Kaluza-Klein Gravity Research Articles

Fermion behavior around Sung-Won Kim wormholes in a generalized Kaluza-Klein gravity

This paper investigates the behavior of fermions in the vicinity of Sung-Won Kim wormholes (Kim S.-W., Phys. Rev. D, 53 (1996) 6889) within the framework of a generalized Kaluza-Klein gravity. The study explores the geometric and quantum implications of introducing an extra dimension into the Sung-Won Kim wormhole model. The impact of this additional dimension on the stability and traversability of the wormholes, as well as on the fermionic equations of motion, is analyzed. By examining the modified Dirac equation in this extended framework, the emergence of geometric phases and quantum holonomies is discussed, providing insights into the topological aspects of fermion dynamics in curved spacetimes.

Dark matter and dark energy from a Kaluza–Klein inspired Brans–Dicke gravity with barotropic fluid

We study the Kaluza–Klein inspired Brans–Dicke model with barotropic matter. Following from our previous work, the traditional Kaluza–Klein gravity action is introduced with an additional scalar field and 2 gauge fields. The compactification process results in a Brans–Dicke model with a dilaton coupled to the tower of scalar fields whereas a gauge field from 5-dimensional metric forms a set of mutually orthogonal vectors with 2 additional gauge fields. The barotropic matter is then introduced to complete a realistic set up. To demonstrate the analytical solutions of the model, we consider the case in which only 2 lowest modes becoming relevant for physics at low scale. After derivation, equations of motion and Einstein field equations form a set of autonomous system. The dynamical system is analysed to obtain various critical points. Interestingly, by only inclusion of barotropic matter, the model provides us the critical points which capable of determining the presences of dark matter, dark energy and phantom dark energy.

Kaluza–Klein gravity and cosmology emerging from G. Perelman’s entropy functionals and quantum geometric information flows

We elaborate on quantum geometric information flows, QGIFs, and emergent (modified) Einstein-Maxwell and Kaluza-Klein, KK, theories formulated in Lagrange-Hamilton and general covariant variables. There are considered nonholonomic deformations of Grigory Perelman's F- and W-functionals (originally postulated for Riemannian metrics) for describing relativistic geometric flows, gravity and matter field interactions, and associated statistical thermodynamic systems. We argue that the concept of Perelman W-entropy presents more general and alternative possibilities to characterize geometric flow evolution, GIF, and gravity models than the Bekenstein-Hawking and another area-holographic type entropies. Formulating the theory of QGIFs, a set of fundamental geometric, probability, and quantum concepts, and methods of computation, are reconsidered for curved spacetime and (relativistic) phase spaces. Such generalized metric-affine spaces are modeled as nonholonomic Lorentz manifolds, (co) tangent Lorentz bundles, and associated vector bundles. Using geometric and entropic and thermodynamic values, we define QGIF versions of the von Neumann entropy, relative and conditional entropy, mutual information, etc. There are analyzed certain important inequalities and possible applications of G. Perelman and related entanglement and R\'{e}nyi entropies to theories of KK QGIFs and emergent gravitational and electromagnetic interactions. New classes of exact cosmological solutions for GIFs and respective quasiperiodic evolution scenarios are elaborated. We show how classical and quantum thermodynamic values can be computed for cosmological quasiperiodic solutions and speculate how such constructions can be used for explaining structure formation in dark energy and dark matter physics.

Interacting Tsallis holographic dark energy in higher dimensional cosmology

We discuss Tsallis holographic dark energy (THDE) model in higher dimension. An interacting dark energy model is proposed with Generalized Chaplygin Gas (GCG) in the framework of Compact Kaluza-Klein gravity. It is shown that a stable configuration can be found in the present epoch which is also compatible with the observed value of the density parameter. It is noted that dark energy (DE) might have evolved from a phantom phase in the past. Nature of dark energy is found to depend on the coupling parameter of the interaction. Classical stability consideration is also found to put an upper bound on the model parameter.

