Five-dimensional Spacetime Research Articles

Branes with asymmetric geometries in the bulk and localization of scalar fields

The model of a domain wall (“thick brane”) in a noncompact five-dimensional space-time with asymmetric geometries of AdS type aside the brane is proposed. This model is generated by fermion self-interaction in the presence of gravity. Asymmetric geometries in the bulk are provided by a space defect in the scalar field potential and the related defect of cosmological constant. The possibility of localization of scalar modes on such “thick branes” is studied. Bibliography: 21 titles.

Non-Abelian Gauge Field Localized on Walls with Four-Dimensional World Volume

A mechanism using the position-dependent gauge coupling is proposed to localize non-Abelian gauge fields on domain walls in five-dimensional space-time. Low-energy effective theory posseses a massless vector field, and a mass gap. The four-dimensional gauge invariance is maintained intact. We obtain perturbatively the four-dimensional Coulomb law for static sources on the domain wall. BPS domain wall solutions with the localization mechanism are explicitly constructed in the U(1)xU(1) supersymmetric gauge theory coupling to the non-Abelian gauge fields only through the cubic prepotential, which is consistent with the general principle of supersymmetry in five-dimensional space-time.

The phase diagram of Yang-Mills theory with a compact extra dimension

We present a non-perturbative study of the phase diagram of SU(2) Yang-Mills theory in a five-dimensional spacetime with a compact extra dimension. The nonrenormalizable theory is regularized on an anisotropic lattice and investigated through numerical simulations in a regime characterized by a hierarchy between the scale of lowenergy physics, the inverse compactification radius, and the cutoff scale. We map out the structure of the phase diagram and the pattern of lines corresponding to fixed values of the ratio between the mass of the fifth component of the gauge field and the non-perturbative mass gap of the four-dimensional modes. We discuss different limits of the model, and comment on the implications of our findings.

Quasinormal modes of the scalar field in five-dimensional Lovelock black hole spacetime

In this paper, using the third-order WKB approximation, we investigate the quasinormal frequencies of the scalar field in the background of a five-dimensional Lovelock black hole. We find that the ultraviolet correction to Einstein theory in the Lovelock theory makes the scalar field decay more slowly and oscillate more quickly, and the cosmological constant makes the scalar field decay more slowly and oscillate more slowly in the Lovelock black hole background.

Simple generalizations of anti-de Sitter spacetime

We consider new cosmological solutions which generalize the cosmological patch of the anti-de Sitter (AdS) spacetime, allowing for fluids with equations of state such that w ≠ −1. We use them to derive the associated full manifolds. We find that these solutions can all be embedded in flat five-dimensional spacetime with −− + + + signature, revealing deformed hyperboloids. The topology and some aspects of the causal structure of these spaces are therefore unchanged, and closed time-like curves are identified, before a covering space is considered. However the structure of Killing vector fields is entirely different and so we may expect a different structure of Killing horizons in these solutions.

Black holes in Einstein–Gauss–Bonnet gravity with a string cloud background

We obtain a black hole solution in the Einstein–Gauss–Bonnet theory for the string cloud model in a five-dimensional spacetime. We analyze the event horizons and naked singularities. Later, we compute the Hawking temperature TH, the specific heat C, the entropy S, and the Helmholtz free energy F of the black hole. The entropy was computed using the Wald formulation. In addition, the quantum correction to the Wald's entropy is considered for the string cloud source.We mainly explore the thermodynamical global and local stability of the system with vanishing or non-vanishing cosmological constant. The global thermodynamic phase structure indicates that the Hawking–Page transition is achieved for this model. Further, we observe that there exist stable black holes with small radii and that these regions are enlarged when choosing small values of the string cloud density and of the Gauss–Bonnet parameter. Besides, the rate of evaporation for these black holes are studied, determining whether the evaporation time is finite or not. Then, we concentrate on the dynamical stability of the system, studying the effective potential for s-waves propagating on the string cloud background.

Orbifold family unification inSO(2N)gauge theory

We study the possibility of family unification on the basis of SO(2N) gauge theory on the five-dimensional space-time, $M^4\times S^1/Z_2$. Several SO(10), $SU(4) \times SU(2)_L \times SU(2)_R$ or SU(5) multiplets come from a single bulk multiplet of SO(2N) after the orbifold breaking. Other multiplets including brane fields are necessary to compose three families of quarks and leptons.

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.

