Extra force and extra mass from non-compact Kaluza-Klein theory in a cosmological model

Using the Hamilton-Jacobi formalism, we study extra force and extra mass in a recently introduced non-compact Kaluza-Klein cosmological model. We examine the inertial 4D mass m₀ of the inflaton field on a 4D FRW bulk in two examples. We find that m₀ has a geometrical origin and antigravitational effects on a non-inertial 4D bulk should be a consequence of the motion of the fifth coordinate with respect to the 4D bulk.Received: 1 April 2005, Revised: 13 May 2005, Published online: 28 June 2005PACS: 04.20.Jb, 11.10.Kk, 98.80.Cq     

Kaluza-Klein solutions with non-compact internal spaces

Einstein's equations with a cosmological constant in arbitrary dimensions admit solutions with unobservable internal space and flat four-dimensional space. Internal space is non-compact, has finite volume and admits a compact group of symmetries. No fine tuning of parameters is needed to obtain a vanishing four-dimensional cosmological constant.     

On the spectrum of Kaluza-Klein theories with non-compact internal spaces

We investigate the conditions under which Kaluza-Klein theories with non-compact internal spaces admit a discrete spectrum.     

Kaluza-Klein theory from the viewpoint of gauge theory of gravity

We consider Kaluza-Klein theory based on the fiber bundle. We obtain the modified Kaluza-Klein metric as an invariant line element of a bundle. Its reduced action includes a higher derivative action in gravitation as well as a term linear inR.     

An attractor universe in six-dimensional N = 2 supergravity Kaluza-Klein theory

Cosmological solutions are investigated in six-dimensional, N = 2 supergravity Kaluza-Klein theory. It is shown that the solution of (the four-dimensional Friedmann universe)×(a constant S²) is the attractor, i.e. all the cosmological solutions starting from arbitrary initial conditions (apart from the time reversal ones) approach the above space-time asymptotically without any fine-tuning. The Friedmann solution is asymptotically “unique” in the later stage of the universe in six-dimensional N = 2 supergravity.     

On Kaluza-Klein theory

Assuming the compactification of 4 + K-dimensional space-time implied in Kaluza-Kleintype theories, we consider the case in which the internal manifold is a quotient space, $\text{G}\text{H}$. We develop normal mode expansions on the internal manifold and show that the conventional gravitational plus Yang-Mills theory (realizing local G symmetry) is obtained in the leading approximation. The higher terms in the expansions give rise to field theories of massive particles. In particular, for the original Kaluza-Klein 4 + 1-dimensional theory, the higher excitations describe massive, charged, purely spin-2 particles. These belong to infinite dimensional representations of an O(1,2).     

The Kaluza-Klein theory and four-dimensional spacetime

The conventional electromagnetism, which includes Maxwell's field equations and the Lorentz force relation, does not provide an explanation of well-known electromagnetic phenomena, such as the Aharonov-Bohm interference effect and the Meissner-Ochsenfeld effect in superconductors. In this paper, it is shown that the Kaluza-Klein five-dimensional theory suggests a simple explanation of these effects on a unified basis.     

Fermion tunneling from squashed black holes in the GSdel universe and charged Kaluza-Klein space-time

This paper is devoted to the investigation the fermion tunneling radiation of squashed black holes in the G6del universe and charged Kaluza-Klein space-time. For black holes with different dimensions, establishing a set of appropriate matrices γμ for the general covariant Dirac equation plays an important role in the semi-classical tunneling method. By constructing two sets of γμ matrices, we have successfully derived the tunneling probability and Hawking temperature of the black holes.     

A two-level Kaluza-Klein theory

Let the Lie groups G and H act on the manifold P in such a way that P fibres as a principal G-bundle over P/G and as an H-bundle over P/H. We find that every pair (,) where is an H-invariant connection form in PP/G and is a G-invariant connection form in PP/H corresponds uniquely to a connection form in PP/(H×G) and a cross-section of a vector bundle with base P/(H×G).     

Kaluza-Klein bubble like structure and celestial sphere in the inflationary universe

We consider five dimensional deSitter spacetimes with a deficit angle due to the presence of a closed 2-brane and identify one dimension as an extra dimension. From the four dimensional viewpoint we can see that the spacetime has a structure similar to a Kaluza-Klein bubble of nothing, that is, four dimensional spacetime ends at the 2-brane. Since a spatial section of the full deSitter spacetime has the topology of a sphere, the boundary surface surrounds the remaining four dimensional spacetime, and can be considered as the celestial sphere. After the spacetime is created from nothing via an instanton which we describe, some four dimensional observers in it see the celestial sphere falling down, and will be in contact with a 2-brane attached on it.     

On evolution of the universe

We consider the model of evolution of the Universe where the Big Bang is regarded as an explosion of a photon superstar. The inflationary epoch is not necessary in the model. The model describes the fundamental phenomena observed: the Universe is expanding at an increasing rate, it is homogeneous and isotropic and contains no antimatter, and its metrics is almost flat.     

Kaluza-Klein theory and Machian cosmology

We interpret the 15 equations of Kaluza-Klein gravity as 10 Einstein equations, 1 wave equation and 4 equations of motion. An exact cosmological solution of the apparently empty 5D field equations describes a 4D fluid with an effective density and pressure induced by the curvature associated with the fifth dimension. The rest mass of a particle in the fluid depends on the global solution and changes slowly with time. This approach to Kaluza-Klein theory in general results in Machian cosmologies.     

Cosmological applications in Kaluza-Klein theory

The field equations of Kaluza–Klein (KK) theory have been applied in the domain of cosmology. These equations are solved for a flat universe by taking the gravitational and the cosmological constants as a function of time t. We use Taylor’s expansion of cosmological function, Λ(t), up to the first order of the time t. The cosmological parameters are calculated and some cosmological problems are discussed.     

The temperature dependent effective potential in Kaluza-Klein theory

The temperature dependent part of the effective potential to order ħ for the Kaluza-Klein theory is calculated for several examples using quantum mechanical rather than field theoretic methods.     

An orifice-string in the standard Kaluza-Klein theory

In the standard Kaluza-Klein theory an orifice solution is proposed which can be spliced into a four-dimensional Reissner-Nordstrom space-time. From the point of view of a four-dimensional observer, the obtained orifice solution can be treated as a string moving in a Wheeler superspace of four geometries.Kyrgyz State University, Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 78–81, June, 1993.