scholarly journals HIGHER DIMENSIONAL VAIDYA-LIKE SPACE-TIME WITH ELECTROMAGNETIC FIELDS AND COSMOLOGICAL CONSTANT

1992 ◽  
Vol 41 (9) ◽  
pp. 1389
Author(s):  
LI JIAN-ZENG
Keyword(s):  
Cosmological Constant ◽  
Electromagnetic Fields ◽  
Space Time ◽  
Higher Dimensional

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 Exact solutions to Einstein–Maxwell theory on Eguchi–Hanson space

2017 ◽  
Vol 32 (17) ◽  
pp. 1750098 ◽  
Author(s):  
A. M. Ghezelbash ◽  
V. Kumar
Keyword(s):  
Cosmological Constant ◽  
Exact Solutions ◽  
De Sitter Space ◽  
Space Time ◽  
De Sitter ◽  
Maxwell Theory ◽  
Analytical Functions ◽  
Higher Dimensional ◽  
All Solutions ◽  
Metric Functions

In this paper, we construct explicit analytical exact solutions to the six and higher-dimensional Einstein–Maxwell theory. In all solutions, a subspace of the metric is the Eguchi–Hanson space where the metric functions are completely determined in terms of known analytical functions. Moreover, we find the solutions can be extended from nonstationary exact solutions to Einstein–Maxwell theory with cosmological constant. We show that the solutions are asymptotically expanding patches of de Sitter space–time.

scholarly journals New reflections on higher dimensional linearized gravity

2019 ◽  
Vol 65 (5 Sept-Oct) ◽  
pp. 536
Author(s):  
C. García-Quintero ◽  
A. Ortiz ◽  
And J. A. Nieto
Keyword(s):  
Quantum Gravity ◽  
Cosmological Constant ◽  
De Sitter Space ◽  
Space Time ◽  
Graviton Mass ◽  
De Sitter ◽  
Linearized Gravity ◽  
Background Space ◽  
Higher Dimensional

We make a number of remarks on linearized gravity with cosmological constant in any dimension, which we argue, can be useful in a quantum gravity framework. For this purpose we assume that the background space-time metric corresponds to the de Sitter or anti-de Sitter space. Moreover, we make some interesting observations, putting special attention on the possible scenario of  a graviton-tachyon connection, via the graviton mass and the cosmological constant correspondence. We compare our proposed formalism with the Novello and Neves approach.

MANIFOLD-SPLITTING REGULARIZATION, SELF-LINKING, TWISTING, WRITHING NUMBERS OF SPACE-TIME RIBBONS and POLYAKOV’S PROOF OF FERMI-BOSE TRANSMUTATIONS

1988 ◽  
Vol 03 (08) ◽  
pp. 1959-1979 ◽  
Author(s):  
CHIA-HSIUNG TZE
Keyword(s):  
Integral Formula ◽  
Space Time ◽  
Gauge Fields ◽  
Alternative Formulation ◽  
Complex Numbers ◽  
Closed Space ◽  
Feynman Path ◽  
Higher Dimensional ◽  
Linking Coefficient ◽  
In Memoriam

We present an alternative formulation of Polyakov’s regularization of Gauss’ integral formula for a single closed Feynman path. A key element in his proof of the D=3 fermi-bose transmutations induced by topological gauge fields, this regularization is linked here with the existence and properties of a nontrivial topological invariant for a closed space ribbon. This self-linking coefficient, an integer, is the sum of two differential characteristics of the ribbon, its twisting and writhing numbers. These invariants form the basis for a physical interpretation of our regularization. Their connection to Polyakov’s spinorization is discussed. We further generalize our construction to the self-linking, twisting and writhing of higher dimensional d=n (odd) submanifolds in D=(2n+1) space-time. Our comprehensive analysis intends to supplement Polyakov’s work as it identifies a natural path to its higher dimensional mathematical and physical generalizations. Combining the theorems of White on self-linking of manifolds and of Adams on nontrivial Hopf fibre bundles and the four composition-division algebras, we argue that besides Polyakov’s case where (d, D)=(1, 3) tied to complex numbers, the potentially interesting extensions are two chiral models with (d, D)=(3, 7) and (7, 15) uniquely linked to quaternions and octonions. In Memoriam Richard P. Feynman

Relativistic star solutions in higher-dimensional pseudospheroidal space-time

Pramana ◽  
2010 ◽  
Vol 74 (4) ◽  
pp. 513-523 ◽  
Author(s):  
P. K. Chattopadhyay ◽  
B. C. Paul
Keyword(s):  
Space Time ◽  
Relativistic Star ◽  
Higher Dimensional

SYMMETRIES OF CERTAIN PHYSICAL THEORIES AND THE JORDAN ALGEBRAS

1992 ◽  
Vol 07 (15) ◽  
pp. 3623-3637 ◽  
Author(s):  
R. FOOT ◽  
G. C. JOSHI
Keyword(s):  
Jordan Algebra ◽  
Space Time ◽  
Jordan Algebras ◽  
Bosonic String ◽  
The Other ◽  
Structure Group ◽  
Division Algebras ◽  
Hermitian Matrices ◽  
Higher Dimensional ◽  
Algebraic Framework

It is shown that the sequence of Jordan algebras [Formula: see text], whose elements are the 3 × 3 Hermitian matrices over the division algebras ℝ, [Formula: see text], ℚ and [Formula: see text], can be associated with the bosonic string as well as the superstring. The construction reveals that the space–time symmetries of the first-quantized bosonic string and superstring actions can be related. The bosonic string and the superstring are associated with the exceptional Jordan algebra while the other Jordan algebras in the [Formula: see text] sequence can be related to parastring theories. We then proceed to further investigate a connection between the symmetries of supersymmetric Lagrangians and the transformations associated with the structure group of [Formula: see text]. The N = 1 on-shell supersymmetric Lagrangians in 3, 4 and 6-dimensions with a spin 0 field and a spin 1/2 field are incorporated within the Jordan-algebraic framework. We also make some remarks concerning a possible role for the division algebras in the construction of higher-dimensional extended objects.

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.

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