Five-dimensional metricf(R)gravity and the accelerated universe

The metric $f(R)$ theories of gravity are generalized to five-dimensional spacetimes. By assuming a hypersurface-orthogonal Killing vector field representing the compact fifth dimension, the five-dimensional theories are reduced to their four-dimensional formalism. Then we study the cosmology of a special class of $f(R)=\ensuremath{\alpha}{R}^{m}$ models in a spatially flat Friedmann-Robertson-Walker spacetime. It is shown that the parameter $m$ can be constrained to a certain range by the current observed deceleration parameter, and its lower bound corresponds to the Kaluza-Klein theory. It turns out that both expansion and contraction of the extra dimension may prescribe the smooth transition from the deceleration era to the acceleration era in the recent past as well as an accelerated scenario for the present Universe. Hence, five-dimensional $f(R)$ gravity can naturally account for the present accelerated expansion of the Universe. Moreover, the models predict a transition from acceleration to deceleration in the future, followed by a cosmic recollapse within finite time. This differs from the prediction of the five-dimensional Brans-Dicke theory but is inconsistent with a recent prediction based on loop quantum cosmology.

Brane cosmology and motion of test particles in five-dimensional warped product spacetimes

In the braneworld scenario ordinary standard model matter and on-gravitational fields are confined by some trapping mechanism to the 4-dimensional universe constituting the D3-branes which are embedded in a (4 + n)-dimensional manifold referred to as the bulk (n being the number of extra dimensions). The notion of particle confinement is necessary for theories with non-compact extra dimensions, otherwise, the particles would escape from our 4-dimensional world along unseen directions. In this paper, we have considered a five-dimensional warped product space-time having an exponential warping function which depends both on time as well as on the extra coordinates and a non-compact fifth dimension. Further, we have assumed that the lapse function may either be a constant or a function of both time and of the extra coordinates, and have studied the nature of the geodesics of test particles and analyzed the conditions of stability in this geometrical framework. We have also discussed the possible cosmology of the corresponding (3 + 1)-dimensional hypersurfaces.

Black objects and hoop conjecture in five-dimensional space-time

We numerically investigated the sequences of initial data of a thin spindle and a thin ring in five-dimensional space-time in the context of the cosmic censorship conjecture. We modeled the matter in non-rotating homogeneous spheroidal or toroidal configurations under the momentarily static assumption, solved the Hamiltonian constraint equation and searched the apparent horizons. We discussed when S3 (black-hole) or S1 × S2 (black-ring) horizons (‘black objects’) are formed. By monitoring the location of the maximum Kretchmann invariant, an appearance of ‘naked singularity’ or ‘naked ring’ under special situations is suggested. We also discuss the validity of the hyper-hoop conjecture using a minimum area around the object, and show that the appearance of the ring horizon does not match with this hoop.

Hoop conjecture and the horizon formation cross section in Kaluza-Klein spacetimes

We analyze momentarily static initial data sets of the gravitational field produced by two-point sources in five-dimensional Kaluza-Klein spacetimes. These initial data sets are characterized by the mass, the separation of sources and the size of a extra dimension. Using these initial data sets, we discuss the condition for black hole formation, and propose a new conjecture which is a hybrid of the four-dimensional hoop conjecture and the five-dimensional hyperhoop conjecture. By using the new conjecture, we estimate the cross section of black hole formation due to collisions of particles in Kaluza-Klein spacetimes. We show that the mass dependence of the cross section gives us information about the size and the number of the compactified extra dimensions.

Calculation of the metric in the five-dimensional spacetime

This paper introduces the Wheeler-Dewitt (W-D) equation in the five-dimensional R+R2 theory of gravity, and gets solutions of the W-D equation by separation of variables. Using the Kaluza-Klein theory, the Robertson-Walker metric is extended to the five-dimensional spacetime. With the field equations of the spacetime, the relationship between energy and the cosmological term can be obtained.

Standard cosmological evolution in the f(R) model to Kaluza–Klein cosmology

In this paper, using f(R) theory of gravity we explicitly calculate cosmological evolution in the presence of a perfect fluid source in four- and five-dimensional space–time in which this cosmological evolution in self-creation is presented by Reddy et al (2009 Int. J. Theor. Phys.48 10). An exact cosmological model is presented using a relation between Einstein's gravity field equation components due to a metric with the same component from f(R) theory of gravity. Some physics and kinematical properties of the model are also discussed.

