We propose an extension of basic Kaluza-Klein theory in which the higher-dimensional Lorentzian manifold develops a Cauchy horizon rather than remaining globally hyperbolic as in the conventional framework. In this setting, the $U(1)$-generating Killing field, assumed to exist in Kaluza-Klein theory, undergoes a transition in its causal character, from spacelike in the globally hyperbolic region to timelike in an acausal extension through a horizon. This yields a (lower-dimensional) quotient manifold whose metric changes signature from Lorentzian to Riemannian. In this way, one observes a singular, signature changing transition emerging rather naturally from the projection of a globally smooth, even analytic, Lorentzian geometry ``up in the bundle''. This reveals a ``signature change without signature change'' scenario -- a phrasing inspired by John Wheeler -- and extends the usual Kaluza-Klein framework in a conceptually natural direction.
We consider a condition for a charge confinement and gravito-electromagnetic wave solutions in the Nonsymmetric Kaluza-Klein Theory.We consider also an influence of a cosmological constant on a static,spherically symmetric solution.We remind to the reader some fudamentals of the Nonsymmetric Kaluza-Klein Theory and a geometrcal background behind the theory.Simultaneously we give some remarks concerning misunderstanding connected to several notions of the Nonsymmetric Kaluza-Klein Theory,Einstein Unified Field Theory,geometrization and unification of physical interactions .We reconsider Dirac f…
We discuss the Kaluza-Klein reduction of spaces with (anti-)self-dual Weyl tensor and point out the emergence of the Einstein-Weyl equations for the reduction from four to three dimensions. As a byproduct we get a simple expression for the gravitational instanton density in terms of the Kaluza-Klein functions.
Kaluza-Klein reduction of conformally flat spaces is considered for arbitrary dimensions. The corresponding equations are particularly elegant for the reduction from four to three dimensions. Assuming circular symmetry leads to explicit solutions which also arise from specific two-dimensional dilaton gravity actions.
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 highe…
The stability of squashed Kaluza-Klein black holes is studied. The squashed Kaluza-Klein black hole looks like five dimensional black hole in the vicinity of horizon and four dimensional Minkowski spacetime with a circle at infinity. In this sense, squashed Kaluza-Klein black holes can be regarded as black holes in the Kaluza-Klein spacetimes. Using the symmetry of squashed Kaluza-Klein black holes, $SU(2)\times U(1)\simeq U(2)$, we obtain master equations for a part of the metric perturbations relevant to the stability. The analysis based on the master equations gives a strong evidence for th…
Although it is well known that Kaluza-Klein and Yang-Mills theories define equivalent structures on principal bundles, the general conditions for equivalence of their Lagrangians have not been explicitly stated. In this paper we address the conditions for equivalence. The formulation of these conditions is based on previous work in which the Dirac and Einstein equations were unified in a tetrad formulation of the Kaluza-Klein model. This Kaluza-Klein model is derived from mapping a bispinor field to a set of SL(2,R) x U(1) gauge potentials and a complex scalar field. (A straightforward derivat…
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 IX ansatz recently introduced in \cite{bcs}. 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 BPS states in M/String theory is briefly discussed.
This work is constructed on two main concepts: Killing-Yano symmetry and the Kaluza-Klein theory. Those concepts are reviewed in the first three chapters. In the fourth chapter firstly Killing-Yano equations of valence-2 are obtained for a general 5-dimensional metric and then reduced for the Minkowski metric. It is seen that in order to save the existence of Killing-Yano tensors with the fifth components some conditions must be satisfied
We use local counterterm prescriptions for asymptotically flat space to compute the action and conserved quantities in five-dimensional Kaluza-Klein theories. As an application of these prescriptions we compute the mass of the Kaluza-Klein magnetic monopole. We find consistent results with previous approaches that employ a background subtraction.
