Kaluza–Klein reduction of a quadratic curvature model

Palatini variational principle is implemented on a five dimensional quadratic curvature gravity model, rendering two sets of equations, which can be interpreted as the field equations and the stress-energy tensor. Unification of gravity with electromagnetism and the scalar dilaton field is achieved through the Kaluza–Klein dimensional reduction mechanism. The reduced curvature invariant, field equations and the stress-energy tensor are obtained in the actual four dimensional spacetime. The structure of the interactions among the constituent fields is exhibited in detail. It is shown that the Lorentz force density naturally emerges from the reduced field equations and the equations of the standard Kaluza–Klein theory are demonstrated to be intrinsically contained in this model.     

4D Einstein equations in a 5D general Kaluza–Klein space

Based on the new point of view on space–time–matter theory developed in our paper (Bejancu, Gen Rel Grav, 2013), we obtain the $4D$ 4 D Einstein equations in a general $5D$ 5 D Kaluza–Klein space with electromagnetic potentials. In particular, we recover the $4D$ 4 D Einstein equations obtained by Wesson and Ponce de Leon (J Math Phys 33:3883, 1992) in case the electromagnetic potentials vanish identically on $\bar{M}$ M ¯ . The Riemannian horizontal connection and the $4D$ 4 D tensor calculus on $\bar{M}$ M ¯ , are the main tools in the study.     

A 5D noncompact and non Ricci flat Kaluza–Klein Cosmology

A model universe is proposed in the framework of 5D noncompact Kaluza–Klein cosmology which is not Ricci flat. The 4D part as the Robertson–Walker metric is coupled to conventional perfect fluid, and its extra-dimensional part is coupled to a dark pressure through a scalar field. It is shown that neither early inflation nor current acceleration of the 4D universe would happen if the nonvacuum states of the scalar field would contribute to 4D cosmology.     

Xanthopoulos Theorem in the Kaluza–Klein Theory

It is shown that if _AB is an exact solution of the Einstein vacuum field equations in 4 + 1 dimensions, R^ _AB = 0, and l _A is a null vector field, then _AB + l _A l _B is also an exact solution of the Einstein equations R^ _AB = 0 if and only if the perturbation l _A l _B satisfies the Einstein equations linearized about _AB. Then, making use of the Kaluza–Klein approach, it is shown that this result allows us to obtain exact solutions of the Einstein–Maxwell equations (possibly coupled to a scalar field) by solving a system of linear equations.     

4D Equations of motion and fifth force in a 5D general Kaluza–Klein space

In this paper we present a new point of view on space–time–matter (STM) theory. First, some weak points from earlier research papers on STM theory are presented. Then, we obtain in a covariant form the fully general $4D$ 4 D equations of motion for STM theory. This enables us to classify the $5D$ 5 D motions and to give a new definition of the fifth force in $4D$ 4 D physics.     

Geometrization of the Gauge Connection within a Kaluza–Klein Theory

We geometrize a generic (abelian and non-abelian) gauge coupling within the framework of a Kaluza–Klein theory, by choosing a suitable matter-field dependence on the extra coordinates. We first extend the Nöther theorem to a multidimensional spacetime, the Cartesian product of a 4-dimensional Minkowski space and a compact homogeneous manifold (whose isometries reflect the gauge symmetry). On such a “vacuum” configuration, the extra-dimensional components of the field momentum correspond to the gauge charges. Then we analyze the structure of a Dirac algebra for a spacetime with the Kaluza–Klein restrictions. By splitting the corresponding free-field Lagrangian, we show how the gauge coupling terms arise.     

On some developments in the Nonsymmetric Kaluza–Klein Theory

We consider a condition for charge confinement and gravito-electromagnetic wave solutions in nonsymmetric Kaluza–Klein theory. We consider also the influence of the cosmological constant on a static, spherically symmetric solution. We remind the reader of some fundamentals of nonsymmetric Kaluza–Klein theory and the geometrical background behind the theory. Simultaneously we make some remarks concerning a misunderstanding connected to several notions of Kaluza–Klein Theory, Einstein Unified Field Theory, geometrization and unification of physical interactions. We reconsider the Dirac field in nonsymmetric Kaluza–Klein theory.     

Stars in five-dimensional Kaluza–Klein gravity

The European Physical Journal C - We study the effect of ρ 0–γ mixing in e + e −→π + π − and its relevance for the comparison of the square modulus of...     

