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.     

Comment on the nonsymmetric Kaluza-Klein theory with material sources

In this paper we consider some new numerical predictions of the nonsymmetric Kaluza-Klein theory with non-zero material sources. We prove that they do not contradict any experimental data in the solar system and on the surface of a neutron star. We deal also with equations for geodesics and spin sources in the nonsymmetric Kaluza-Klein theory. We discuss some details from the nonsymmetric Kaluza-Klein theory.     

Torsion-induced gauge field doubling in Kaluza-Klein theory

Torsion in Kaluza-Klein theory is considered. It is shown that a part of the components of the torsion tensor can be identified with the components of gauge fields different from the gauge fields of the Kaluza-Klein theory, while the other part can be identified with the field strength tensor of these gauge fields. The gauge fields introduced this way acquire a geometrically induced mass. It is shown that the torsion in the internal space allows to generate any a priori given mass in Kaluza-Klein theory.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 11–15, June, 1988.In conclusion, I want to thank Yu. S. Vladimirov for a discussion of the results of this paper.     

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.     

Acceleration of particles in Einstein-Maxwell-dilaton black holes

It has recently been pointed out that, under certain conditions, the energy of particles accelerated by black holes in the center-of-mass frame can become arbitrarily high. In this paper, we study the collision of two particles in the case of four-dimensional charged nonrotating, extremal charged rotating and near-extremal charged rotating Kaluza-Klein black holes as well as the naked singularity case in Einstein-Maxwell-dilaton theory. We find that the center-of-mass energy for a pair of colliding particles is unlimited at the horizon of charged nonrotating Kaluza-Klein black holes, extremal charged rotating Kaluza-Klein black holes and in the naked singularity case.     

A note on Browne's “source function” in five-dimensional relativity

One of the postulates of the Kaluza-Klein theory is that the lines representing events should be geodesics. Recently a claim has been made that in the Jordan-Thiry version of the theory, this is not only unnecessary, but in fact contradicts experiment. It is the purpose of the present note to show that this conclusion is in error and to point out an undesirable feature of the entire Jordan-Thiry procedure.     

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 early Weyl universe

The consequences of a period of Weyl invariance in the early universe are investigated. It is argued that the natural outcome of such a period is a Kaluza-Klein style compactification of an internal space in which any time variation of the scale factor of this space is absorbed (via a Weyl transformation) into the gravitational coupling. A five-dimensional test model is shown to undergo exponential inflation of the space-time sector due to a false vacuum state of the non-metric part of the connection.     

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.     

Fifth force from Kaluza-Klein unification

We discuss the possible modification of Einstein's theory of gravitation due to the fifth force generated by the Kaluza-Klein dilaton. In particular we discuss the gravitational redshift, the deflection of light, the precession of perihelia, and the time-delay of radar echo around a spherically symmetric black hole in a 7-dimensional Kaluza-Klein unification which hasE ₂ as the internal isometry. It is shown that the long-range effect of the higher-dimensional fifth force is characterized by the dilatonic charge carried by the black hole even when it is neutral.     

Rotating cylindrically symmetric Kaluza-Klein fluid model

Kaluza-Klein field equations for stationary cylindrically symmetric fluid models in standard Einstein theory are formulated and a set of physically viable solutions is reported. This set is believed to be the first such Kaluza-Klein solutions and it includes the Kaluza-Klein counterpart of Davidson’s solution describing spacetime of a perfect fluid in rigid rotation about a regular axis.     

Generalizations of gravitational theory based on group covariance

The mathematical structure, the field equations, and fundamentals of the kinematics of generalizations of general relativity based on semisimple invariance groups are presented. The structure is that of a generalized Kaluza-Klein theory with a subgroup as the gauge group. The group manifold with its Cartan-Killing metric forms the source-free solution. The gauge fields do not vanish even in this case and give rise to additional modes of free motion. The case of the de Sitter groups is presented as an example where the gauge field is tentatively assumed to mediate a spin interaction and give rise to spin motion. Generalization to the conformal group and a theory yielding features of Dirac's large-number hypothesis are discussed. The possibility of further generalizations to include fermions are pointed out. The Kaluza-Klein theory is formulated in terms of principal fibre bundles which need not to be trivial.     

Five-dimensional Kaluza-Klein black holes coupled to massive scalar particles

Spherically symmetric solutions coupled to massive scalar particles in five-dimensional Kaluza-Klein theory are obtained. The solutions contain two event horizons. The inner horizon corresponds to the Schwarzschild black hole and the outer one is a new horizon which is produced by the massive scalar particles. It is found that the massive modes contribute an effective cosmological constant to the four-dimensional Einstein theory.     

Gauge theory of gravitation in higher-dimensional space-time and its dimensional reduction

It is shown that the Euler invariant type action of an O(d) gauge theory in d dimensions is a surface term and becomes the (d − 1)-dimensional gauge theory of gravitation. Its Kaluza-Klein dimensional reduction gives a theory which contains the ordinary Einstein gravity.     

Counting the microstates of a Kerr black hole in M theory

We show that an extremal Kerr black hole, appropriately lifted to M theory, can be transformed to a Kaluza-Klein black hole in M theory, or a D0-D6 charged black hole in string theory. Since all the microstates of the latter have recently been identified, one can exactly reproduce the entropy of an extremal Kerr black hole. We also show that the topology of the event horizon is not well defined in M theory.     

Kaluza-Klein theory from the viewpoint of gauge theory of gravity

We consider Kaluza-Klein theory based on the fiber bundle. We obtain the modified Kaluza-Klein metric as an invariant line element of a bundle. Its reduced action includes a higher derivative action in gravitation as well as a term linear inR.     

Dual doubled geometry

We probe doubled geometry with dual fundamental branes, i.e. solitons. Restricting ourselves first to solitonic branes with more than two transverse directions we find that the doubled geometry requires an effective wrapping rule for the solitonic branes which is dual to the wrapping rule for fundamental branes. This dual wrapping rule can be understood by the presence of Kaluza-Klein monopoles. Extending our analysis to supersymmetric solitonic branes with less than or equal to two transverse directions we show that such solitons are precisely obtained by applying the same dual wrapping rule to these cases as well. This extended wrapping rule cannot be explained by the standard Kaluza-Klein monopole alone. Instead, it suggests the existence of a class of generalized Kaluza-Klein monopoles in ten-dimensional string theory.     

Finsler and Kaluza-Klein gauge theories

A comparison of Kaluza-Klein and Finsler-type gauge theories is sketched. It is shown that the two can be related by a mapping between fiber spaces which is equivalent to a transformation from one representation of the gauge group to another. The Finsler theory lends itself to an interpretation of the mapping operators as being geometrically similar to Yang-Mills potentials. The equations of motion in this theory contain fields which are comparable to connections instead of curvatures. This gives a new geometrical framework for unified field theories.     

Defect branes

We discuss some general properties of “defect branes”, i.e. branes of co-dimension two, in (toroidally compactified) IIA/IIB string theory. In particular, we give a full classification of the supersymmetric defect branes in dimensions 3?D?10 as well as their higher-dimensional string and M-theory origin as branes and a set of “generalized” Kaluza-Klein monopoles. We point out a relation between the generalized Kaluza-Klein monopole solutions and a particular type of mixed-symmetry tensors. These mixed-symmetry tensors can be defined at the linearized level as duals of the supergravity potentials that describe propagating degrees of freedom. It is noted that the number of supersymmetric defect branes is always twice the number of corresponding central charges in the supersymmetry algebra.