The Kaluza-Klein idea of extra spacetime dimensions continues to pervade current attempts to unify the fundamental forces, but in ways somewhat different from that originally envisaged. We present a modern perspective on the role of internal dimensions in physics, focussing in particular on superstring theory. A novel result is the interpretation of Kaluza-Klein string states as extreme black holes.(Talk delivered at the Oskar Klein Centenary Nobel Symposium, Stockholm, September 19-21, 1994.)
Using the SL(2,R)-duality in a dimensionally reduced spacetime in (the bosonic sector of) five-dimensional minimal supergravity, we construct general Kaluza-Klein black hole solutions which carry six independent charges, its mass, angular momentum along four dimensions, electric and magnetic charges of the Maxwell fields in addition to Kaluza-Klein electric and magnetic monopole charges.
We compute the Kaluza-Klein spectrum of the non-supersymmetric SO(3)$\,\times\,$SO(3)-invariant AdS$_4$ vacuum of 11-dimensional supergravity, whose lowest-lying Kaluza-Klein modes belong to a consistent truncation to 4-dimensional ${\cal N}=8$ supergravity and are stable. We show that, nonetheless, the higher Kaluza-Klein modes become tachyonic so that this non-supersymmetric AdS$_4$ vacuum is perturbatively unstable within 11-dimensional supergravity. This represents the first example of unstable higher Kaluza-Klein modes and provides further evidence for the AdS swampland conjecture, which …
We explore the obsevability of extra dimensions through 5-dimensional squashed Kaluza-Klein black holes residing in the Kaluza-Klein spacetime. With the expectation that the Hawking radiation reflects the 5-dimensional nature of the squashed horizon, we study the Hawking radiation of a scalar field in the squashed black hole background. As a result, we show that the luminosity of Hawking radiation tells us the size of the extra dimension, namely, the squashed Kaluza-Klein black holes open a window to extra dimensions.
We present a Kaluza-Klein reduction for the Unruh response that a brane, in an AdS bulk would experience due to its acceleration. The Unruh radiation is realised as particle production on the brane for each of the Kaluza-Klein modes. A correction, coming from the massive modes, is calculated for the standard Unruh effect in Minkowski spacetime and it is found that the response coming from these modes is exponentially suppressed.
We construct exact solutions of the Einstein-Maxwell-Dilaton field equations in five dimensions, which describe general configurations of charged and static black holes sitting on a Kaluza-Klein bubble. More specifically we discuss the configurations describing two black holes sitting on a Kaluza-Klein bubble and also the general charged static black Saturn balanced by a Kaluza-Klein bubble. A straightforward extension of the solution generating technique leads to a new solution describing the charged static black Saturn on the Taub-bolt instanton. We compute the conserved charges and investig…
A brief review is given of black holes in Kaluza-Klein theory. This includes both solutions which are homogeneous around the compact extra dimension and those which are not.
In the paper we consider some consequences of the Nonsymmetric Kaluza-Klein (Jordan-Thiry) Theory. We calculate: primordial fluctuation spectrum functions, spectral indices, and first derivatives of spectral indices.
Spherically symmetric, vacuum solutions in 5D and 7D Kaluza-Klein theory are obtained. These solutions are flux tubes with constant cross-sectional size, located between (+) and (-) Kaluza-Klein's ``electrical'' and ``magnetic'' charges disposed respectively at $\pm\infty$ and filled by constant Kaluza-Klein ``electrical'' and ``magnetic'' fields. These objects are surprisingly similar to the flux tubes which forms between two monopoles in Type-II superconductors and also the hypothesized color field flux tube that is thought to form between two quarks in the QCD vacuum.
We study evaporation process of black strings which are typical examples of Kaluza-Klein black holes. Taking into account the backreaction of the Hawking radiation, we deduce the evolution equation for the radion field. By solving the evolution equation, we find that the shape of the internal space is necked by the Hawking radiation and the amount of the deformation becomes large as the evaporation proceeds. Based on this analysis, we speculate that the Kaluza-Klein black holes would be excised from the Kaluza-Klein spacetime before the onset of the Gregory-Laflamme instability and therefore b…
We reconsider Schoen and Yau's proof of the positive mass theorem from the extra dimensional point of view, and we introduce a modified argument to prove the theorem in the Kaluza-Klein picture. We consider in this study an alternative condition to Jang's equation, which makes the argument more physically intuitive.