Eikonal scattering in Kaluza-Klein gravity

We study eikonal scattering in the context of Kaluza-Klein theory by considering a massless scalar field coupled to Einstein’s gravity in 5D compactified to 4D on a manifold M4 × S1. We also examine various different kinematic limits of the resulting eikonal. In the ultra-relativistic scattering case we find correspondence with the time delay calculated for a massless particle moving in a compactified version of the Aichelburg-Sexl shock-wave geometry. In the case of a massless Kaluza-Klein scalar scattering off a heavy Kaluza-Klein mode a similar calculation yields the deflection angle of a massless particle in the geometry of an extremal, Q = 2M , Einstein-Maxwell-dilaton 4D black hole. We also discuss a related case in the scattering of dilatons off a large stack of D0-branes or D6-branes in dimensionally reduced D = 10 type IIA string theory.

Improved upper bounds on Kaluza–Klein gravity with current Solar System experiments and observations

As an extension of previous works on classical tests of Kaluza-Klein (KK) gravity and as an attempt to find more stringent constraints on this theory, its effects on physical experiments and astronomical observations conducted in the Solar System are studied. We investigate the gravitational time delay at inferior conjunction caused by KK gravity, and use new Solar System ephemerides and the observation of \textit{Cassini} to strengthen constraints on KK gravity by up to two orders of magnitude. These improved upper bounds mean that the fifth-dimensional space in the soliton case is a very flat extra dimension in the Solar System, even in the vicinity of the Sun.

Geometric free energy of toric AdS4/CFT3 models

We study the supersymmetric free energy of three dimensional Chern-Simons-matter theories holographically dual to AdS$_4$ times toric Sasaki-Einstein seven-manifolds. In the large $N$ limit, we argue that the square of the free energy can be written as a quartic polynomial of trial R-charges. The coefficients of the polynomial are determined geometrically from the toric diagrams. We present the coefficients of the quartic polynomial explicitly for generic toric diagrams with up to 6 vertices, and some particular diagrams with 8 vertices. Decomposing the trial R-charges into mesonic and baryonic variables, and eliminating the baryonic ones, we show that the quartic polynomial reproduces the inverse of the Martelli-Sparks-Yau volume function. On the gravity side, we explore the possibility of using the same quartic polynomial as the prepotential in the AdS gauged supergravity. Comparing Kaluza-Klein gravity and gauged supergravity descriptions, we find perfect agreement in the mesonic sector but some discrepancy in the baryonic sector.

Kaluza–Klein wormholes with the compactified fifth dimension

We consider wormhole solutions in five-dimensional Kaluza–Klein gravity in the presence of a massless ghost four-dimensional scalar field. The system possesses two types of topological nontriviality connected with the presence of the scalar field and of a magnetic charge. Mathematically, the presence of the charge appears in the fact that the S3 part of a spacetime metric is the Hopf bundle S3 →S2 with fiber S1. We show that the fifth dimension spanned on the sphere S1 is compactified in the sense that asymptotically, at large distances from the throat, the size of S1 is equal to some constant, the value of which can be chosen to lie, say, in the Planck region. Then, from the four-dimensional point of view, such a wormhole contains a radial magnetic (monopole) field, and an asymptotic four-dimensional observer sees a wormhole with the compactified fifth dimension.

Emergent Gravity/Non-linear U (1) Gauge Theory Correspondence

We revisit a five dimensional Kaluza-Klein gravity, in presence of a cosmological constant, with a renewed interest in a type IIA string theory. An irreducible space-time curvature scalar K, leading to a non-perturbation theory of emergent quantum gravity, is addressed on a D4-brane underlying a two form gauge theory. An appropriate ansatz for a two form in the non-linear U (1) gauge theory is explored to obtain a nontrivial geometric torsion in a second order formalism. The quantum geometries, underlying torsion, in a low energy limit is shown to describe an AdS5 -brane black hole in Einstein vacuum. In the limit, we analyze the non-perturbation curvature K on S1 and argue for a plausible strong-weak coupling duality between a five dimensional non-perturbation curvature theory and the 4D perturbation non-linear gauge theory.

Constraints on Kaluza–Klein gravity from Gravity Probe B

Using measurements of geodetic precession from Gravity Probe B, we constrain possible departures from Einstein's General Relativity for a spinning test body in Kaluza-Klein gravity with one additional space dimension. We consider the two known static and spherically symmetric solutions of the 5D field equations (the soliton and canonical metrics) and obtain new limits on the free parameters associated with each. The theory is consistent with observation but must be "close to 4D" in both cases.

