–TIME

2003 ◽  
Vol 12 (04) ◽  
pp. 639-648 ◽  
Author(s):  
S. G. GHOSH ◽  
A. BANERJEE
Keyword(s):  
Gravitational Collapse ◽  
Dimensional Space ◽  
Dust Cloud ◽  
Naked Singularity ◽  
Space Time ◽  
Higher Dimensional Space Time ◽  
Higher Dimensional ◽  
Dimensional Space Time ◽  
Self Similar

We investigate the occurrence and nature of a naked singularity in the gravitational collapse of an inhomogeneous dust cloud described by a self-similar higher dimensional Tolman–Bondi space–time. Bound, marginally bound and unbound space–times are analyzed. The degree of inhomogeneity of the collapsing matter necessary to form a naked singularity is given.

scholarly journals NAKED SINGULARITIES IN HIGHER DIMENSIONAL GRAVITATIONAL COLLAPSE

2003 ◽  
Vol 12 (07) ◽  
pp. 1255-1263 ◽  
Author(s):  
ASIT BANERJEE ◽  
UJJAL DEBNATH ◽  
SUBENOY CHAKRABORTY
Keyword(s):  
Dimensional Space ◽  
Naked Singularity ◽  
Space Time ◽  
Naked Singularities ◽  
Five Dimensions ◽  
Higher Dimensional Space Time ◽  
Higher Dimensional ◽  
Dimensional Space Time ◽  
Five Dimension

Spherically symmetric inhomogeneous dust collapse has been studied in higher dimensional space–time and the factors responsible for the appearance of a naked singularity are analyzed in the region close to the centre for the marginally bound case. It is clearly demonstrated that in the former case naked singularities do not appear in the space–time having more than five dimension, which appears to a strong result. The non-marginally bound collapse is also examined in five dimensions and the role of shear in developing naked singularities in this space–time is discussed in details. The five-dimensional space–time is chosen in the later case because we have exact solution in closed form only in five dimension and not in any other case.

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 HIGHER DIMENSIONAL INHOMOGENEOUS DUST COLLAPSE AND COSMIC CENSORSHIP

2002 ◽  
Vol 17 (20) ◽  
pp. 2747-2747
Author(s):  
A. BEESHAM
Keyword(s):  
Black Holes ◽  
Cosmic Censorship ◽  
De Sitter Spacetime ◽  
De Sitter ◽  
Naked Singularities ◽  
Singularity Theorems ◽  
Sitter Spacetime ◽  
Higher Dimensional ◽  
Cosmic Censorship Hypothesis ◽  
Strong Curvature

The singularity theorems of general relativity predict that gravitational collapse finally ends up in a spacetime singularity1. The cosmic censorship hypothesis (CCH) states that such a singularity is covered by an event horizon2. Despite much effort, there is no rigorous formulation or proof of the CCH. In view of this, examples that appear to violate the CCH and lead to naked singularities, in which non-spacelike curves can emerge, rather than black holes, are important to shed more light on the issue. We have studied several collapse scenarios which can lead to both situations3. In the case of the Vaidya-de Sitter spacetime4, we have shown that the naked singularities that arise are of the strong curvature type. Both types of singularities can also arise in higher dimensional Vaidya and Tolman-Bondi spacetimes, but black holes are favoured in some sense by the higher dimensions. The charged Vaidya-de Sitter spacetime also exhibits both types of singularities5.

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.

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