Five-dimensional Kaluza-Klein Theory Research Articles

Connection dynamics of reduced five-dimensional Kaluza-Klein theory and its deparametrization

The connection dynamics of the 5-dimensional Kaluza-Klein theory reduced on 4-dimensional spacetime is obtained by performing the Hamiltonian analysis and canonical transformations. Deparametrization is achieved in the spherically symmetric model of the theory without introducing additional matter fields beyond the 5-dimensional gravity. Thus the physical time evolution and the physical spatial coordinate can be provided by the geometrical degrees of freedom in the higher dimensional spacetime.

Dyonic black holes in nonlinear electrodynamics from Kaluza–Klein theory with a Gauss–Bonnet term

Five-dimensional Kaluza–Klein theory with an Einstein–Gauss–Bonnet Lagrangian induces nonlinear corrections to the four-dimensional Maxwell equations, which however remain second-order. Although these corrections do not have effect on the purely electric or magnetic monopole solutions for pointlike charges, they affect the dyonic solutions, smoothing the electric field at the origin for positive values of the Gauss–Bonnet coupling constant. We investigate these solutions in flat space, and then extend them in the presence of a minimal coupling to gravity, obtaining exact charged black hole solutions that generalize the Reissner–Nordström metric.

Kaluza-Klein Dilatonic Matter: a Simplified Toy Model

We construct a field theoretical toy model for dilatonic matter using the five-dimensional Kaluza-Klein theory in the compactified approach. Kaluza’s ideas and basic aspects of compactification are examined in order to find an action with well-defined sectors. Through linearization of gravity sector, we obtain the propagators and interactions that allow to calculate differential cross sections at tree–level. We study some processes between photons and Kaluza-Klein particles, associated with the first massive mode of the scalar field. Finally, we make some discussion about possible applications and extensions of this model.

F(R) Gravity in a Kaluza–Klein Theory with Degenerate Metric

f(R) gravity is examined in the context of a five-dimensional Kaluza-Klein theory with degenerate metric. In this theory electromagnetism is described by two vector fields, and there is a reflection symmetry between them which unifies them with gravitation. For matter, it is shown how the Lagrangian may be any function and still generate the same equations of motion, provided that some simple conditions are satisfied. The field equations are derived, and it is found that f(R) gravity is not consistent with the reflection symmetry.

PP-wave solutions of the Weyl–Yang theory of gravity with a five-dimensional Kaluza–Klein ansatz

A Yang–Mills-type quadratic gravity model is considered in the framework of a five-dimensional Kaluza–Klein theory. Field equations and stress–energy tensors are presented in differential forms. A five-dimensional classical Kaluza–Klein metric ansatz is investigated, which consists of a four-dimensional plane-fronted gravitational wave with parallel rays as its sub-metric along with a non-trivial dilaton and gauge fields. It is found that the solution is equivalent to plane-gravitational waves in terms of a spin-0 dilaton and a spin-1 photon. Some special cases are discussed, and it is shown that only the plane-electromagnetic waves with helicity-1 states carried non-zero energy–momentum.

A doubly rotating black ring with dipole charge

We present a dipole-charged generalisation of the Pomeransky-Sen'kov black ring in five-dimensional Kaluza-Klein theory. It rotates in two independent directions, although one of the rotations has been tuned to achieve balance, so that the space-time does not contain any conical singularities. This solution was constructed using the inverse-scattering method in six-dimensional vacuum gravity. We then study various physical properties of this solution, with particular emphasis on the new features that the dipole charge introduces.

A new approach to static numerical relativity and its application to Kaluza–Klein black holes

We propose a framework for solving the Einstein equation for static and Euclidean metrics. First, we address the issue of gauge-fixing by borrowing from the Ricci-flow literature the so-called DeTurck trick, which renders the Einstein equation strictly elliptic and generalizes the usual harmonic-coordinate gauge. We then study two algorithms, Ricci-flow and Newton's method, for solving the resulting Einstein–DeTurck equation. We illustrate the use of these methods by studying localized black holes and non-uniform black strings in five-dimensional Kaluza–Klein theory, improving on previous calculations of their thermodynamic and geometric properties. We study spectra of various operators for these solutions, in particular finding the negative modes of the Lichnerowicz operator. We classify the localized solutions into two branches that meet at a minimum temperature. We find good evidence for a merger between the localized and non-uniform solutions. We also find a narrow window of localized solutions that possess negative modes yet have positive specific heat.

