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.     

Solution of dirac equation in a singularity-free Kaluza-Klein cosmological model

The singularity-free solution of (4 + D) -dimensional Einstein field equations for the Kaluza-Klein cosmological model is obtained. Then the Dirac equations are solved in this model.     

A Quasi-Spherical Gravitational Wave Solution in Kaluza-Klein Theory

An exact solution of the source-free Kaluza-Klein field equations is presented. It is a 5D generalization of the Robinson-Trautman quasispherical gravitational wave with a cosmological constant. The properties of the 5D solution are briefly described.     

A Class of Kaluza-Klein Solutions Curved in 4D and Flat in 5D

We give a broad class of solutions of the Kaluza-Klein equations that is static, spherically symmetric in 3D, curved in 4D and flat in 5D. These solutions generalize others that have been applied in cosmology and astrophysics.     

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.     

Variable Modified Chaplygin Gas in Anisotropic Universe with Kaluza-Klein Metric

In this work, we have considered Kaluza-Klein Cosmology for anisotropic universe where the universe is filled with Variable Modified Chaplygin Gas (VMCG). Here we find normal scalar field ? and the self interacting potential V(?) to describe the VMCG Cosmology. We have also graphically analyzed the geometrical parameters named Statefinder Parameters in anisotropic Kaluza-Klein model. Next, we have considered a Kaluza-Klein model of interacting VMCG with dark matter in the Einstein gravity framework. Here we construct the three dimensional autonomous dynamical system of equations for this interacting model with the assumption that the dark energy and the dark matter interacts between themselves and for that we also choose the interaction term. We convert that interaction term to its dimensionless form and perform stability analysis and solve them numerically. We obtain a stable scaling solution of the equations in Kaluza-Klein model and graphically represent solutions.     

Kaluza-Klein Universe with Cosmic Strings and Bulk Viscosity in a Scalar-Tensor Theory of Gravitation

A five dimensional Kaluza-Klein space-time is considered in the frame work of a scalar-tensor theory proposed by Saez and Ballester (Phys. Lett. A 113, 467, 1985) when the source for energy momentum tensor is a bulk viscous fluid containing one dimensional strings. A barotropic equation of state for the pressure and density is assumed to get a determinate solution of the field equations. Also the bulk viscous pressure is assumed to be proportional to the energy density. The physical and kinematical properties of the model are also discussed.     

Kaluza-Klein Cosmological Model in f(R,T) Gravity

A five dimensional Kaluza-Klein space-time is considered in the presence of perfect fluid source in f(R,T) gravity proposed by Harko et al. ( [gr-qc], 2011). A cosmological model with a negative constant deceleration parameter with an appropriate choice of a function f(T) is presented. To find a determinate solution of the field equations it is assumed that scalar of expansion is proportional to the shear scalar of the space time. The physical behavior of the model is also studied.     

Spherically symmetric solutions in five-dimensional general relativity

The most general time-independent spherically symmetric (in the usual three space dimensions) solution to the five-dimensional vacuum Einstein equations is found, subject to the existence of a Killing vector in the fifth direction. The significance of these solutions is discussed within the context of a previously proposed extension of the Kaluza-Klein model in which the universe, although (4+1)-dimensional, has evolved over cosmic times into an effectively (3+l)-dimensional one.     

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.     

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.     

Early Universe with Variable Cosmological Constants in Higher Dimensional Space Time

The field equations with variable cosmological and gravitational constants are consider in the presence of perfect fluid for Kaluza-Klein type cosmological model. The exact solutions of the field equations are obtained by using the gamma law equation of state p=(γ−1)ρ in which the parameter γ depends on scale factor R. The functional form of γ(R) is used to analyze a wide range of cosmological solution at early universe for two phases in cosmic history: inflationary phase and radiation dominated phase. The corresponding physical interpretation of cosmological solution are also discussed in the framework of higher dimensional space time.     

Cosmological Kaluza-Klein monopoles

A solution of a pair of monopoles in 5D Kaluza-Klein theory without matter fields is given. The scale of the internal space is the same as that of the outer space. Its euclidean version is useful for calculating the wave function of the universe with monopoles.     

Einstein-Weyl from Kaluza-Klein

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.     

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.     

Centrifugal deformations of the gravitational kink

The Kaluza-Klein reduction of 4d conformally flat spacetimes is reconsidered. The corresponding 3d equations are shown to be equivalent to 2d gravitational kink equations augmented by a centrifugal term. For space-like gauge fields and non-trivial values of the centrifugal term the gravitational kink solutions describe a spacetime that is divided in two disconnected regions.     

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.     

Exact solutions of embedding the four-dimensional perfect fluid in a five- or higher-dimensional Einstein spacetime and the cosmological interpretations

We investigate an exact solution that describes the embedding of the four-dimensional (4D) perfect fluid in a five-dimensional (5D) Einstein spacetime. The effective metric of the 4D perfect fluid as a hypersurface with induced matter is equivalent to the Robertson–Walker metric of cosmology. This general solution shows interconnections among many 5D solutions, such as the solution in the braneworld scenario and the topological black hole with cosmological constant. If the 5D cosmological constant is positive, the metric periodically depends on the extra dimension. Thus we can compactify the extra dimension on S¹${\mathrm{S}}^1$ and study the phenomenological issues. We also generalize the metric ansatz to the higher-dimensional case, in which the 4D part of the Einstein equations can be reduced to a linear equation.     

A cosmological solution of a 5D space-time-mass gravity in vacuum

A cosmological solution is obtained in a 5D space-time-mass cosmological model by applying a homogeneous and isotropic metric, whose tensorsg _ij (i, j =0–4) are functions of both timet and massm, to the field equations in vacuum. It shows that in this theoryg ₄₄of the fifth coordinate is contracted not only by special functional form oft as in the Kaluza-Klein theory but also by that ofm. This procedure realizes the universe which evolves into a conventional 4D radiation-dominated era from a 5D vacuum era.