BIANCHI IX GROUP-MANIFOLD REDUCTIONS OF GRAVITY

2005 ◽  
Vol 20 (40) ◽  
pp. 3115-3125
Author(s):  
ROMAN LINARES
Keyword(s):  
Lie Algebras ◽  
Three Dimensional ◽  
Einstein Gravity ◽  
Spin Connection ◽  
Higher Dimension ◽  
Dimensional Theory ◽  
Bianchi Ix ◽  
Group Manifold ◽  
Manifold Reduction ◽  
Kaluza Klein

We exhibit a new way to perform the group-manifold reduction of pure Einstein gravity in the vielbein formulation when the compactification group manifold is S3. The new Bianchi IX group-manifold reduction is obtained by exploiting the two three-dimensional Lie algebras that the S3 group manifold admits. As an application of the new reduction we show that there exists a domain wall solution to the lower-dimensional theory which upon uplifting to the higher-dimension turns out to be the self-dual (in the nonvanishing components of both curvature and spin connection) Kaluza–Klein monopole.

scholarly journals ASTROPHYSICAL EVIDENCE FOR AN EXTRA DIMENSION: PHENOMENOLOGY OF A KALUZA–KLEIN THEORY

2013 ◽  
Vol 28 (18) ◽  
pp. 1330013
Author(s):  
D. PUGLIESE ◽  
G. MONTANI
Keyword(s):  
Three Dimensional ◽  
Geometric Theory ◽  
Relativistic Astrophysics ◽  
Dimensional Theory ◽  
Static Vacuum ◽  
Construction Of Self ◽  
Klein Theory ◽  
The Stability ◽  
Vacuum Solutions ◽  
Kaluza Klein

In this brief review, we discuss the viability of a multi-dimensional geometrical theory with one compactified dimension. We discuss the case of a Kaluza–Klein (KK) fifth-dimensional theory, addressing the problem by an overview of the astrophysical phenomenology associated with this five-dimensional (5D) theory. By comparing the predictions of our model with the features of the ordinary (four-dimensional (4D)) Relativistic Astrophysics, we highlight some small but finite discrepancies, expectably detectible from the observations. We consider a class of static, vacuum solutions of free electromagnetic KK equations with three-dimensional (3D) spherical symmetry. We explore the stability of the particle dynamics in these spacetimes, the construction of self-gravitating stellar models and the emission spectrum generated by a charged particle falling on this stellar object. The matter dynamics in these geometries has been treated by a multipole approach adapted to the geometric theory with a compactified dimension.

scholarly journals Generalized spinning particles on $${\mathcal {S}}^2$$ in accord with the Bianchi classification

2021 ◽  
Vol 81 (3) ◽  
Author(s):  
Anton Galajinsky
Keyword(s):  
External Field ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Degrees Of Freedom ◽  
Scalar Potential ◽  
Three Dimensional ◽  
Dirac Monopole ◽  
Spinning Particles ◽  
Group Manifold ◽  
Internal Degrees Of Freedom

AbstractMotivated by recent studies of superconformal mechanics extended by spin degrees of freedom, we construct minimally superintegrable models of generalized spinning particles on $${\mathcal {S}}^2$$ S 2 , the internal degrees of freedom of which are represented by a 3-vector obeying the structure relations of a three-dimensional real Lie algebra. Extensions involving an external field of the Dirac monopole, or the motion on the group manifold of SU(2), or a scalar potential giving rise to two quadratic constants of the motion are discussed. A procedure how to build similar models, which rely upon real Lie algebras with dimensions $$d=4,5,6$$ d = 4 , 5 , 6 , is elucidated.

DIRAC FIELD IN THE EIGHT-DIMENSIONAL KALUZA-KLEIN THEORY

1992 ◽  
Vol 07 (02) ◽  
pp. 103-116 ◽  
Author(s):  
A. MACIAS ◽  
H. DEHNEN
Keyword(s):  
Higgs Mechanism ◽  
Dirac Field ◽  
Dimensional Theory ◽  
Gauge Bosons ◽  
Mixing Angles ◽  
Curved Space ◽  
Left Handed ◽  
Group Manifold ◽  
Klein Theory ◽  
Kaluza Klein

We consider the eight-dimensional Kaluza-Klein theory where the extra dimensions are a SU(2)×U(1) group manifold. A Dirac-field is coupled to the metric field. As a result we obtain that the four-dimensional theory is non-chiral and contains no-kind of Higgs mechanism to predict gauge bosons, quark and lepton masses and mixing angles, although it exhibit to possess all gauge bosons and fermionic isospin couplings for left-handed particles of a Weinberg-Salam theory in a curved space-time.

Membrane theory

2017 ◽  
Author(s):  
David J. Steigmann
Keyword(s):  
Three Dimensional ◽  
Thin Sheets ◽  
Two Dimensional ◽  
Leading Order ◽  
Membrane Theory ◽  
Dimensional Theory ◽  
Small Thickness

This chapter develops two-dimensional membrane theory as a leading order small-thickness approximation to the three-dimensional theory for thin sheets. Applications to axisymmetric equilibria are developed in detail, and applied to describe the phenomenon of bulge propagation in cylinders.

Stability and instability of some nonlinear dispersive solitary waves in higher dimension

1996 ◽  
Vol 126 (1) ◽  
pp. 89-112 ◽  
Author(s):  
Anne de Bouard
Keyword(s):  
Solitary Waves ◽  
Acoustic Waves ◽  
Vries Equation ◽  
Three Dimensional ◽  
Higher Dimension ◽  
Ion Acoustic Waves ◽  
Stability And Instability ◽  
Ion Acoustic ◽  
De Vries ◽  
The Stability

We study the stability of positive radially symmetric solitary waves for a three dimensional generalisation of the Korteweg de Vries equation, which describes nonlinear ion-acoustic waves in a magnetised plasma, and for a generalisation in dimension two of the Benjamin–Bona–Mahony equation.

Free Vibrations of Thick, Complete Conical Shells of Revolution From a Three-Dimensional Theory

2005 ◽  
Vol 72 (5) ◽  
pp. 797-800 ◽  
Author(s):  
Jae-Hoon Kang ◽  
Arthur W. Leissa
Keyword(s):  
Ritz Method ◽  
Three Dimensional ◽  
Axial Direction ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Vibration Frequencies ◽  
Shells Of Revolution ◽  
Dimensional Theory ◽  
Conical Shells ◽  
Cylindrical Coordinate

A three-dimensional (3D) method of analysis is presented for determining the free vibration frequencies and mode shapes of thick, complete (not truncated) conical shells of revolution in which the bottom edges are normal to the midsurface of the shells based upon the circular cylindrical coordinate system using the Ritz method. Comparisons are made between the frequencies and the corresponding mode shapes of the conical shells from the authors' former analysis with bottom edges parallel to the axial direction and the present analysis with the edges normal to shell midsurfaces.

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