Related papers: Consistency analysis of Kaluza-Klein geometric sig…
Geometric $\sigma$-models have been defined as purely geometric theories of scalar fields coupled to gravity. By construction, these theories possess arbitrarily chosen vacuum solutions. Using this fact, one can build a Kaluza--Klein…
Unimodular theory incorporating the Kaluza-Klein construction in five dimensions leads, after reduction to four dimensions, to a new class of scalar-tensor theory. The vacuum cosmological solutions display a bouncing, non singular behavior.…
The usual approach to Kaluza-Klein considers a spacetime of the form $M_4 \times K$ and identifies the isometry group of the internal vacuum metric, $g_K^0$, with the gauge group in four dimensions. In these notes we discuss a variant…
We show that the problem of stabilization of extra dimensions in Kaluza-Klein type cosmology may be solved in a theory of gravity involving high-order curvature invariants. The method suggested (employing a slow-change approximation) can…
In this paper, I explain how gauge symmetry can be broken in a geometric way, \`{a} la Kaluza-Klein. In higher dimensional gravitational theories, one usually considers the extra dimensions to be ``frozen'' in time. However, the internal…
A new 5-dimensional Classical Unified Field Theory of Kaluza-Klein type is formulated using 2 separate scalar fields which are related in such a way as to make the 5-dimensional matter-geometry coupling parameter constant. It is shown that…
We consider the Einstein flow on a product manifold with one factor being a compact quotient of 3-dimensional hyperbolic space without boundary and the other factor being a flat torus of fixed arbitrary dimension. We consider initial data…
The transition from formulations with extra dimensions to Kaluza-Klein theories, aimed at extending the Standard Model, bears the ingredients of hidden symmetries and the Kaluza-Klein mechanism for mass generation. We explore these…
We consider Kaluza-Klein (KK) models where internal spaces are compact Einstein spaces. These spaces are stabilized by background matter (e.g., monopole form-fields). We perturb this background by a compact matter source (e.g., the system…
The unimodular version of the Kaluza-Klein theory is briefly recalled, and its projection on the $4$-dimensional spacetime is constructed. Imposing unimodularity condition on the $5$-dimensional Kaluza-Klein metric, det$g_{AB}=1$ is…
Kaluza-Klein theory is a 5-dimensional Einstein general relativity; it has the interest of describing on an equal footing the laws of gravitation and electromagnetism in a geometrically unified way. We present it in Chapter 1, and we…
In this paper we imitate the traditional method which is used customarily in the General Relativity and some mathematical literatures to derive the Gauss-Codazzi-Ricci equations for dimensional reduction. It would be more distinct…
We study a six-dimensional Kaluza-Klein theory with spacetime topology $M_4 \times S^2$ and analyze the gauge sector arising from dimensional reduction. Using normalized Killing vectors on $S^2$, we explicitly construct the reduced…
Exact solution are obtained for a homogeneous spacially isotropic cosmological model in a matter free space with or without cosmological consant for a n-dimensional Kaluza-Klein type of metric in the rest mass varying theory of gravity…
Using the language of differential forms, the Kaluza-Klein theory in 4+1 dimensions is derived. This theory unifies electromagnetic and gravitational interactions in four dimensions when the extra space dimension is compactified. Without…
An important feature of Kaluza-Klein theories is their ability to relate fundamental physical constants to the radii of higher dimensions. In previous Kaluza-Klein theory, which unifies the electromagnetic field with gravity as…
By assuming that the geometry of spacetime is uniquely determined by the energy momentum tensor of matter alone, i.e. without any interactions, enables us to construct the Lagrangian from which the metric of higher dimensional spacetime…
The purpose of this work is to demonstrate how an arbitrarily chosen background of the Universe can be made a solution of a simple geometric sigma model. Geometric sigma models are purely geometric theories in which spacetime coordinates…
Kaluza-Klein theory, by which we mean vacuum gravity in 5-dimensions, with asymptotics that are a product of a circle with Minkowski spacetime, has a variety of different static black hole solutions; localized black holes and the…
In this paper, I construct a class of everywhere regular geometric sigma models that possess bouncing solutions. Precisely, I show that every bouncing metric can be made a solution of such a model. My previous attempt to do so by employing…