Using a Kaluza-Klein dimensional reduction, and further imposing a conformal Killing symmetry on the reduced metric generated by the dilaton, we show an Ansatz that yields many of the known stationary axisymmetric solutions to TMG.
S-duality of hetertotic / type II string theory compactified on a six dimensional torus requires the existence of Kaluza-Klein dyons, carrying winding charge. We identify the zero modes of the Kaluza-Klein monopole solution which are responsible for these dyonic excitations, and show that we get the correct degeneracy of dyons as predicted by S-duality. The self-dual harmonic two form on the Euclidean Taub-NUT space plays a crucial role in this construction.
Kaluza-Klein modes of fermions in a 5-dimensional toy model are considered. The number of Kaluza-Klein modes that survive after integration over extra dimensions is finite in this space. Moreover the extra dimensional piece of the kinetic term induces no mass for the higher Kaluza-Klein modes on contrary to the standard lore.
We study static vortex type solutions of pure gravity for $D \geq 4+1 $. Non-singular vortex solutions can be obtained by considering periodic Kaluza-Klein monopoles. We also show that away from the center of the vortices the space is described by the gravitational instantons derived from minimal surfaces.
There are documents which show that Wolfgang Pauli developed in 1953 the first consistent generalization of the five-dimensional theory of Kaluza, Klein, Fock and others to a higher dimensional internal space. Because he saw no way to give masses to the gauge bosons, he refrained from publishing his results formally.
Kaluza--Klein compactification in quantum field theory is analysed from the perturbation theory viewpoint. Renormalisation group analysis for compactification size dependence of the coupling constant is proposed.
In this paper we investigate the strong gravitational lensing in a charged squashed Kaluza-Klein black hole. We suppose that the supermassive black hole in the galaxy center can be considered by a charged squashed Kaluza-Klein black hole and then we study the strong gravitational lensing theory and estimate the numerical values for parameters and observables of it. We explore the effects of the scale of extra dimension $ρ_0$ and the charge of black hole $ρ_q$ on these parameters and observables.
Based on the equivalence between a gauge theory for the translation group and general relativity, a teleparallel version of the non-abelian Kaluza-Klein theory is constructed. In this theory, only the fiber-space turns out to be higher-dimensional, spacetime being kept always four-dimensional. The resulting model is a gauge theory that unifies, in the Kaluza-Klein sense, gravitational and gauge fields. In contrast to the ordinary Kaluza-Klein models, this theory defines a natural length-scale for the compact sub-manifold of the fiber space, which is shown to be of the order of the Planck lengt…
In this work, we study the generalized Klein-Gordon oscillator with interactions on a curved background within the Kaluza-Klein theory. We solve the generalized Klein-Gordon oscillator in the cosmic string space-time with a linear scalar potential and obtain the energy eigenvalue and corresponding eigenfunction. We show that the energy spectrum depends on the global parameters characterizing the space-time and the confining potential parameter. We also solve the generalized Klein-Gordon oscillator in a magnetic cosmic string background in the Kaluza-Klein theory with a linear scalar potential …
Exceptional field theories yield duality covariant formulations of supergravity. We show that they provide a highly efficient tool to compute the Kaluza-Klein mass spectra associated to compactifications around various background geometries relevant for string theory and holographic applications. This includes geometries with little to no remaining symmetries, hardly accessible to standard methods. As an illustration, we work out the masses of some higher Kaluza-Klein multiplets around warped geometries corresponding to some prominent ${\cal N} = 2$ supersymmetric AdS vacua in maximal supergra…
A free test particle in 5-dimensional Kaluza-Klein spacetime will show its electricity in the reduced 4-dimensional spacetime when it moves along the fifth dimension. In the light of this observation, we study the coupling of a 5-dimensional dust field with the Kaluza-Klein gravity. It turns out that the dust field can curve the 5-dimensional spacetime in such a way that it provides exactly the source of the electromagnetic field in the 4-dimensional spacetime after the dimensional reduction.
