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.     

Fermions and stability in quantum Kaluza-Klein theories

The effective action for spinor fields propagating in a time-dependent Kaluza-Klein background geometry is calculated explicitly to one-loop order in an adiabatic approximation. This result is used in a stability analysis of the Candelas-Weinberg model. It is found that the “internal” space (which we choose to be an odd-dimensional sphere S_N) is stable against small, uniform oscillations only if the ratio of the number of scalar fields to the number of spinor fields is greater than a certain minimum value.It is also shown that oscillations of the internal space produce conformal gravity waves in the four-dimensional space.     

On the interbasis expansion for the Kaluza-Klein monopole system

We study the interbasis expansion of the wave-functions of the Kaluza-Klein monopole system in the parabolic coordinate system with respect to the spherical coordinate system, and vice versa. We show that the coefficients of the expansion are proportional to Clebsch-Gordan coefficients. We analyse the discrete and continuous spectrum as well, briefly discuss the feature that the (reduced) Kaluza-Klein monopole system is separable in three coordinate systems, and the fact that there are five functionally independent integrals of motion, respectively observables, a property which characterizes this system as super-integrable.     

O(4,2) dynamical symmetry of the Kaluza-Klein monopole

The o(4)/o(3,1) dynamical symmetry of the Gross-Perry-Sorkin monopole in five-dimensional Kaluza-Klein theory (which also describes the asymptotic scattering of BPS monopoles) is extended, in analogy to the Kepler problem, to the conformal algebra of o(4,2).     

Kaluza-Klein electric monopole in a six-dimensional poincaré gauge theory of gravitation

We found a solution to the six-dimensional Poincaré gauge theory that can be interpreted as the gravitational field and the electric field of an electric monopole in four-dimensional spacetime. The extra dimensions are curled up into a compact space of a size characterized by the Planck length.     

Fermions and octonions

We analyse further the algebraic structure of dependent fermions, namely ones interrelated by the vertex operator construction. They are associated with special sorts of lattice systems which are introduced and discussed. The explicit evaluation of the relevant cocycles leads to the result that the operator product expansion of the fermions is related in a precise way to one or another of the division algebras given by complex numbers, quaternions or octonions. The latter case is seen to be realised in the light cone formalism of superstring theory.     

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.     

Kaluza-Klein cosmologies

In generalized Kaluza-Klein theories the scale set by the size of the extra space-dimensions is close to the grand unification scale of supersymmetric GUT's with minimal number of Higgs supermultiplets. In view of this observation, we explore cosmologies in which the “effective” dimensionality of space depends on time. Such cosmologies are studied in higher-dimensional Jordan-Brans-Dicke theories, and in 10- and 11-dimensional supergravity. The preferential expansion of three space-like dimensions is noted in the latter theory. Cosmology in pure higher-dimensional Einstein theory, where there is no preferential expansion of three space-like dimensions, has been discussed by Chodos and Detweiler.     

q-deformed Fermions

This is a study of q-Fermions resulting from q-deformed algebra of harmonic oscillators arising from two distinct algebras. Employing the first algebra, the Fock states are constructed for the generalized Fermions obeying Pauli exclusion principle. The distribution function and other thermodynamic properties such as the internal energy and entropy are derived. Another generalization of fermions from a different q-deformed algebra is investigated which deals with q-fermions not obeying the exclusion principle. Fock states are constructed for this system. The basic numbers appropriate for this system are determined as a direct consequence of the algebra. We also establish the Jackson Derivative, which is required for the q-calculus needed to describe these generalized Fermions.     

Anomalous Fermions

Based on the recent model of quantum mechanical black holes, it is shown that at energies corresponding to length scales large compared to the Compton wavelength, fermions would exhibit a bosonization in character. It is also argued that in two and one spatial dimensions, fermions would exhibit, in addition, handedness and other features, characteristics which are otherwise suggested by conventional arguments. Finally, all these conclusions are verified and recent experimental confirmation is also cited.     