Quantum light-cone fluctuations in compactified spacetimes

We treat the effects of compactified spatial dimensions on the propagation of light in the uncompactified directions in the context of linearized quantum gravity. We find that the flight times of pulses can fluctuate due to modification of the graviton vacuum by the compactification. In the case of a five-dimensional Kaluza-Klein theory, the mean variation in flight time can grow logarithmically with the flight distance. This effect is in principle observable, but too small to serve as a realistic probe of the existence of extra dimensions. This differs from the conclusion reached in an earlier work. We also examine the effect of the compactification on the widths of spectral lines, and find that there is a small line narrowing effect. This effect is also small for compactification well above the Planck scale, but might serve as a test of the existence of extra dimensions.

Rotating black holes on Kaluza-Klein bubbles

Using the solitonic solution-generating techniques, we generate a new exact solution which describes a pair of rotating black holes on a Kaluza-Klein bubble as a vacuum solution in the five-dimensional Kaluza-Klein theory. We also investigate the properties of this solution. Two black holes with topology ${S}^{3}$ are rotating along the same direction even though the directions of intrinsic spin of the black holes are different. The bubble plays a role in holding two black holes. In the static case, it coincides with the solution found by Elvang and Horowitz.

Boosted black holes on Kaluza-Klein bubbles

We construct an exact stationary solution of black-hole--bubble sequence in the five-dimensional Kaluza-Klein theory by using solitonic solution-generating techniques. The solution describes two stationary black holes with topology ${S}^{3}$ on a Kaluza-Klein bubble and has a linear momentum component in the compactified direction. We call the solution boosted black holes on Kaluza-Klein bubble because it has the linear momentum. The Arnowitt-Deser-Misner mass and the linear momentum depend on the two boosted velocity parameters of black holes. In the effective four-dimensional theory, the solution has an electric charge which is proportional to the linear momentum. The solution includes the static solution found by Elvang and Horowitz. The small and the big black holes limits are investigated. The relation between the solution and the single boosted black string are considered.

Electric Redshift and Quasars

A new redshift mechanism—the electric redshift—is proposed, in accord with the five-dimensional Kaluza-Klein theory, which unifies Einsteinian general relativity and Maxwellian electromagnetic theory. It is shown that a dense, massive, and charged object can significantly shift a light ray that is emitted from the object's surface toward the red as compared with the gravitational redshift. A compact, electrically charged object with density and mass comparable to those of a neutron star can impart a redshift as great as quasars have. Therefore, if quasars are dense, massive, and electrically charged objects, their large redshifts do not imply that all quasars are extremely distant; thus, the luminosity of quasars and their association with low-redshift galaxies can be understood. This interpretation does not conflict with big bang cosmology, because the electric redshifts are negligible for normal stars, galaxies, and large-scale matter, which are not dense and electrically charged.

Casimir Effect at Finite Temperature in the Presence ofCompactified Universal Extra Dimensions

We analyse the Casimir effect for parallel plates at finite temperaturein the presence of compactified universal extra dimensions andanalytically show the thermal corrections to the effect in detail. TheCasimir effect for different sizes of universal extra dimensions isinvestigated to test the five-dimensional Kaluza–Klein theory.