Boosted cylindrical magnetized Kaluza–Klein wormhole

In this work, we consider a vacuum solution of Kaluza–Klein theory with cylindrical symmetry. We investigate the physical properties of the solution as viewed in four dimensional spacetime, which turns out to be a stationary, cylindrical wormhole supported by a scalar field and a magnetic field oriented along the wormhole. We then apply a boost to the five dimensional solution along the extra dimension, and perform the Kaluza–Klein reduction. As a result, we show that the new solution is still a wormhole with a radial electric field and a magnetic field stretched along the wormhole throat.     

Stars in five-dimensional Kaluza–Klein gravity

In the five-dimensional Kaluza–Klein (KK) theory there is a well known class of static and electromagnetic-free KK-equations characterized by a naked singularity behavior, namely the Generalized Schwarzschild solution (GSS). We present here a set of interior solutions of five-dimensional KK-equations. These equations have been numerically integrated to match the GSS in the vacuum. The solutions are candidates to describe the possible interior perfect fluid source of the exterior GSS metric and thus they can be models for stars for static, neutral astrophysical objects in the ordinary (four-dimensional) spacetime.     

Geometric bounds on Kaluza–Klein masses

We point out geometric upper and lower bounds on the masses of bosonic and fermionic Kaluza–Klein excitations in the context of theories with large extra dimensions. The characteristic compactification length scale is set by the diameter of the internal manifold. Based on geometrical and topological considerations, we find that certain choices of compactification manifolds are more favored for phenomenological purposes. Received: 11 August 2000 / Revised version: 30 January 2001 / Published online: 3 May 2001     

Einstein–Rosen solutions from Kaluza–Klein theory

From a time-dependent boost-rotational symmetric vacuum solution of the Einstein Equations in five dimensions, through the Kaluza–Klein reduction the corresponding Einstein–Maxwell-dilaton solutions are obtained. The four dimensional counterpart turns out to be generalized Einstein–Rosen spacetimes representing unpolarized gravitational waves traveling in an inhomogeneous cosmology. Restricting the parameters we are able to obtain different 4D time-dependent solutions equipped with scalar and electromagnetic fields.     

Charged black holes on Kaluza–Klein bubbles

We construct exact solutions of the Einstein–Maxwell field equations in five dimensions, which describe general configurations of charged and static black holes sitting on a Kaluza–Klein bubble. More specifically we discuss the configurations describing two black holes sitting on a Kaluza–Klein bubble and also the general charged static black Saturn balanced by a Kaluza–Klein bubble. A straightforward extension of the solution-generating technique leads to a new solution describing the charged static black Saturn on the Taub-bolt instanton. We compute the conserved charges and investigate some of the thermodynamic properties of these systems.     

A Bohmian approach to the perturbations of non-linear Klein–Gordon equation

In the framework of Bohmian quantum mechanics, the Klein–Gordon equation can be seen as representing a particle with mass m which is guided by a guiding wave ?(x) in a causal manner. Here a relevant question is whether Bohmian quantum mechanics is applicable to a non-linear Klein–Gordon equation? We examine this approach for ?⁴(x) and sine-Gordon potentials. It turns out that this method leads to equations for quantum states which are identical to those derived by field theoretical methods used for quantum solitons. Moreover, the quantum force exerted on the particle can be determined. This method can be used for other non-linear potentials as well.     

Klein–Gordon equation from the path integral formalism

By using Feynman's path integral formalism in the second order for the relativistic Lagrangian for a spinless particle in a gauge field and applying the covariant derivative instead of the commonly used derivative, but without knowing the operator expressions for the momentum and energy, one can obtain the Klein–Gordon equation. Received: 9 March 2001 / Published online: 13 June 2001     

A five-dimensional perspective on the Klein–Gordon equation

We discuss the Klein–Gordon (KG) equation using a path-integral approach in 5D space–time. We explicitly show that the KG equation in flat space–time admits a consistent probabilistic interpretation with positively defined probability density. However, the probabilistic interpretation is not covariant. In the non-relativistic limit, the formalism reduces naturally to that of the Schrödinger equation. We further discuss other interpretations of the KG equation (and their non-relativistic limits) resulting from the 5D space–time picture. Finally, we apply our results to the problem of hydrogenic spectra and calculate the canonical sum of the hydrogenic atom.