Fermions and expanding universe

The coupledDirac-Einstein equations for a homogeneous isotropic space-time forbid aclosed universe but lead to the standard cosmological model for aflat universe. Therefore only theopen universe is left as a nontrivial situation. There some of the desired cosmological effects emerge in a natural way:inflation, creation ex nihilo, etc.     

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.     

Fermions without spinors

The classical Kähler equation for an inhomogeneous differential form is analysed in some detail with respect to the physical properties of its Minkowski space solutions. Although the components of the field contain only integer representations of the Lorentz group for a physical interpretation of the quantum theory, we impose fermionic commutators. The electromagnetic interactions are identical to those of a Dirac spinor field with an extra fourfold degeneracy. Possibilities for the interpretation of the extra degrees of freedom are discussed.     

Kaluza-Klein dark matter

We propose that cold dark matter is made of Kaluza-Klein particles and explore avenues for its detection. The lightest Kaluza-Klein state is an excellent dark matter candidate if standard model particles propagate in extra dimensions and Kaluza-Klein parity is conserved. We consider Kaluza-Klein gauge bosons. In sharp contrast to the case of supersymmetric dark matter, these annihilate to hard positrons, neutrinos, and photons with unsuppressed rates. Direct detection signals are also promising. These conclusions are generic to bosonic dark matter candidates.     

On Kaluza-Klein relativity

Starting with the hypothesis that space-time is locally embedded in a (4+n)-dimensiorial flat spaceM _4+n, a geometric Kaluza-Klein theory is derived withSO(10) gauge symmetry and an additional spin-2 field represented by the second fundamental formb _ij . This quadratic form imposes a natural boundary on the complementary subspace orthogonal to the space-time, regarded as the internal space. The Gauss-Coddazi-Ricci equations are combined to produce low-energy field equations whereb _i enters as a source field. High-energy dynamics are described by a continuum of space-time perturbations inM _{4+ n} induced byb _ij , satisfying Einstein-Yang-Mills equations. The spaceM _4+n is regarded as a particular space representing the ground state of a more general theory yet to be constructed.Research supported in part by the CNPq (Brazil).     

On Kaluza-Klein theory

Assuming the compactification of 4 + K-dimensional space-time implied in Kaluza-Kleintype theories, we consider the case in which the internal manifold is a quotient space, $\text{G}\text{H}$. We develop normal mode expansions on the internal manifold and show that the conventional gravitational plus Yang-Mills theory (realizing local G symmetry) is obtained in the leading approximation. The higher terms in the expansions give rise to field theories of massive particles. In particular, for the original Kaluza-Klein 4 + 1-dimensional theory, the higher excitations describe massive, charged, purely spin-2 particles. These belong to infinite dimensional representations of an O(1,2).     

Kaluza-Klein monopoles and gauged sigma-models

We propose an effective action for the eleven-dimensional (bosonic) Kaluza-Klein monopole solution. The construction of the action requires that the background fields admit an Abelian isometry group. The corresponding sigma-model is gauged with respect to this isometry. The gauged sigma-model is the source for the monopole solution. A direct (double) dimensional reduction of the action leads to the effective action of a 10-dimensional D-6-brane (IIA Kaluza-Klein monopole). We also show that the effective action of the 10-dimensional heterotic Kaluza-Klein monopole (which is a truncation of the IIA monopole action) is T-dual to the effective action of the solitonic 5-brane. We briefly discuss the kappa-symmetric extension of our proposal and the possible role of gauged sigma-models in connection with the conjectured M-theory 9-brane.     

Kaluza-Klein theory and Machian cosmology

We interpret the 15 equations of Kaluza-Klein gravity as 10 Einstein equations, 1 wave equation and 4 equations of motion. An exact cosmological solution of the apparently empty 5D field equations describes a 4D fluid with an effective density and pressure induced by the curvature associated with the fifth dimension. The rest mass of a particle in the fluid depends on the global solution and changes slowly with time. This approach to Kaluza-Klein theory in general results in Machian cosmologies.