Stability of the Kaluza-Klein wormhole soliton

We show that the electrically charged wormhole soliton solution of sourceless five-dimensional general relativity is classically stable against radial perturbations, except in the special case of a massless soliton.On leave of absence from: Département de Physique Théorique, Université de Constantine, Constantine, Algeria     

Confining the scalar field of the Kaluza-Klein wormhole soliton

The Maison five-to-three dimensional reduction, generalized to the case of five-dimensional general relativity with sources, is applied to the problem of confining the scalar field of the Kaluza-Klein wormhole soliton by a very weak perfect fluid source, without affecting the spatial geometry of this localized solution.     

The motion of Kaluza-Klein monopoles

A scheme is proposed and justified for examining the motion of the five dimensional Kaluza-Klein monopoles at low energy. The classical and quantum scattering is discussed and it is shown that for all separations and at small velocities the monopoles do not interact with one another.     

Trapping the Kaluza-Klein scalar

The Kaluza-Klein unified theory predicts the existence of a Brans-Dicke type scalar field with = 0. Solar system experiments do, however, imply that gravitational scalar fields must be suppressed either by a very weak coupling to matter ( > 500) or a self-interaction. Here the consequences of a self-interaction potential of the Kaluza-Klein scalar are investigated. By suppressing the scalar field in this way, the one-body metric reduces to the Schwarzschild solution. The cosmologies of the scalar-tensor model are, however, very different from cosmologies of Einstein's theory, since here the time evolution of the cosmic scale-factor is determined only by the initial conditions. These may be chosen so that the theory is compatible with the hypothesis of primordial nucleosynthesis.     

The equivalence principle and Kaluza-Klein monopoles

It is reported that there is a unique static and spherically symmetric classical solution to the five-dimensional Kaluza-Klein theory which carries magnetic charge as well as electric charge, and satisfies the equivalence principle.     

The Kaluza-Klein theory and four-dimensional spacetime

The conventional electromagnetism, which includes Maxwell's field equations and the Lorentz force relation, does not provide an explanation of well-known electromagnetic phenomena, such as the Aharonov-Bohm interference effect and the Meissner-Ochsenfeld effect in superconductors. In this paper, it is shown that the Kaluza-Klein five-dimensional theory suggests a simple explanation of these effects on a unified basis.     

Instability of the Kaluza-Klein vacuum

It is argued that the ground state of the Kaluza-Klein unified theory is unstable against a process of semiclassical barrier penetration. This is related to the fact that the positive energy conjecture does not hold for the Kaluza-Klein theory; an explicit counter-example is given. The reasoning presented here assumes that in general relativity one should include manifolds of non-vacuum topology. It is argued that the existence of elementary fermions (not present in the original Kaluza-Klein theory) would stabilize the Kaluza-Klein vacuum.     

The evolution of the universe from non-compact Kaluza-Klein theory

We develop a 5D mechanism, inspired by Campbells theorem, to explain the (neutral scalar field governed) evolution of the universe from an initially inflationary expansion that has a change of phase towards a decelerated expansion and thereafter evolves towards the present day observed accelerated (quintessential) expansion.Received: 4 October 2004, Published online: 23 November 2004PACS: 04.20.Jb, 11.10.Kk, 98.80.Cq     

Quantum coherence down the wormhole

It is shown that pure quantum states will appear to decay into mixed states in any theory of quantum gravity that allows the topology of spacetime to be non simply connected. The reason is that the final state may contain little closed universes. There is no way one can detect the existence of these closed universes, or measure their quantum state. This means that the part of the final state that is in asymptotically flat spacetime, appears to be in a mixed state. The loss of quantum coherence in particle collisions is estimated. It comes from a wormhole connecting two asymptotically euclidean regions. The effect would be significant for scalar particles. It would make any scalar field that was not coupled to a Yang-Mills field constant throughout spacetime. It could have an important effect on Higgs particles but the effect would be small for particles of higher spin.     

The stability of some Kaluza-Klein cosmological models

The stability is examined of some exact Kaluza-Klein cosmological solutions that possess static extra dimensions and standard Friedman behaviour for the remaining three spatial dimensions. It is shown that even when the extra dimensions are asymptotically static they produce a deviation from Friedman behaviour in the observable three spatial dimensions. A similar effect is found for models with anisotropically expanding three-spaces.     

The soliton connection

It is pointed out that the linear scattering problem for a non-linear evolution equation which admits soliton solutions may be described in terms of a linear connection on a principal SL(2, ). The equation in question is satisfied if and only if the curvature of this connection vanishes. Some other properties of the curvature are identified. The sine-Gordon, Korteweg-de Vries and modified Korteweg-de Vries equations are treated explicitly.On leave of absence. Visit supported by NSF Grant 36217 and by the Norman Foundation.     

The regularity of geodesics in impulsive pp-waves

We consider the geodesic equation in impulsive pp-wave space-times in Rosen form, where the metric is of Lipschitz regularity. We prove that the geodesics (in the sense of Carathéodory) are actually continuously differentiable, thereby rigorously justifying the ${\mathcal C}^1$ -matching procedure which has been used in the literature to explicitly derive the geodesics in space-times of this form.     

Fermions and the Kaluza-Klein monopole

This paper investigates the behavior of light charged matter in the presence of the recently constructed Kaluza-Klein monopole, starting with a mechanism for obtaining such matter in the first place. For scalars the separation of variables is identical to that for the ordinary Dirac monopole, but the geometrical picture sheds some light on the strange quantum numbers of the resulting states. Fer fermions there is a new repulsive potential, even in the lowest partial wave. This renders the hamiltonian self-adjoint without any family of extensions, in contrast to the Dirac pole. Consideration of quantum effects on long-distance physics, however, modifies the basic monopole solution and restores the usual fermion physics.     

Nonlinear perturbations of the Kaluza-Klein monopole

We consider the nonlinear stability of the Kaluza-Klein monopole viewed as the static solution of the five-dimensional vacuum Einstein equations. Using both numerical and analytical methods, we give evidence that the Kaluza-Klein monopole is asymptotically stable within the cohomogeneity-two biaxial Bianchi type-IX ansatz recently introduced by Bizoń, Chmaj, and Schmidt. We also show that for sufficiently large perturbations the Kaluza-Klein monopole loses stability and collapses to a Kaluza-Klein black hole. The relevance of our results for the stability of Bogomol'nyi-Prasad-Sommerfield states in M or string theory is briefly discussed.     

The properties and geodesics related to the NUT--Taub-like spacetime

Some properties related to the NUT--Taub-like spacetime, such as the surface of infinite red-shift, horizon, singularity and the area of the NUT--Taub-like black hole are discussed. Furthermore, the geodesics in the NUT--Taub-like spacetime are obtained in some special cases. Specifically, the circular orbits for a massive particle are derived, which can reduce to the cases of the Schwarzschild spacetime and the NUT--Taub spacetime when m^*=0 and m^*\ll M, respectively.     

The motion of charged particles in Kaluza-Klein space-time

The equations of motion for charged particles are derived from the geodesic hypothesis in the five-dimensional Kaluza-Klein theory. It is shown that even within this purely classical framework the theory does not describe low mass charged particles, and that in the background of a Kaluza-Klein monopole, the long range scalr field has striking observable consequences for electron motion, even at very large distances.