Spinor calculus on five-dimensional spacetimes

Penrose’s spinor calculus of four-dimensional Lorentzian geometry is extended to the case of five-dimensional Lorentzian geometry. Such fruitful ideas in Penrose’s spinor calculus as the spin covariant derivative, the curvature spinors, or the definition of the spin coefficients on a spin frame can be carried over to the spinor calculus in five-dimensional Lorentzian geometry. The algebraic and differential properties of the curvature spinors are studied in detail, and as an application, we extend the well-known four-dimensional Newman–Penrose formalism to a five-dimensional spacetime.

A higher dimensional generalization of the geodesic part of the Goldberg–Sachs theorem

In more than four spacetime dimensions, a multiple Weyl-aligned null direction (WAND) need not be geodesic. It is proved that any higher dimensional Einstein spacetime admitting a non-geodesic multiple WAND also admits a geodesic multiple WAND. All five-dimensional Einstein spacetimes admitting a non-geodesic multiple WAND are determined.

Higher-dimensional numerical relativity: Formulation and code tests

We derive a formalism of numerical relativity for higher-dimensional spacetimes and develop numerical codes for simulating a wide variety of five-dimensional (5D) spacetimes for the first time. First, the Baumgarte-Shapiro-Shibata-Nakamura formalism is extended for arbitrary spacetime dimensions $D\ensuremath{\ge}4$, and then, the so-called cartoon method, which was originally proposed as a robust method for simulating axisymmetric 4D spacetimes, is described for 5D spacetimes of several types of symmetries. Implementing 5D numerical relativity codes with the cartoon methods, we perform test simulations by evolving a 5D Schwarzschild spacetime and a 5D spacetime composed of a gravitational-wave packet of small amplitude. The numerical simulations are stably performed for a sufficiently long time, as done in the 4D case, and the obtained numerical results agree well with the analytic solutions: The numerical solutions are shown to converge at the correct order. We also confirm that a long-term accurate evolution of the 5D Schwarzschild spacetime is feasible using the so-called puncture approach. In addition, we derive the Landau-Lifshitz pseudotensor in arbitrary dimensions, and show that it gives a robust tool for computing the energy flux of gravitational waves. The formulations and methods developed in this paper provide a powerful tool for studying nonlinear dynamics of higher-dimensional gravity.

Extended general relativity: Large-scale antigravity and short-scale gravity with [formula omitted] from five-dimensional vacuum

Considering a five-dimensional (5D) Riemannian spacetime with a particular stationary Ricci-flat metric, we obtain in the framework of the induced matter theory an effective 4D static and spherically symmetric metric which give us ordinary gravitational solutions on small (planetary and astrophysical) scales, but repulsive (anti gravitational) forces on very large (cosmological) scales with ω=−1. Our approach is an unified manner to describe dark energy, dark matter and ordinary matter. We illustrate the theory with two examples, the solar system and the great attractor. From the geometrical point of view, these results follow from the assumption that exists a confining force that make possible that test particles move on a given 4D hypersurface.

Uniqueness of rotating charged black holes in five-dimensional minimal gauged supergravity

We study a five-dimensional spacetime admitting, in the presence of torsion, a non-degenerate conformal Killing–Yano 2-form which is closed with respect to both the usual exterior differentiation and the exterior differentiation with torsion. Furthermore, assuming that the torsion is closed and co-closed with respect to the exterior differentiation with torsion, we prove that such a spacetime is the only spacetime given by the Chong–Cvetič–Lü–Pope solution for stationary, rotating charged black holes with two independent angular momenta in five-dimensional minimal gauged supergravity.

Top Yukawa deviation in extra dimension

We suggest a simple one-Higgs-doublet model living in the bulk of five-dimensional spacetime compactified on S 1 / Z 2 , in which the top Yukawa coupling can be smaller than the naive standard-model expectation, i.e. the top quark mass divided by the Higgs vacuum expectation value. If we find only single Higgs particle at the LHC and also observe the top Yukawa deviation, our scenario becomes a realistic candidate beyond the standard model. The Yukawa deviation comes from the fact that the wave function profile of the free physical Higgs field can become different from that of the vacuum expectation value, due to the presence of the brane-localized Higgs potentials. In the Brane-Localized Fermion scenario, we find sizable top Yukawa deviation, which could be checked at the LHC experiment, with a dominant Higgs production channel being the WW fusion. We also study the Bulk Fermion scenario with brane-localized Higgs potential, which resembles the Universal Extra Dimension model with a stable dark matter candidate. We show that both scenarios are consistent with the current electroweak precision measurements.