In previous paper, we present an SO(3) Wu-Yang-like Kaluza-Klein dyon so- lution satisfies the Einstein equation in the seven-dimensional spacetimes. In this note, we will show an alternative approach using an orthonormal frame, the Cartan's structure equations, and calculating the affine spin connection one-form,curvature tensor and Ricci tensor. The results from these two different methods are coincident.
We study the hydrodynamics of relativistic fluids with several conserved global charges (i.e., several species of particles) by performing a Kaluza-Klein dimensional reduction of a neutral fluid on a N-torus. Via fluid/gravity correspondence, this allows us to describe the long-wavelength dynamics of black branes with several Kaluza-Klein charges. We obtain the equation of state and transport coefficients of the charged fluid directly from those of the higher-dimensional neutral fluid. We specialize these results for the fluids dual to Kaluza-Klein black branes.
We construct a class of stationary and axisymmetric solutions to the 5D Einstein-Maxwell-dilaton gravity, which describe configurations of charged rotating black objects with Kaluza-Klein asymptotics. The solutions are constructed by uplifting a vacuum seed solution to six dimensions, performing a boost, and a subsequent circle reduction. We investigate the physical properties of the charged solutions, and obtain their general relations to the properties of the vacuum seed. We also derive the gyromagnetic ratio and the Smarr-like relations. As particular cases we study three solutions, which d…
We calculate dimensional reduction of gravitational flux tube solutions in the scheme of Kaluza-Klein theory. The fifth dimension is compacified to a region of Planck size. Assuming the width of the tube to be also Planck size we obtain string-like object with physical fields originated from an initial 5D metric. The dynamics of these fields is inner one.
We consider a Kaluza-Klein vacuum solution which is closely related to the Gross-Perry-Sorkin (GPS) magnetic monopole. The solution can be obtained from the Euclidean Taub-NUT solution with an extra compact fifth spatial dimension within the formalism of Kaluza-Klein reduction. We study its physical properties as appearing in $(3+1)$ spacetime dimensions, which turns out to be a static magnetic monopole. We then boost the GPS magnetic monopole along the extra dimension, and perform the Kaluza-Klein reduction. The resulting four-dimensional spacetime is a rotating stationary system, with both e…
Relying upon the equivalence between a gauge theory for the translation group and general relativity, a teleparallel version of the original Kaluza-Klein theory is developed. In this model, only the internal space (fiber) turns out to be five dimensional, spacetime being kept always four dimensional. A five-dimensional translational gauge theory is obtained which unifies, in the sense of Kaluza-Klein theories, gravitational and electromagnetic interactions.
The dynamics of a string near a Kaluza-Klein black hole are studied. Solutions to the classical string equations of motion are obtained using the world sheet velocity of light as an expansion parameter. The electrically and magnetically charged cases are considered separately. Solutions for string coordinates are obtained in terms of the world-sheet coordinate $τ$. It is shown that the Kaluza-Klein radius increases/decreases with $τ$ for electrically/magnetically charged black hole.
We propose a new nonabelian Kaluza-Klein dyon solution in the seven-dimensional spacetimes. This is a Wu-Yang-like Kaluza-Klein dyon. The dyonic metric is spherically symmetric, two spherical coordinate systems are used, and the metric admits SO(3) Killing vectors. It can be verified that the Einstein equation is satisfied in seven-dimensional spacetimes. The stress-energy tensor of the Yang-Mills field in Einstein equation is derived from Ricci tensor automatically, not put by hand from outside. The Ricci scalar curvature \bar{R} vanishes. The four-dimensional part of the dyonic metric is jus…
We investigate the geodetic precession effect of a parallely transported spin-vector along a circular geodesic in the five-dimensional squashed Kaluza-Klein black hole spacetime. Then we derive the higher-dimensional correction of the precession angle to the general relativity. We find that the correction is proportional to the square of (size of extra dimension)/(gravitational radius of central object).
