A HAMILTONIAN TREATMENT OF FIVE-DIMENSIONAL KALUZA–KLEIN GRAVITY

We give a Hamiltonian treatment of 5D vacuum Kaluza–Klein theory that is unrestricted in the extra coordinate dependence. When the extra coordinate dependence is removed from the 5D metric we recover the Hamiltonian for gravity and electromagetism nonminimally coupled to a scalar field. The energies of 5D uncharged and charged soliton solutions are calculated via the Hamiltonian and are identified with the total mass. The expressions for the total mass are shown to agree with the sum of scalar and gravitational masses calculated from the scalar-tensor induced matter in 4D. A semi-classical derivation of the temperature for the uncharged solitons is calculated and it is shown that the only nontrivial member of the 5D class is the 4D Schwarzschild solution trivially embedded in 5D, and therefore the entropy obeys the one-quarter area law.

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PHYSICAL ASPECTS OF SOLITONS IN (4+1) GRAVITY

International Journal of Modern Physics D ◽

10.1142/s0218271895000430 ◽

1995 ◽

Vol 04 (05) ◽

pp. 639-659 ◽

Cited By ~ 12

Author(s):

ANDREW BILLYARD ◽

PAUL S. WESSON ◽

DIMITRI KALLIGAS

Keyword(s):

Physical Properties ◽

Extra Dimension ◽

Dimensional Case ◽

Schwarzschild Solution ◽

Circular Orbits ◽

Know How ◽

Fifth Dimension ◽

Klein Theory ◽

Limiting Case ◽

Kaluza Klein

The augmentation of general relativity’s spacetime by one or more dimensions is described by Kaluza-Klein theory and is within testable limits. Should an extra dimension be observable and significant, it would be beneficial to know how physical properties would differ from “conventional” relativity. In examining the class of five-dimensional solutions analogous to the four-dimensional Schwarzschild solution, we examine where the origin to the system is located and note that it can differ from the four-dimensional case. Furthermore, we study circular orbits and find that the 5D case is much richer; photons can have stable circular orbits in some instances, and stable orbits can exist right to the new origin in others. Finally, we derive both gravitational and inertial masses and find that they do not generally agree, although they can in a limiting case. For all three examinations, it is possible to obtain the four-dimensional results in one limiting case, that of the Schwarzschild solution plus a flat fifth dimension, and that the differences between 4D and 5D occur when the fifth dimension obtains any sort of significance.

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THE EMBEDDING OF THE SPACETIME IN FIVE DIMENSIONS

International Journal of Modern Physics A ◽

10.1142/s0217751x02013332 ◽

2002 ◽

Vol 17 (29) ◽

pp. 4287-4295

Author(s):

C. ROMERO

Keyword(s):

Differential Geometry ◽

Geometrical Structure ◽

Embedding Theorems ◽

Five Dimensions ◽

Matter Theory ◽

Klein Theory ◽

Induced Matter ◽

Kaluza Klein

We briefly review the problem of embedding the spacetime in five dimensions and discuss the geometrical structure of a non-compactified version of Kaluza-Klein theory, known as induced-matter theory. We also highlight the importance of the embedding theorems of differential geometry in the context of embedding theories and present new results which may be considered as extensions of the Campbell-Magaard theorem.

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KALUZA–KLEIN SOLITONS RE-EXAMINED

International Journal of Modern Physics D ◽

10.1142/s0218271808011973 ◽

2008 ◽

Vol 17 (02) ◽

pp. 237-256 ◽

Cited By ~ 6

Author(s):

J. PONCE DE LEON

Keyword(s):

Geometrical Approach ◽

Black String ◽

String Solution ◽

Time Coordinate ◽

Single Solution ◽

Klein Theory ◽

Zero Moment ◽

Induced Matter ◽

Kaluza Klein ◽

Owen Set

In 4 + 1 gravity the assumption that the five-dimensional metric is independent of the fifth coordinate permits the extra dimension to be either spacelike or timelike. As a consequence of this, the time coordinate and the extra coordinate are interchangeable, which in turn allows the conception of different scenarios in 4D from a single solution in 5D. In this paper, we make a thorough investigation of all possible 4D scenarios, associated with this interchange, for the well-known Kramer–Gross–Perry–Davidson–Owen set of solutions. We show that there are three families of solutions with very distinct geometrical and physical properties. They correspond to different sets of values of the parameters which characterize the solutions in 5D. The solutions of physical interest are identified on the basis of physical requirements on the induced matter in 4D. We find that only one family satisfies these requirements; the other two violate the positivity of mass-energy density. The "physical" solutions possess a lightlike singularity which coincides with the horizon. The Schwarzschild black string solution as well as the zero moment dipole solution of Gross and Perry are obtained in different limits. These are analyzed in the context of Lake's geometrical approach. We demonstrate that the parameters of the solutions in 5D are not free, as previously considered. Instead, they are totally determined by measurements in 4D — namely, by the surface gravitational potential of the astrophysical phenomena, like the Sun or other stars, modeled in Kaluza–Klein theory. This is an important result which may help in observations for an experimental/observational test of the theory.