New states of gauge theories on a circle

We study a one-dimensional large-N U(N) gauge theory on a circle as a toy model of higher dimensional Yang-Mills theories at finite temperature. To investigate the profile of the thermodynamical potential in this model, we evaluate a stochastic time evolution of several states, and find that an unstable confinement phase at high temperature does not decay to a stable deconfinement phase directly. Before it reaches the deconfinement phase, it develops to several intermediate states. These states are characterised by the expectation values of the Polyakov loop operators, which wind the temporal circle different times. We reveal that these intermediate states are the saddle point solutions of the theory, and similar solutions exist in a wide class of SU(N) and U(N) gauge theories on S 1 including QCD and pure Yang-Mills theories in various dimensions. We also consider a Kaluza-Klein gravity, which is the gravity dual of the one-dimensional gauge theory on a spatial S 1, and show that these solutions may be related to multi black holes localised on the S 1. Then we present a connection between the stochastic time evolution of the gauge theory and the dynamical decay process of a black string though the Gregory-Laflamme instability.

Dilatonic effects near naked singularities

Static spherically symmetric solutions of 4d Brans-Dicke theory include a set of naked singularity solutions. Dilatonic effects near the naked singularities result in either a shielding or an antishielding effect from intruding massive test particles. One result is that for a portion of the solution parameter space, no communication between the singularity and a distant observer is possible via massive particle exchanges. Kaluza-Klein gravity is considered as a special case.

Stars in five-dimensional Kaluza–Klein gravity

In the five-dimensional Kaluza–Klein (KK) theory there is a well known class of static and electromagnetic-free KK-equations characterized by a naked singularity behavior, namely the Generalized Schwarzschild solution (GSS). We present here a set of interior solutions of five-dimensional KK-equations. These equations have been numerically integrated to match the GSS in the vacuum. The solutions are candidates to describe the possible interior perfect fluid source of the exterior GSS metric and thus they can be models for stars for static, neutral astrophysical objects in the ordinary (four-dimensional) spacetime.

On the energy conditions in non-compact Kaluza-Klein gravity

We investigate a few cosmological solutions in non-compact five-dimensional space-time which is both Ricci-flat and conformally flat. We then study the reduced solutions on the brane in detail by applying the four energy conditions, which categorize our model in some classes. These classes of solutions can describe the universe including accelerating expansion with either abnormal matter (when matter specifically violates the strong energy condition, it is called abnormal) or a phantom model of dark energy and a Stephani universe which is dominated by abnormal matter describing vacuum energy.

Static wormholes on the brane inspired by Kaluza-Klein gravity

We use static solutions of 5-dimensional Kaluza-Klein gravity to generate several classes of static, spherically symmetric spacetimes which are analytic solutions to the equation (4)R = 0, where (4)R is the four-dimensional Ricci scalar. In the Randall & Sundrum scenario they can be interpreted as vacuum solutions on the brane. The solutions contain the Schwarzschild black hole, and generate new families of traversable Lorenzian wormholes as well as nakedly singular spacetimes. They generalize a number of previously known solutions in the literature, e.g., the temporal and spatial Schwarzschild solutions of braneworld theory as well as the class of self-dual Lorenzian wormholes.A major departure of our solutions from Lorenzian wormholes a la Morris and Thorne is that, for certain values of the parameters of the solutions, they contain three spherical surfaces (instead of one) which are extremal and have finite area. Two of them have the same size, meet the ``flare-out" requirements, and show the typical violation of the energy conditions that characterizes a wormhole throat. The other extremal sphere is ``flaring-in" in the sense that its sectional area is a local maximum and the weak, null and dominant energy conditions are satisfied in its neighborhood. After bouncing back at this second surface a traveler crosses into another space which is the double of the one she/he started in. Another interesting feature is that the size of the throat can be less than the Schwarzschild radius 2M, which no longer defines the horizon, i.e., to a distant observer a particle or light falling down crosses the Schwarzschild radius in a finite time.

Modern cosmologies from empty Kaluza-Klein solutions in 5D

We show that the empty five-dimensional solutions of Davidson-Sonnenschtein-Vozmediano, Phys. Rev. D 32 (1985) 1330, in the ``old'' Kaluza-Klein gravity, under appropriate interpretation can generate an ample variety of cosmological models in 4D, which include the higher-dimensional modifications to general relativity predicted by ``modern" versions of noncompactified 5D gravity as, e.g., induced-matter and braneworld theories. This is the first time that these solutions are investigated in a systematic way as embeddings for cosmological models in 4D. They provide a different formulation, which is complementary to the approaches used in current versions of 5D relativity.

