Five-dimensional Spacetime Research Articles

Radion stabilization in the presence of a Wilson line phase

We study the stabilization of an extra-dimensional radius in the presence of a Wilson line phase of an extra $U(1)$ gauge symmetry on a five-dimensional space-time, using the effective potential relating both the radion and the Wilson line phase at the one-loop level. We find that the radion can be stabilized by the introduction of a small number of fermions.

Dynamics of test particles in the general five-dimensional Myers-Perry spacetime

We present the complete set of analytical solutions of the geodesic equations in the general five-dimensional Myers-Perry spacetime in terms of the Weierstrass $\ensuremath{\wp}$, $\ensuremath{\zeta}$, and $\ensuremath{\sigma}$ functions. We analyze the underlying polynomials in the polar and radial equations, which depend on the parameters of the metric and the conserved quantities of a test particle, and characterize the motion by their zeros. We exemplify the efficiency of the analytical method on the basis of the explicit construction of test particle orbits and by addressing observables in this spacetime.

Geometrical and hydrodynamic aspects of five-dimensional Schwarzschild black hole

Exploiting the five-dimensional Schwarzschild black hole, we study the geometrical natures of the higher dimensional black hole to yield the (6+1) dimensional global embedding Minkowski space structure. We next obtain the Hawking temperature on this five-dimensional manifold, whose result is different from the four-dimensional one. On the contrary, the radial component of the Einstein equation for the massive particles or photons on the five-dimensional spacetime is shown to have the same form as the four-dimensional black hole one. Moreover, we construct the effective potential on equatorial plane of the restricted three-brane to investigate the behavior of the particles or photons on this restricted brane.

Holographic entanglement entropy in insulator/superconductor transition with Born-Infeld electrodynamics

We investigate the holographic entanglement entropy in the insulator/superconductor phase transition for the Born-Infeld electrodynamics with full backreaction in five-dimensional AdS soliton spacetime. We note that the holographic entanglement entropy is a good probe to study the properties of the phase transition, and the Born-Infeld factor $b$ has no effect on the critical chemical potential $\mu_c$. We find that both in the half space and the belt one, the non-monotonic behavior of the entanglement entropy versus the chemical potential is a general property, and the entanglement entropy increases with the increase of the Born-Infeld factor in the superconductor phase. Particularly, there exists confinement/deconfinement phase transition in the strip geometry and the critical width $\ell_c$ is dependent of the Born-Infeld parameter.

Holographic thermalization, quasinormal modes and superradiance in Kerr-AdS

Black holes in anti-de Sitter (AdS) backgrounds play a pivotal role in the gauge/gravity duality where they determine, among other things, the approach to equilibrium of the dual field theory. We undertake a detailed analysis of perturbed Kerr-AdS black holes in four- and five-dimensional spacetimes, including the computation of its quasinormal modes, hydrodynamic modes and superradiantly unstable modes. Our results shed light on the possibility of new black hole phases with a single Killing field, possible new holographic phenomena and phases in the presence of a rotating chemical potential, and close a crucial gap in our understanding of linearized perturbations of black holes in anti-de Sitter scenarios.

Five-dimensional generalized $$f(R)$$ f ( R ) gravity with curvature–matter coupling

The generalized \(f(R)\) gravity with curvature–matter coupling in five-dimensional (5D) spacetime can be established by assuming a hypersurface-orthogonal space-like Killing vector field of 5D spacetime, and it can be reduced to the 4D formalism of FRW universe. This theory is quite general and can give the corresponding results for Einstein gravity, and \(f(R)\) gravity with both no-coupling and non-minimal coupling in 5D spacetime as special cases, that is, we would give some new results besides previous ones given by Huang et al. in Phys Rev D 81:064003, 2010. Furthermore, in order to get some insight into the effects of this theory on the 4D spacetime, by considering a specific type of models with \(f_{1}(R)=f_{2}(R)=\alpha R^{m}\) and \(B(L_{m})=L_{m}=-\rho \), we not only discuss the constraints on the model parameters \(m,n\), but also illustrate the evolutionary trajectories of the scale factor \(a(t)\), the deceleration parameter \(q(t)\), and the scalar field \(\epsilon (t),\phi (t)\) in the reduced 4D spacetime. The research results show that this type of \(f(R)\) gravity models given by us could explain the current accelerated expansion of our universe without introducing dark energy.