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The Schwarzschild solution in non-Abelian Kaluza-Klein theory

Classical and Quantum Gravity ◽

10.1088/0264-9381/7/8/019 ◽

1990 ◽

Vol 7 (8) ◽

pp. 1425-1432

Author(s):

M Arik ◽

E Hizel ◽

A Mostafazadeh

Keyword(s):

Schwarzschild Solution ◽

Klein Theory ◽

Kaluza Klein

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Stabilization of test particles in induced matter Kaluza–Klein theory

Classical and Quantum Gravity ◽

10.1088/0264-9381/23/20/021 ◽

2006 ◽

Vol 23 (20) ◽

pp. 6015-6029 ◽

Cited By ~ 11

Author(s):

S Jalalzadeh ◽

B Vakili ◽

F Ahmadi ◽

H R Sepangi

Keyword(s):

Test Particles ◽

Klein Theory ◽

Induced Matter ◽

Kaluza Klein

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INDUCING CHARGES AND CURRENTS FROM EXTRA DIMENSIONS

Modern Physics Letters A ◽

10.1142/s0217732308023839 ◽

2008 ◽

Vol 23 (03) ◽

pp. 197-203 ◽

Cited By ~ 2

Author(s):

M. A. S. CRUZ ◽

F. DAHIA ◽

C. ROMERO

Keyword(s):

Extra Dimensions ◽

Maxwell Equations ◽

Dimensional Space ◽

Einstein Equations ◽

Matter Theory ◽

Klein Theory ◽

Fundamental Equations ◽

Induced Matter ◽

Minkowskian Geometry ◽

Kaluza Klein

In a particular variant of Kaluza–Klein theory, the so-called induced-matter theory (IMT), it is shown that any configuration of matter may be geometrically induced from a five-dimensional vacuum space. By using a similar approach we show that any distribution of charges and currents may also be induced from a five-dimensional space. Although in the case of IMT the geometry is Riemannian and the fundamental equations are the five-dimensional Einstein equations in vacuum, here we consider a Minkowskian geometry and five-dimensional Maxwell equations in vacuum.

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Prediction of Weinberg Angle in Discretized Kaluza-Klein Theory

VNU Journal of Science Mathematics - Physics ◽

10.25073/2588-1124/vnumap.4350 ◽

2019 ◽

Vol 35 (3) ◽

Author(s):

Nguyen Van Dat

Keyword(s):

Coupling Constant ◽

New Approach ◽

Electron Positron ◽

The Standard Model ◽

Single Coupling ◽

Klein Theory ◽

Weinberg Angle ◽

The One ◽

Collider Experiment ◽

Kaluza Klein

In Discretized Kaluza-Klein theory (DKKT) the gauge fields emerge as components of gravity with a single coupling constant. Therefore, it provide a new approach to fix the parameters of the Standard Model, and in particular the Weinberg angle. We show that in our approach using DKKT, the predicted value of Weinberg angle is exactly the one measured in the electron-positron collider experiment at Q = 91.2 GeV/c. The result is compared with the one predicted the group theoretic methods.

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On the consistency of self-consistent dimensional reduction

Canadian Journal of Physics ◽

10.1139/p86-119 ◽

1986 ◽

Vol 64 (5) ◽

pp. 641-643 ◽

Cited By ~ 2

Author(s):

G. Kunstatter ◽

D. J. Toms

Keyword(s):

Dimensional Reduction ◽

Gauge Coupling ◽

Coupling Constant ◽

Gauge Dependence ◽

Loop Approximation ◽

Self Consistent ◽

Klein Theory ◽

The One ◽

Self Consistency ◽

Kaluza Klein

Several aspects of self-consistent dimensional reduction in Kaluza–Klein theory are addressed. First, the validity of the one-loop approximation in quantum gravity with a cosmological constant is discussed. Second, a distinction is made between mathematical self-consistency and physical self-consistency. Finally, the possible gauge dependence of the physical predictions for the radius and gauge coupling constant is analyzed within the context of recent theorems concerning the gauge invariance of the one-loop gravitational effective action.

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