Kaluza-Klein Manifolds Research Articles

Evanescent ergosurface instability

Some exotic compact objects possess evanescent ergosurfaces: timelike submanifolds on which a Killing vector field, which is timelike everywhere else, becomes null. We show that any manifold possessing an evanescent ergosurface but no event horizon exhibits a linear instability of a peculiar kind: either there are solutions to the linear wave equation which concentrate a finite amount of energy into an arbitrarily small spatial region, or the energy of waves measured by a stationary family of observers can be amplified by an arbitrarily large amount. In certain circumstances we can rule out the first type of instability. We also provide a generalisation to asymptotically Kaluza-Klein manifolds. This instability bears some similarity with the "ergoregion instability" of Friedman, and we use many of the results from the recent proof of this instability by Moschidis.

Vacuum instability in Kaluza–Klein manifolds

The purpose of this work in to analyze particle creation in spaces with extra dimensions. We consider, in particular, a massive scalar field propagating in a Kaluza–Klein manifold subject to a constant electric field. We compute the rate of particle creation from vacuum by using techniques rooted in the spectral zeta function formalism. The results we obtain show explicitly how the presence of the extra-dimensions and their specific geometric characteristics, influence the rate at which pairs of particles and anti-particles are generated.

New asymptotic Anti-de Sitter solution with a timelike extra dimension in 5D relativity

In 5D relativity, the usual 4D cosmological constant is determined by the extra dimension. If the extra dimension is spacelike, one can get a positive cosmological constant Λ and a 4D de Sitter (dS) space. In this paper we present that, if the extra dimension is timelike oppositely, the negative Λ will be emerged and the induced 4D space will be an asymptotic Anti-de Sitter (AdS). Under the minimum assumption, we solve the Kaluza–Klein equation RAB=0 in a canonical system and obtain the AdS solution in a general case. The result shows that an AdS space is induced naturally from a Kaluza–Klein manifold on a hypersurface (brane). The Lagrangian of test particle indicates the equation of motion can be geodesics if the 4D metric is independent of extra dimension. The causality is well respected because it is appropriately defined by a null higher dimensional interval. In this 5D relativity, the holographic principle can be used safely because the brane is asymptotic Euclidean AdS in the bulk. We also explore some possible holographic duality implications about the field/operator correspondence and the two-points correlation functions.

Particles and fields within a unification scheme

We discuss properties of particles and fields in a multi-dimensional space-time, where the geometrization of gauge interactions can be performed. For instance, in a 5-dimensional Kaluza-Klein manifold we argue that the motion of charged spinning bodies is obtain in a Papapetrou-like formulation. As far as spinors are concerned, we outline how the gauge coupling can be recognized by a proper dependence on extra-coordinates and by the dimensional reduction procedure.

A second-order variational principle for the Lorentz force equation: conjugacy and bifurcation

We give the notion of a conjugate instant along a solution of the relativistic Lorentz force equation (LFE). Electromagnetic conjugate instants are defined as zeros of solutions of the linearized LFE with fixed value of the charge-to-mass ratio; equivalently, we show that electromagnetic conjugate points are the critical values of the corresponding electromagnetic exponential map. We prove a second-order variational principle relating every solution of the LFE to a canonical lightlike geodesic in a Kaluza–Klein manifold, whose metric is defined using the value of the charge-to-mass ratio. Electromagnetic conjugate instants correspond to conjugate points along the lightlike geodesic, and therefore they are isolated; based on such correspondence and on a recent result of bifurcation for light rays, we prove a bifurcation result for solutions of the LFE in the exact case.

Geometric Origin of Physical Constants in a Kaluza-Klein Tetrad Model

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 dimensionless components of a Kaluza-Klein metric, i) all fields have the same physical dimensions, ii) the Lagrangian has no explicit dependence on any physical constants except mass, and hence iii) all physical constants in the field equations except for mass originate from geometry. While it seems natural in Kaluza-Klein theory to add fermion fields by defining higher-dimensional bispinor fields on the Kaluza-Klein manifold, these Kaluza-Klein theories do not satisfy conditions (i), (ii), and (iii). In this paper, we show how conditions (i), (ii), and (iii) can be satisfied by including bispinor fields in a tetrad formulation of the Kaluza-Klein model, as well as in an equivalent teleparallel model. This demonstrates an unexpected feature of Dirac's bispinor equation, since conditions (i), (ii), (iii) imply a special relation among the terms in the Kaluza-Klein or teleparallel Lagrangian that would not be satisfied in general.

Measuring a Kaluza-Klein radius smaller than the Planck length

Hestenes has shown that a bispinor field on a Minkowski space-time is equivalent to an orthonormal tetrad of one-forms together with a complex scalar field. More recently, the Dirac and Einstein equations were unified in a tetrad formulation of a Kaluza-Klein model which gives precisely the usual Dirac-Einstein Lagrangian. In this model, Dirac's bispinor equation is obtained in the limit for which the radius of higher compact dimensions of the Kaluza-Klein manifold becomes vanishingly small compared with the Planck length. For a small but finite radius, the Kaluza-Klein model predicts the velocity splitting of single fermion wave packets. That is, the model predicts that a single fermion wave packet will split into two wave packets with slightly different group velocities. The observation of such wave packet splits would determine the size of the Kaluza-Klein radius. If wave packet splits were not observed in experiments with currently achievable accuracies, the Kaluza-Klein radius would be bounded by at most ${10}^{\ensuremath{-}25}$ times the Planck length.

A new derivation of the tensor form of Dirac's equation

In this paper we show that the classical Einstein-Yang-Mills-Dirac equations for the gravitational, W boson, and fermion fields can all be derived from a tetrad of vector fields on a Kaluza-Klein manifold.

Coupling constant ratios from the Kaluza-Klein manifolds Mpqr

Abstract Seven-dimensional compact manifolds M pqr with isometry group SU(3) × SU(3) × U(1), are used to calculate ratios of gauge coupling constants, in the framework of Kaluza-Klein theory.

PCT invariance and the orientability of Kaluza-Klein manifolds

The O(2) gauge theory associated with a non-product S 1 fibre bundle over a four-dimensional base space is investigated. Upon demonstrating explicitly the relationship between global charge conservation and the orientability of the fibre bundle space, we discuss restrictions to be imposed upon the structures of five-dimensional manifolds that are to underlie physically realistic spacetimes.