scholarly journals Gravitational collapse of type II fluid in higher dimensional space-times

2002 ◽  
Vol 65 (12) ◽  
Author(s):  
S. G. Ghosh ◽  
Naresh Dadhich
Keyword(s):  
Gravitational Collapse ◽  
Dimensional Space ◽  
Type Ii ◽  
Higher Dimensional ◽  
Type Ii Fluid

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 ON THE BEKENSTEIN–HAWKING ENTROPY, NONCOMMUTATIVE BRANES AND LOGARITHMIC CORRECTIONS

2006 ◽  
Vol 21 (22) ◽  
pp. 4449-4461 ◽  
Author(s):  
AXEL KRAUSE
Keyword(s):  
String Theory ◽  
Event Horizon ◽  
Dimensional Space ◽  
Logarithmic Correction ◽  
Type Ii ◽  
Logarithmic Corrections ◽  
Higher Dimensional ◽  
M Theory ◽  
Microscopic Origin

We extend our earlier work on the possible microscopic origin of the Bekenstein–Hawking entropy to higher-dimensional space–times. The mechanism of counting chain-like states is shown to work for space–times with event horizon wrapped by a Euclidean doublet (E1,M1)+(E2,M2) of electric–magnetic dual brane pairs of type II string-theory or M-theory. Noncommutativity on the brane worldvolume enters naturally the derivation of the Bekenstein–Hawking entropy including the correct prefactor. Moreover, a logarithmic correction with prefactor 1/2 is predicted.

scholarly journals Higher-dimensional inhomogeneous composite fluids: energy conditions

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Byron P Brassel ◽  
Sunil D Maharaj ◽  
Rituparno Goswami
Keyword(s):  
Energy Conditions ◽  
Fluid Distribution ◽  
Shear Stresses ◽  
Type I ◽  
Type Ii ◽  
Four Dimensions ◽  
Higher Dimensional ◽  
Matter Fields ◽  
Inhomogeneous Composite ◽  
Type Ii Fluid

Abstract The energy conditions are studied, in the relativistic astrophysical setting, for higher-dimensional Hawking–Ellis Type I and Type II matter fields. The null, weak, dominant and strong energy conditions are investigated for a higher-dimensional inhomogeneous, composite fluid distribution consisting of anisotropy, shear stresses, non-vanishing viscosity as well as a null dust and null string energy density. These conditions are expressed as a system of six equations in the matter variables where the presence of the higher dimension $N$ is explicit. The form and structure of the energy conditions is influenced by the geometry of the $(N-2)$-sphere. The energy conditions for the higher-dimensional Type II fluid are also generated, and it is shown that under certain restrictions the conditions for a Type I fluid are regained. All previous treatments for four dimensions are contained in our work.

Celestial Tapestry

2020 ◽  
Author(s):  
Nicholas Mee
Keyword(s):  
Mathematics Curriculum ◽  
Dimensional Space ◽  
Golden Section ◽  
Single Point ◽  
Historical Context ◽  
Computer Art ◽  
Lightning Strike ◽  
Secret Message ◽  
Axiomatic Method ◽  
Higher Dimensional

Celestial Tapestry places mathematics within a vibrant cultural and historical context, highlighting links to the visual arts and design, and broader areas of artistic creativity. Threads are woven together telling of surprising influences that have passed between the arts and mathematics. The story involves many intriguing characters: Gaston Julia, who laid the foundations for fractals and computer art while recovering in hospital after suffering serious injury in the First World War; Charles Howard, Hinton who was imprisoned for bigamy but whose books had a huge influence on twentieth-century art; Michael Scott, the Scottish necromancer who was the dedicatee of Fibonacci’s Book of Calculation, the most important medieval book of mathematics; Richard of Wallingford, the pioneer clockmaker who suffered from leprosy and who never recovered from a lightning strike on his bedchamber; Alicia Stott Boole, the Victorian housewife who amazed mathematicians with her intuition for higher-dimensional space. The book includes more than 200 colour illustrations, puzzles to engage the reader, and many remarkable tales: the secret message in Hans Holbein’s The Ambassadors; the link between Viking runes, a Milanese banking dynasty, and modern sculpture; the connection between astrology, religion, and the Apocalypse; binary numbers and the I Ching. It also explains topics on the school mathematics curriculum: algorithms; arithmetic progressions; combinations and permutations; number sequences; the axiomatic method; geometrical proof; tessellations and polyhedra, as well as many essential topics for arts and humanities students: single-point perspective; fractals; computer art; the golden section; the higher-dimensional inspiration behind modern art.

scholarly journals Aperiodic Crystals

2014 ◽  
Vol 70 (a1) ◽  
pp. C1-C1 ◽  
Author(s):  
Ted Janssen ◽  
Aloysio Janner
Keyword(s):  
Physical Properties ◽  
Dimensional Space ◽  
X Rays ◽  
New Techniques ◽  
New Family ◽  
Modulated Phases ◽  
Open Questions ◽  
Higher Dimensional ◽  
Lattice Periodicity ◽  
Aperiodic Crystals

2014 is the International Year of Crystallography. During at least fifty years after the discovery of diffraction of X-rays by crystals, it was believed that crystals have lattice periodicity, and crystals were defined by this property. Now it has become clear that there is a large class of compounds with interesting properties that should be called crystals as well, but are not lattice periodic. A method has been developed to describe and analyze these aperiodic crystals, using a higher-dimensional space. In this lecture the discovery of aperiodic crystals and the development of the formalism of the so-called superspace will be described. There are several classes of such materials. After the incommensurate modulated phases, incommensurate magnetic crystals, incommensurate composites and quasicrystals were discovered. They could all be studied using the same technique. Their main properties of these classes and the ways to characterize them will be discussed. The new family of aperiodic crystals has led also to new physical properties, to new techniques in crystallography and to interesting mathematical questions. Much has been done in the last fifty years by hundreds of crystallographers, crystal growers, physicists, chemists, mineralogists and mathematicians. Many new insights have been obtained. But there are still many questions, also of fundamental nature, to be answered. We end with a discussion of these open questions.

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