THE EQUIVALENCE PRINCIPLE IN KALUZA–KLEIN GRAVITY

In four-dimensional general relativity the space–time outside of an isolated spherical star is described by a unique line element, which is the Schwarzschild metric. As a consequence, the "gravitational" mass and the "inertial" mass of a star are equal to each other. However, theories that envision our world as being embedded in a larger universe, with more than four dimensions, permit a number of possible non-Schwarzschild 4D exteriors, which typically lead to different masses, violating the weak equivalence principle of ordinary general relativity. Therefore, the question arises as to whether the violation of this principle, i.e. the equality of gravitational and inertial mass, is a necessary consequence of the existence of extra dimensions. In this paper, in the context of Kaluza–Klein gravity in 5D, we show that the answer to this question is negative. We find a one-parameter family of asymptotically flat non-Schwarzschild static exteriors for which the inertial and gravitational masses are equal to each other, and equal to the Deser–Soldate mass. This family is consistent with the Newtonian weak field limit as well as with the general-relativistic Schwarzschild limit. Thus, we conclude that the existence of an extra dimension, and the corresponding non-Schwarzschild exterior, does not necessarily require different masses. However, to an observer in 4D, it does affect the motion of test particles in 4D, which is a consequence of the departure from the usual (4D) law of geodesic motion.

State-relevant Maxwell’s equation from Kaluza-Klein theory

We study a five-dimensional perfect fluid coupled with Kaluza-Klein gravity. By dimensional reduction, a modified form of Maxwell's equation is obtained, which is relevant to the equation of state of the source. Since the relativistic magnetohydrodynamics and the three-dimensional formulation are widely used to study space matter, we derive the modified Maxwell's equations and relativistic magnetohydrodynamics in $3+1$ form. We then take an ideal Fermi gas as an example to study the modified effect, which can be visible under high-density or high-energy conditions, while the traditional Maxwell's equation can be regarded as a result in the low density and low temperature limit. We also indicate the possibility to test the state-relevant effect of Kaluza-Klein theory in a telluric laboratory.

PHYSICAL SINGULARITY IN THE REGULAR SPACE–TIME AND FUNDAMENTAL LENGTH

It is shown that formally regular solutions in 5D Kaluza–Klein gravity have singularities. This phenomenon is connected with the existence of a minimal length in nature. The calculation of the derivative of the G55 metric component leads to the appearance of the Dirac δ-function. In this case, the Ricci scalar becomes singular since there is a square of this derivative.

Exterior spacetime for stellar models in five-dimensional Kaluza–Klein gravity

It is well known that Birkhoff's theorem is no longer valid in theories with more than four dimensions. Thus, in these theories the effective four-dimensional picture allows the existence of different possible, non-Schwarzschild, scenarios for the description of the spacetime outside of a spherical star, contrary to four-dimensional general relativity. We investigate the exterior spacetime of a spherically symmetric star in the context of Kaluza–Klein gravity. We take a well-known family of static spherically symmetric solutions of the Einstein equations in an empty five-dimensional universe, and analyse possible stellar exteriors that are conformal to the metric induced on four-dimensional hypersurfaces orthogonal to the extra dimension. We show that all these non-Schwarzschild exteriors can continuously be matched with the interior of the star, indicating that the matching conditions at the boundary of a star do not require an unique exterior. Then, without making any assumptions about the interior solution, we prove the following statement: the condition that in the weak-field limit we recover the usual Newtonian physics singles out an unique exterior. This exterior is ‘similar’ to a Scharzschild vacuum in the sense that it has no effect on gravitational interactions. However, it is more realistic because instead of being absolutely empty, it is consistent with the existence of quantum zero-point fields (Wesson 1992 Phys. Essays, Orion 5 591). We also examine the question of how the deviation from the Schwarzschild vacuum exterior would affect the parameters of a neutron star. In the context of a model star of uniform density, we show that the general relativity upper limit M/R < 4/9 is significantly increased as we go away from the Schwarzschild vacuum exterior. We find that, in principle, the compactness limit of a star can be larger than 1/2, without being a black hole. The generality of our approach is also discussed.