Hydrostatic Equilibrium of a Perfect Fluid Sphere with Exterior Higher-Dimensional Schwarzschild Spacetime

We discuss the question of how the number of dimensions of space and time can influence the equilibrium configurations of stars. We find that dimensionality does increase the effect of mass but not the contribution of the pressure, which is the same in any dimension. In the presence of a (positive) cosmological constant the condition of hydrostatic equilibrium imposes a lower limit on mass and matter density. We show how this limit depends on the number of dimensions and suggest that $\Lambda > 0$ is more effective in 4D than in higher dimensions. We obtain a general limit for the degree of compactification (gravitational potential on the boundary) of perfect fluid stars in $D$-dimensions. We argue that the effects of gravity are stronger in 4D than in any other number of dimensions. The generality of the results is also discussed

Mass and Charge in Brane-World and Non-Compact Kaluza-Klein Theories in 5 Dim

In classical Kaluza-Klein theory, with compactified extra dimensions and without scalar field, the rest mass as well as the electric charge of test particles are constants of motion. We show that in the case of a large extra dimension this is no longer so. We propose the Hamilton-Jacobi formalism, instead of the geodesic equation, for the study of test particles moving in a five-dimensional background metric. This formalism has a number of advantages: (i) it provides a clear and invariant definition of rest mass, without the ambiguities associated with the choice of the parameters used along the motion in 5D and 4D, (ii) the electromagnetic field can be easily incorporated in the discussion, and (iii) we avoid the difficulties associated with the "splitting" of the geodesic equation. For particles moving in a general 5D metric, we show how the effective rest mass, as measured by an observer in 4D, varies as a consequence of the large extra dimension. Also, the fifth component of the momentum changes along the motion. This component can be identified with the electric charge of test particles. With this interpretation, both the rest mass and the charge vary along the trajectory. The constant of motion is now a combination of these quantities. We study the cosmological variations of charge and rest mass in a five-dimensional bulk metric which is used to embed the standard k = 0 FRW universes. The time variations in the fine structure "constant" and the Thomson cross section are also discussed.Comment: V2: References added, discussion extended. V3 is identical to V2, references updated. To appear in General Relativity and Gravitatio

Equivalence Between Space-Time-Matter and Brane-World Theories

We study the relationship between space-time-matter (STM) and brane theories. These two theories look very different at first sight, and have different motivation for the introduction of a large extra dimension. However, we show that they are equivalent to each other. First we demonstrate that STM predicts local and non-local high-energy corrections to general relativity in 4D, which are identical to those predicted by brane-world models. Secondly, we notice that in brane models the usual matter in 4D is a consequence of the dependence of five-dimensional metrics on the extra coordinate. If the 5D bulk metric is independent of the extra dimension, then the brane is void of matter. Thus, in brane theory matter and geometry are unified, which is exactly the paradigm proposed in STM. Consequently, these two 5D theories share the same concepts and predict the same physics. This is important not only from a theoretical point of view, but also in practice. We propose to use a combination of both methods to alleviate the difficult task of finding solutions on the brane. We show an explicit example that illustrate the feasibility of our proposal.Comment: Typos corrected, three references added. To appear in Mod. Phys. Let

Efficient fiber-optical interface for nanophotonic devices

We demonstrate a method for efficient coupling of guided light from a single mode optical fiber to nanophotonic devices. Our approach makes use of single-sided conical tapered optical fibers that are evanescently coupled over the last ~10 um to a nanophotonic waveguide. By means of adiabatic mode transfer using a properly chosen taper, single-mode fiber-waveguide coupling efficiencies as high as 97(1)% are achieved. Efficient coupling is obtained for a wide range of device geometries which are either singly-clamped on a chip or attached to the fiber, demonstrating a promising approach for integrated nanophotonic circuits, quantum optical and nanoscale sensing applications.Comment: 7 pages, 4 figures, includes supplementary informatio

Late time cosmic acceleration from vacuum Brans-Dicke theory in 5D

We show that the scalar-vacuum Brans-Dicke equations in 5D are equivalent to Brans-Dicke theory in 4D with a self interacting potential and an effective matter field. The cosmological implication, in the context of FRW models, is that the observed accelerated expansion of the universe comes naturally from the condition that the scalar field is not a ghost, i.e., $\omega > - 3/2$. We find an effective matter-dominated 4D universe which shows accelerated expansion if $- 3/2 < \omega < - 1$. We study the question of whether accelerated expansion can be made compatible with large values of $\omega$, within the framework of a 5D scalar-vacuum Brans-Dicke theory with variable, instead of constant, parameter $\omega$. In this framework, and based on a general class of solutions of the field equations, we demonstrate that accelerated expansion is incompatible with large values of $\omega$.Comment: In V2 the summary section is expanded. To be published in Classical and Quantum Gravity

Transition from decelerated to accelerated cosmic expansion in braneworld universes