A low-dimensional analogue of holographic baryons

Baryons in holographic QCD correspond to topological solitons in the bulk. The most prominent example is the Sakai–Sugimoto model, where the bulk soliton in the five-dimensional spacetime of AdS-type can be approximated by the flat space self-dual Yang–Mills instanton with a small size. Recently, the validity of this approximation has been verified by comparison with the numerical field theory solution. However, multi-solitons and solitons with finite density are currently beyond numerical field theory computations. Various approximations have been applied to investigate these important issues and have led to proposals for finite density configurations that include dyonic salt and baryonic popcorn. Here we introduce and investigate a low-dimensional analogue of the Sakai–Sugimoto model, in which the bulk soliton can be approximated by a flat space sigma model instanton. The bulk theory is a baby Skyrme model in a three-dimensional spacetime with negative curvature. The advantage of the lower-dimensional theory is that numerical simulations of multi-solitons and finite density solutions can be performed and compared with flat space instanton approximations. In particular, analogues of dyonic salt and baryonic popcorn configurations are found and analysed.

Gravity in five-dimensional warped product spacetimes with time-dependent warp factor

We have considered gravity in a 5-dimensional warped product spacetime with a time-dependent warp factor and time-dependent extra dimension. The braneworld has been described by a spatially flat FRW-type metric. The five-dimensional field equations have been constructed and solved, and the status of the energy conditions have been examined. In the high energy regime, the bulk is assumed to be sourced by a scalar field. The effective cosmological constant of the 4-dimensional universe is a variable quantity monitored by the time-dependent warp factor, and leads to a geometric interpretation of dynamical dark energy.

Five-Dimensional Space-Times with a Variable Gravitational and Cosmological Constant

We have presented cosmological models in five-dimensional Kaluza-Klein space-time with a variable gravitational constant (G) and cosmological constant (Λ). We have investigated Einstein’s field equations for five-dimensional Kaluza-Klein space-time in the presence of perfect fluid with time dependent G and Λ. A variety of solutions have been found in which G increases and Λ decreases with time t, which matches with current observation. The properties of fluid and kinematical parameters have been discussed in detail.

Brane worlds in critical gravity

Recently, Lu and Pope proposed critical gravities in [Phys. Rev. Lett. 106, 181302 (2011)]. In this paper we construct analytic brane solutions in critical gravity with matter. The Gibbons-Hawking surface term and junction condition are investigated, and the thin and thick brane solutions are obtained. All these branes are embedded in five-dimensional anti-de Sitter spacetimes. Our solutions are stable against scalar perturbations, and the zero modes of scalar perturbations cannot be localized on the branes.

Stabilizing matter and gauge fields localized on walls

Both non-Abelian gauge fields and minimally interacting massless matter fields are localized on a domain wall in the five-dimensional spacetime. Field-dependent gauge coupling naturally gives a position-dependent coupling to localize non-Abelian gauge fields on the domain wall. An economical field content allows us to eliminate a moduli for a instability, and to demonstrate the positivity of the position-dependent coupling in the entire moduli space. Effective Lagrangian similar to the chiral Lagrangian is found with a new feature of different coupling strengths for adjoint and singlet matter that depend on the width of the domain wall.

Multi-step Fermi normal coordinates

We generalize the concept of Fermi normal coordinates adapted to a geodesic to the case where the tangent space to the manifold at the base point is decomposed into a direct product of an arbitrary number of subspaces, so that we follow several geodesics in turn to find the point with given coordinates. We compute the connection and the metric as integrals of the Riemann tensor. We calculate explicitly an example of a five-dimensional brane inflation spacetime. In the case of one subspace (Riemann normal coordinates) or two subspaces, we recover some results previously found by Nesterov, using somewhat different techniques.

Kalb–Ramond field localization on the Bloch brane

This work deals with new results on the Kalb-Ramond (KR) field localization in braneworld models. We consider a five-dimensional warped spacetime with an embedded 4D thick brane which is generated by two real scalar fields coupled with gravity (the so called Bloch brane). We find a KR field zero mode localized with the inclusion of the dilaton coupling. Analyzing the massive spectrum, we detected a series of resonant modes that arise from the solutions of the Schr\"odinger-like equation for KR field. The effects of the brane thickness and of the dilaton coupling over the resonance structures are determined. Such analysis is extended to the resonance lifetimes of the massive modes, allowing a better understanding on the localization mechanism of the model.

Effective [formula omitted] gravity from the higher-dimensional Kaluza–Klein and Randall–Sundrum theories

We explore the four-dimensional effective F(T) gravity with T the torsion scalar in teleparallelism originating from higher-dimensional space–time theories, in particular the Kaluza–Klein (KK) and Randall–Sundrum (RS) theories. First, through the KK dimensional reduction from the five-dimensional space–time, we obtain the four-dimensional effective theory of F(T) gravity with its coupling to a scalar field. Second, taking the RS type-II model in which there exist the five-dimensional Anti-de Sitter (AdS) space–time with four-dimensional Friedmann–Lemaître–Robertson–Walker (FLRW) brane, we find that there will appear the contribution of F(T) gravity on the four-dimensional FLRW brane. It is demonstrated that inflation and the dark energy dominated stage can be realized in the KK and RS models, respectively, due to the effect of only the torsion in teleparallelism without that of the curvature.