In this work, we consider a vacuum solution of Kaluza-Klein theory with cylindrical symmetry. We investigate the physical properties of the solution as viewed in four dimensional spacetime, which turns out to be a stationary, cylindrical wormhole supported by a scalar field and a magnetic field oriented along the wormhole.We then apply a boost to the five dimensional solution along the extra dimension, and perform the Kaluza-Klein reduction. As a result, we show that the new solution is still a wormhole with a radial electric field and a magnetic field stretched along the wormhole throat.
In this paper we study a Kaluza-Klein bubble-type spacetime with a magnetic field first obtained by Sarbach and Lehner in 2005. It is shown that this solution can be derived via a Harrison transformation of a vacuum Kaluza-Klein bubble, and its physical and geometrical quantities are determined. For certain ranges of the magnetic field parameter, this solution carries negative mass. Furthermore, for a given value of magnetic flux, there exist two branches of solutions, and the branch with lower mass is thermodynamically favoured. In light of these properties we interpret the spacetime as anoth…
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.
We discuss Hawking radiation from a five-dimensional squashed Kaluza-Klein black hole on the basis of the tunneling mechanism. A simple manner, which was recently suggested by Umetsu, is possible to extend the original derivation by Parikh and Wilczek to various black holes. That is, we use the two-dimensional effective metric, which is obtained by the dimensional reduction near the horizon, as the background metric. By using same manner, we derive both the desired result of the Hawking temperature and the effect of the back reaction associated with the radiation in the squashed Kaluza-Klein b…
The solution of the 5D Kaluza-Klein's theory is obtained. This solution is a Lorentzian wormhole between two event horizons. It is shown that this solution can sew with (4D Reissner-Nordström's solution + Maxwell's electrical field) on the event horizon. Such construction is composite wormhole connecting two asymptotically flat region. From the viewpoint of infinite observer this wormhole is an electrical charge. According to J. Wheeler terminology this is "charge without charge".
We investigate solutions of the Klein-Gordon equation in a class of five dimensional geometries presenting the same symmetries and asymptotic structure as the Gross-Perry-Sorkin monopole solution. Apart from globally regular metrics, we consider also squashed Kaluza-Klein black holes backgrounds.
We study motions of photons in an unmagnetized cold homogeneous plasma medium in the five-dimensional charged static squashed Kaluza-Klein black hole spacetime. In this case, a photon behaves as a massive particle in a four-dimensional spherically symmetric spacetime. We consider the light deflection by the squashed Kaluza-Klein black hole surrounded by the plasma in a weak-field limit. We derive corrections of the deflection angle to general relativity, which are related to the size of the extra dimension, the charge of the black hole and the ratio between the plasma and the photon frequencie…
This is a pedagogical introduction to original Kaluza-Klein theory and its salient features. Most of the technical calculations are given in detail and the nature of gravitons is discussed.
A theory in which 16-dimensional curved Clifford space (C-space) provides a realization of Kaluza-Klein theory is investigated. No extra dimensions of spacetime are needed: "extra dimensions" are in C-space. It is shown that the covariant Dirac equation in C-space contains Yang-Mills fields of the U(1)xSU(2)xSU(3) group as parts of the generalized spin connection of the C-space.
In phenomenological models with extra dimensions there is a natural symmetry group associated to a brane universe, -- the group of rotations of normal bundle of the brane. We consider Kaluza-Klein gauge fields corresponding to this group and show that they can be localized on the brane in models with warped extra dimensions. These gauge fields are coupled to matter fields which have nonzero rotation moment around the brane. In a particular example of a four-dimensional brane embedded into six-dimensional asymptotically anti-deSitter space, we calculate effective four-dimensional coupling const…
We study the scalar perturbation in the background of the charged Kaluza-Klein black holes with squashed horizons. We find that the position of infinite discontinuities of the heat capacities can be reflected in quasinormal spectrum. This shows the possible non-trivial relation between the thermodynamical and dynamical properties of black holes.