Braneworld theory provides a natural setting to treat, at a classical level, the cosmological effects of vacuum energy. Non-static extra dimensions can generally lead to a variable vacuum energy, which in turn may explain the present accelerated cosmic expansion. We concentrate our attention in models where the vacuum energy decreases as an inverse power law of the scale factor. These models agree with the observed accelerating universe, while fitting simultaneously the observational data for the density and deceleration parameter. The redshift at which the vacuum energy can start to dominate depends on the mass density of ordinary matter. For Omega = 0.3, the transition from decelerated to accelerated cosmic expansion occurs at z approx 0.48 +/- 0.20, which is compatible with SNe data. We set a lower bound on the deceleration parameter today, namely q > - 1 + 3 Omega/2, i.e., q > - 0.55 for Omega = 0.3. The future evolution of the universe crucially depends on the time when vacuum starts to dominate over ordinary matter. If it dominates only recently, at an epoch z < 0.64, then the universe is accelerating today and will continue that way forever. If vacuum dominates earlier, at z > 0.64, then the deceleration comes back and the universe recollapses at some point in the distant future. In the first case, quintessence and Cardassian expansion can be formally interpreted as the low energy limit of our model, although they are entirely different in philosophy. In the second case there is no correspondence between these models and ours.Comment: In V2 typos are corrected and one reference is added for section 1. To appear in General Relativity and Gravitatio

Anisotropic Brane Cosmology with Variable GG and Λ\Lambda

In this work, the cosmological implications of brane world scenario are investigated when the gravitational coupling $G$ and the cosmological term $\Lambda$ are not constant but rather there are time variation of them. From observational point of view, these time variations are taken in the form $\frac{\dot{G}}{G}\sim H$ and $\Lambda \sim H^{2}$. The behavior of scale factors and different kinematical parameters are investigated for different possible scenarios where the bulk cosmological constant $\Lambda_{5}$ can be zero, positive or negative.Comment: RevTex, 7 figures, 16 page

Exact Solutions of Five Dimensional Anisotropic Cosmologies

We solve the five dimensional vacuum Einstein equations for several kinds of anisotropic geometries. We consider metrics in which the spatial slices are characterized as Bianchi types-II and V, and the scale factors are dependent both on time and a non-compact fifth coordinate. We examine the behavior of the solutions we find, noting for which parameters they exhibit contraction over time of the fifth scale factor, leading naturally to dimensional reduction. We explore these within the context of the induced matter model: a Kaluza-Klein approach that associates the extra geometric terms due to the fifth coordinate with contributions to the four dimensional stress-energy tensor.Comment: 11 page

Accelerated expansion from braneworld models with variable vacuum energy

In braneworld models a variable vacuum energy may appear if the size of the extra dimension changes during the evolution of the universe. In this scenario the acceleration of the universe is related not only to the variation of the cosmological term, but also to the time evolution of $G$ and, possibly, to the variation of other fundamental "constants" as well. This is because the expansion rate of the extra dimension appears in different contexts, notably in expressions concerning the variation of rest mass and electric charge. We concentrate our attention on spatially-flat, homogeneous and isotropic, brane-universes where the matter density decreases as an inverse power of the scale factor, similar (but at different rate) to the power law in FRW-universes of general relativity. We show that these braneworld cosmologies are consistent with the observed accelerating universe and other observational requirements. In particular, $G$ becomes constant and $\Lambda_{(4)} \approx const \times H^2$ asymptotically in time. Another important feature is that the models contain no "adjustable" parameters. All the quantities, even the five-dimensional ones, can be evaluated by means of measurements in 4D. We provide precise constrains on the cosmological parameters and demonstrate that the "effective" equation of state of the universe can, in principle, be determined by measurements of the deceleration parameter alone. We give an explicit expression relating the density parameters $\Omega_{\rho}$, $\Omega_{\Lambda}$ and the deceleration parameter $q$. These results constitute concrete predictions that may help in observations for an experimental/observational test of the model.Comment: References added, typos correcte

Latent solitons, black strings, black branes, and equations of state in Kaluza-Klein models

In Kaluza-Klein models with an arbitrary number of toroidal internal spaces, we investigate soliton solutions which describe the gravitational field of a massive compact object. We single out the physically interesting solution corresponding to a point-like mass. For the general solution we obtain equations of state in the external and internal spaces. These equations demonstrate that the point-like mass soliton has dust-like equations of state in all spaces. We also obtain the PPN parameters, which give the possibility to obtain the formulas for perihelion shift, deflection of light and time delay of radar echoes. Additionally, the gravitational experiments lead to a strong restriction on the parameter of the model: $\tau = -(2.1\pm 2.3)\times 10^{-5}$. The point-like mass solution contradicts this restriction. The condition $\tau=0$ satisfies the experimental limitation and defines a new class of solutions which are indistinguishable from general relativity. We call such solutions latent solitons. Black strings and black branes belong to this class. Moreover, the condition of stability of the internal spaces singles out black strings/branes from the latent solitons and leads uniquely to the black string/brane equations of state $p_i=-\epsilon/2$, in the internal spaces and to the number of the external dimensions $d_0=3$. The investigation of multidimensional static spherically symmetric perfect fluid with dust-like equation of state in the external space confirms the above results.Comment: 8 pages, Revtex4, no figures, minor changes adde