Five-dimensional geometric model of gravitational and electroweak interactions

A geometric model is presented which unifies the three fundamental physical interactions: gravitational, electromagnetic, and weak. All of the indicated fields are unified on the basis of a single geometrical scheme – the geometry of a 5-dimensional metric-affine space-time with curvature, torsion, and nonmetricity. The initial Lagrangian of the proposed interactions unification model consists in one geometrical quantity – the scalar curvature 5R of five-dimensional metric-affine space-time. This initial Lagrangian L = 5R contains within itself a description of not only the three indicated fundamental physical interactions, but also the scalar Higgs fields which govern the induction of masses on the intermediate vector bosons – the carriers of the weak interaction.

Effectively four-dimensional spacetimes emerging from d = 5 Einstein–Gauss–Bonnet gravity

Einstein–Gauss–Bonnet gravity in five-dimensional spacetime provides an excellent example of a theory that, while including higher order curvature corrections to general relativity, still shares many of its features, such as second-order field equations for the metric. We focus on the largely unexplored case where the coupling constants of the theory are such that no constant-curvature solution is allowed, leaving open the question of what the vacuum state should then be. We find that even a slight deviation from the anti-de Sitter Chern–Simons theory, where the vacuum state is five-dimensional AdS spacetime, leads to a complete symmetry breakdown, with the fifth dimension either being compactified into a small circle or shrinking away exponentially with time. A complete family of solutions, including duality relations among them, is uncovered and shown to be unique within a certain class. This dynamical dimensional reduction scenario seems particularly attractive as a means for higher dimensional theories to make contact with our four-dimensional world.

Geodesic motion in the (rotating) black string spacetime

In this article we study the geodesic motion of test particles and light in the five-dimensional (rotating) black string spacetime. If a compact dimension is added to the four-dimensional Schwarzschild or Kerr spacetime, the new five-dimensional metric describes a (rotating) black string. The geodesics in the Schwarzschild and Kerr spacetime have been studied in great detail, however, when a compact dimension is added new behaviour occurs. We present the analytical solutions of the geodesic equations and discuss the possible orbits. The motion in the ordinary four-dimensional Schwarzschild and Kerr spacetime is compared to the motion in the (rotating) black string spacetime.

The Generalized f(R) Model with Coupling in 5D Spacetime

The generalized f(R) gravity with coupling in five-dimensional (5D) spacetime is studied on the basis of both the 4D generalized f(R) gravity with coupling and the pure f(R) gravity without coupling in 5D spacetime. Specifically, by assuming a hypersurface-orthogonal space-like Killing vector field in 5D spacetime, the generalization of the 4D generalized f(R) gravity to 5D can be realized, which can give the reduced 4-metric coupled with two scalar fields. In particular, we discuss a special class of models, i.e., f1(R) = f2(R) = αRm (m ≠ 1), and choose B(Lm) = Lm = −ρ in the homogeneous and isotropic cosmology with the 4D Friedmann—Robertson—Walker metric. The numerical analysis shows that the parameter m can be constrained by means of the current observations for the deceleration parameter, which implies that this generalized f(R) model with coupling in 5D spacetime can account for the present accelerated expansion of the universe.

Stability of charged solitons and formation of boson stars in five-dimensional anti-de Sitter spacetime

We study the stability of charged solitons in five-dimensional anti-de Sitter (AdS) spacetime. We show that for appropriate choices of the parameters of the model these solutions become unstable to form scalar hair. We find that the existence of charged solitons with scalar hair depends crucially on the charge and the mass of the scalar field. We investigate the dependence of the spectrum of solutions on the mass of the scalar field in detail. For positive mass of the scalar field, the hairy solitons can be interpreted as charged boson stars. We find that for a sufficiently small value of the charge of the scalar field a ‘forbidden band’ of the boson star’s mass and charge exists, while all our results indicate that—contrary to the asymptotically flat spacetime case—boson stars in asymptotic AdS can have arbitrarily large charge and mass.

Generalized holographic cosmology

We consider general black hole solutions in five-dimensional spacetime in the presence of a negative cosmological constant. We obtain a cosmological evolution via the gravity/gauge theory duality (holography) by defining appropriate boundary conditions on a four-dimensional boundary hypersurface. The standard counterterms are shown to renormalize the bare parameters of the system (the four-dimensional Newton's constant and cosmological constant). We discuss the thermodynamics of cosmological evolution and present various examples. The standard brane-world scenarios are shown to be special cases of our holographic construction.