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.     

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...     

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.     

Maxwell–Chern–Simons Casimir effect at finite temperature

We will apply the Feynman path integral method to discuss the Casimir force of Maxwell–Chern–Simons gauge field at finite temperature between two parallel ideal conducting wires.     

Cosmological Kaluza–Klein branes in black brane spacetimes

We discuss the cosmological evolution of a brane in the D(>6)$D(>6)$-dimensional black brane spacetime in the context of the Kaluza–Klein (KK) braneworld scheme, i.e., to consider KK compactification on the brane. The bulk spacetime is composed of two copies of a patch of D  -dimensional black three-brane solution. The near-horizon geometry is given by AdS₅×S(D−5)${\mathit{AdS}}_5\times S^{(D-5)}$ while in the asymptotic infinity the spacetime approaches D-dimensional Minkowski. We consider the brane motion from the near-horizon region toward the spatial infinity, which induces cosmology on the brane. As is expected, in the early times, namely when the brane is located in the near-horizon region, the effective cosmology on the brane coincides with that in the second Randall–Sundrum (RS II) model. Then, the brane cosmology starts to deviate from the RS type one since the dynamics of KK compactified dimensions becomes significant. We find that the brane Universe cannot reach the asymptotic infinity, irrespectively of the components of matter on the brane.     

Remarks on gravitational interaction in Kaluza–Klein models

In these remarks, we clarify the problematic aspects of gravitational interaction in a weak-field limit of Kaluza–Klein models. We explain why some models meet the classical gravitational tests, while others do not. We show that variation of the total volume of the internal spaces generates the fifth force. This is the main reason of the problem. It happens for all considered models (linear with respect to the scalar curvature and nonlinear f(R)$f(R)$, with toroidal and spherical compactifications). We explicitly single out the contribution of the fifth force to nonrelativistic gravitational potentials. In the case of models with toroidal compactification, we demonstrate how tension (with and without effects of nonlinearity) of the gravitating source can fix the total volume of the internal space, resulting in the vanishing fifth force and consequently in agreement with the observations. It takes place for latent solitons, black strings and black branes. We also demonstrate a particular example where non-vanishing variations of the internal space volume do not contradict the gravitational experiments. In the case of spherical compactification, the fifth force is replaced by the Yukawa interaction for models with the stabilized internal space. For large Yukawa masses, the effect of this interaction is negligibly small, and considered models satisfy the gravitational tests at the same level of accuracy as general relativity.     

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.     

Experimental Test for Extra Dimensions in Kaluza–Klein Gravity

5D Kaluza–Klein gravity has several nonasymptotically flat solutions which generally, possess both electric and magnetic charges. In this paper we suggest that these solutions can act as quantum virtual handles (wormholes) in spacetime foam models. In the presence of a sufficently large, external electric and/or magnetic field it may be possible to inflate these solutions from a quantum to a classical state. This effect would lead to a possible experimental signal for higher dimensions in multidimensional gravity.     

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.     

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.     

Casimir–Polder potential for a metallic cylinder in cosmic string spacetime

Casimir–Polder potential is investigated for a polarizable microparticle in the geometry of a straight cosmic string with a metallic cylindrical shell. The electromagnetic field Green tensor is evaluated on the imaginary frequency axis. The expressions for the Casimir–Polder potential is derived in the general case of anisotropic polarizability for the both interior and exterior regions of the shell. The potential is decomposed into pure string and shell-induced parts. The latter dominates for points near the shell, whereas the pure string part is dominant near the string and at large distances from the shell. For the isotropic case and in the region inside the shell the both pure string and shell-induced parts in the Casimir–Polder force are repulsive with respect to the string. In the exterior region the shell-induced part of the force is directed toward the cylinder whereas the pure string part remains repulsive with respect to the string. At large distances from the shell the total force is repulsive.     

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.     

Kaluza–Klein modes of bulk fields in a generalized Randall–Sundrum scenario

We consider a generalised two brane Randall–Sundrum model with non-zero cosmological constant on the visible TeV brane. Massive Kaluza–Klein modes for various bulk fields namely graviton, gauge field and antisymmetric second rank Kalb–Ramond field in a such generalized Randall–Sundrum scenario are determined. The masses for the Kaluza–Klein excitations of different bulk fields are found to depend on the brane cosmological constant indicating interesting consequences in warped brane particle phenomenology.     

Dirac Field of Kaluza–Klein Theory in Weitzenböck Space

The Dirac equation in five-dimensional Weitzenbo;auck space is dervied. The effectof spin–spin interaction induced by torsion is revealed by use of the Diracequation in the weak-field situation. A comparison is made of the Dirac equationof Kaluza–Klein theory in three types of spaces. It is concluded that, from thepoint of view of simplicity, the Weitzenböck space is the most suitable one forestablishing Kaluza–Klein theory.     

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.     

Kaluza–Klein reductions and AdS/Ricci-flat correspondence

The AdS/Ricci-flat (AdS/RF) correspondence is a map between families of asymptotically locally AdS solutions on a torus and families of asymptotically flat spacetimes on a sphere. The aim of this work is to perturbatively extend this map to general AdS and asymptotically flat solutions. A prime application for such map would be the development of holography for Minkowski spacetime. In this paper we perform a Kaluza–Klein (KK) reduction of AdS on a torus and of Minkowski on a sphere, keeping all massive KK modes. Such computation is interesting on its own, as there are relatively few examples of such explicit KK reductions in the literature. We perform both KK reductions in parallel to illustrate their similarity. In particular, we show how to construct gauge invariant variables, find the field equations they satisfy, and construct a corresponding effective action. We further diagonalize all equations and find their general solution in closed form. Surprisingly, in the limit of large dimension of the compact manifolds (torus and sphere), the AdS/RF correspondence maps individual KK modes from one side to the other. In a sequel of this paper we will discuss how the AdS/RF maps acts on general linear perturbations.