We construct an exact solution describing the collision of two Kaluza-Klein "bubbles of nothing" in 3+1 dimensions. When the bubbles collide, a curvature singularity forms which is hidden inside an event horizon. However, unlike the formation of ordinary black holes, in this case the spacetime resembles the entire maximally extended Schwarzschild solution. We also point out that there are inequivalent bubbles that can be constructed from Kerr black holes.
Palatini variational principle is implemented on a five dimensional quadratic curvature gravity model, rendering two sets of equations which can be interpreted as the field equations and the stress-energy tensor. Unification of gravity with electromagnetism and the scalar dilaton field is achieved through the Kaluza-Klein dimensional reduction mechanism. The reduced curvature invariant, field equations and the stress-energy tensor in four dimensional spacetime are obtained. The structure of the interactions among the constituent fields is exhibited in detail. It is shown that the Lorentz force…
It is well known that the Kaluza-Klein monopole of Sorkin, Gross and Perry can be obtained from the Euclidean Taub-NUT solution with an extra compact fifth spatial dimension via Kaluza-Klein reduction. In this paper we consider Taub-NUT-like solutions of the vacuum Einstein field equations, with or without cosmological constant, in five dimensions and higher, and similarly perform Kaluza-Klein reductions to obtain new magnetic KK brane solutions in higher dimensions, as well as further sphere reductions to magnetic monopoles in four dimensions. In six dimensions we also employ spatial and time…
We studied the Raychaudhuri equation in Kaluza-Klein space-time. We derived an additional term that is solely due to Kaluza-Klein's unification. This term affects the defocus of world lines near the singularity of charged higher-dimensional black holes. We illustrated it with a static higher-dimensional black hole generated by Einstein-Maxwell equations. It has been found that the term derived modifies the repulsive effect of kaluza Klein scalar on world lines. We proved some mathematical theorems which give an insight into the interior of the black holes.
The parametrized post Newtonian formalism for 5-dimensional metric theories with a compact extra dimension is developed. The relation of the 5-dimensional and 4-dimensional formulations is then analyzed, in order to compare the higher dimensional theories of gravity with experiments. It turns out that the value of post Newtonian parameter $γ$ in the reduced 5-dimensional Kaluza-Klein theory is two times smaller than that in 4-dimensional general relativity. The departure is due to the existence of an extra dimension in the Kaluza-Klein theory. Thus the confrontation between the reduced 4-dimen…
We study the spectrum of gravitational waves generated from inflation in the Randall-Sundrum braneworld. Since the inflationary gravitational waves are of quantum-mechanical origin, the initial configuration of perturbations in the bulk includes Kaluza-Klein quantum fluctuations as well as fluctuations in the zero mode. We show, however, that the initial fluctuations in Kaluza-Klein modes have no significant effect on the late time spectrum, irrespective of the energy scale of inflation and the equation of state parameter in the post-inflationary stage. This is done numerically, using the Wron…
We consider a Kaluza-Klein string solution of five-dimensional spacetime. We study its physical properties as appearing in (3+1) spacetime. This metric embraces several different aspects of solutions. The two most notable examples are the dipole and the boosted dipole solutions. In general, the 4D metric is a rotating stationary solution with both electric and magnetic fields. The extension to the Kaluza-Klein dipole soliton solution is briefly discussed.
In the No-boundary Universe with $d=11$ supergravity, under the $S_n \times S_{11-n}$ Kaluza-Klein ansatz, the only seed instanton for the universe creation is a $S_7 \times S_4$ space. It is proven that for the Freund-Rubin, Englert and Awada-Duff-Pope models the macroscopic universe in which we are living must be 4- instead of 7-dimensional without appealing to the anthropic principle.