Bubbles in Kaluza-Klein theories with spacelike or timelike internal dimensions

Bubbles are pointlike regular solutions of the higher-dimensional Kaluza-Klein equations that appear as naked singularities in four dimensions. We analyze all such possible solutions in five-dimensional (5D) Kaluza-Klein theory that are static and spherically symmetric. We show that they can be obtained by taking unusual choices of the parameters in the dyonic black hole solutions, and find that regularity can only be achieved if their electric charge is zero. However, they can be neutral or possess magnetic charge. We study some of their properties, both in theories where the internal dimension is spacelike as well as timelike. Since bubbles do not have horizons, they have no entropy, nor do they emit any thermal radiation, but they are, in general, nonextremal objects. In the two-timing case, it is remarkable that nonsingular massless monopoles are possible, probably signaling a new pathology of these theories. These two-timing monopoles connect two asymptotically flat regions, and matter can flow from one region to the other. We also present a $C$-type solution that describes neutral bubbles in uniform acceleration, and we use it to construct an instanton that mediates the breaking of a cosmic string by forming bubbles at its ends. The rate for this process is also calculated. Finally, we argue that a similar solution can be constructed for magnetic bubbles, and that it can be used to describe a semiclassical instability of the two-timing vacuum against production of massless monopole pairs.

Phantom scalar fields in five-dimensional Kaluza-Klein theory

The existence of a so-called "phantom" scalar field in some Riemannian spaceV4, i.e., a field in which the effective energy momentum tensorT(sf) vanishes in the five-dimensional Kaluza-Klein theory, is investigated by means of the integrability conditions for relations of the form Φ;μ;ν=kΦ,μΦ,ν+bgμν found in [6]. Phantom fields are found in homogeneous isotropic cosmological models.

KALUZA-KLEIN MAGNETIC MONOPOLES AND WORMHOLES

It is shown that a five-dimensional Kaluza-Klein theory, obtained by a “total space” conformal gauge from a four-dimensional charged dilaton gravity, can describe spacetimes supporting both magnetic monopoles and wormhole geometry.

Decay of magnetic fields in Kaluza-Klein theory.

Magnetic fields in five-dimensional Kaluza-Klein theory compactified on a circle correspond to ``twisted'' identifications of five dimensional Minkowski space. We show that a five dimensional generalisation of the Kerr solution can be analytically continued to construct an instanton that gives rise to two possible decay modes of a magnetic field. One decay mode is the generalisation of the ``bubble decay" of the Kaluza-Klein vacuum described by Witten. The other decay mode, rarer for weak fields, corresponds in four dimensions to the creation of monopole-anti-monopole pairs. An instanton for the latter process is already known and is given by the analytic continuation of the \KK\ Ernst metric, which we show is identical to the five dimensional Kerr solution. We use this fact to illuminate further properties of the decay process. It appears that fundamental fermions can eliminate the bubble decay of the magnetic field, while allowing the pair production of Kaluza-Klein monopoles.

Imitation of matter by a scalar field in five-dimensional Kaluza-Klein theory

The interpretation of the scalar field φ={ie96-1} in the five-dimensional variant of Kaluza-Klein theory is considered. It is proposed that the scalar field be considered as the generalized potential of four material velocities. It can be shown that with additional limitations on the scalar field φ the right side of the split five-dimensional Einstein equations transform to a hydrodynamic energy-momentum tensor for an ideal liquid with a limited set of equations of state. Concrete five-dimensional metrics, which are obligatorily nonstationary, are analyzed from this viewpoint.

CHANGE OF SIGNATURE AND TOPOLOGY IN A FIVE-DIMENSIONAL COSMOLOGICAL MODEL

We study the change of signature of the metric in a five-dimensional Kaluza-Klein theory applied to the description of a primordial cosmology.

Change of signature and topology in a five-dimensional cosmological model

We study the change of signature of the metric in a five-dimensional Kaluza-Klein theory applied to the description of a primordial cosmology. A model is constructed in which the one-dimensional internal space with the topology of S1 is created in the Euclidean region. We also consider the modified case, when the Gauss-Bonnet term is added to the Lagrangian. It produces the inflation of the four-dimensional Robertson-Walker metric, impossible to obtain with the Einstein-Hilbert Lagrangian.

DIRAC FIELD IN THE FIVE-DEMENSIONAL KALUZA-KLEIN THEORY WITH SCALAR FIELD

In this work we investigate the five-dimensional Kaluza-Klein theory with a scalar field contained in the metric, where a Dirac-field is coupled to the metric field. We find that in the four-dimensional theory a nontrivial ground state for the scalar field exists and therefore the mass term in the Dirac equation can be interpreted, for example, as the electron mass.