Kaluza-Klein solitons reexamined

In (4 + 1) gravity the assumption that the five-dimensional metric is independent of the fifth coordinate authorizes the extra dimension to be either spacelike or timelike. As a consequence of this, the time coordinate and the extra coordinate are interchangeable, which in turn allows the conception of different scenarios in 4D from a single solution in 5D. In this paper, we make a thorough investigation of all possible 4D scenarios, associated with this interchange, for the well-known Kramer-Gross-Perry-Davidson-Owen set of solutions. We show that there are {\it three} families of solutions with very distinct geometrical and physical properties. They correspond to different sets of values of the parameters which characterize the solutions in 5D. The solutions of physical interest are identified on the basis of physical requirements on the induced-matter in 4D. We find that only one family satisfies these requirements; the other two violate the positivity of mass-energy density. The "physical" solutions possess a lightlike singularity which coincides with the horizon. The Schwarzschild black string solution as well as the zero moment dipole solution of Gross and Perry are obtained in different limits. These are analyzed in the context of Lake's geometrical approach. We demonstrate that the parameters of the solutions in 5D are not free, as previously considered. Instead, they are totally determined by measurements in 4D. Namely, by the surface gravitational potential of the astrophysical phenomena, like the Sun or other stars, modeled in Kaluza-Klein theory. This is an important result which may help in observations for an experimental/observational test of the theory.Comment: In V2 we include an Appendix, where we examine the conformal approach. Minor changes at the beginning of section 2. In V3 more references are added. Minor editorial changes in the Introduction and Conclusions section

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

Exterior spacetime for stellar models in 5-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 4-dimensional picture allows the existence of different possible, non-Schwarzschild, scenarios for the description of the spacetime outside of a spherical star, contrary to general relativity in 4D. 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 analyze possible stellar exteriors that are conformal to the metric induced on four-dimensional hypersurfaces orthogonal to the extra dimension. All these exteriors are continuously matched with the interior of the star. 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 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. We also examine the question of how would the deviation from the Schwarzschild vacuum exterior 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.Comment: Typos corrected. Accepted for publication in Classical and Quantum Gravit

Levi-Civita spacetimes in multidimensional theories

We obtain the most general static cylindrically symmetric vacuum solutions of the Einstein field equations in $(4 + N)$ dimensions. Under the assumption of separation of variables, we construct a family of Levi-Civita-Kasner vacuum solutions in $(4 + N)$. We discuss the dimensional reduction of the static solutions. Depending on the reduction procedure, they can be interpreted either as a scalar-vacuum generalization of Levi-Civita spacetimes, or as the effective 4D vacuum spacetime outside of an idealized string in braneworld theory.Comment: 7 pages. Accepted for publication in Mod. Phys. Lett. A (MPLA

An exact self-similar solution for an expanding ball of radiation

We give an exact solution of the $5D$ Einstein equations which in 4D can be interpreted as a spherically symmetric dissipative distribution of matter, with heat flux, whose effective density and pressure are nonstatic, nonuniform, and satisfy the equation of state of radiation. The matter satisfies the usual energy and thermodynamic conditions. The energy density and temperature are related by the Stefan-Boltzmann law. The solution admits a homothetic Killing vector in $5D$, which induces the existence of self-similar symmetry in 4D, where the line element as well as the dimensionless matter quantities are invariant under a simple "scaling" group.Comment: New version expanded and improved. To appear in Int. J. Mod. Phys.

Effective spacetime from multi-dimensional gravity

We study the effective spacetimes in lower dimensions that can be extracted from a multidimensional generalization of the Schwarzschild-Tangherlini spacetimes derived by Fadeev, Ivashchuk and Melnikov ({\it Phys. Lett,} {\bf A 161} (1991) 98). The higher-dimensional spacetime has $D = (4 + n + m)$ dimensions, where $n$ and $m$ are the number of "internal" and "external" extra dimensions, respectively. We analyze the effective $(4 + n)$ spacetime obtained after dimensional reduction of the $m$ external dimensions. We find that when the $m$ extra dimensions are compact (i) the physics in lower dimensions is independent of $m$ and the character of the singularities in higher dimensions, and (ii) the total gravitational mass $M$ of the effective matter distribution is less than the Schwarzshild mass. In contrast, when the $m$ extra dimensions are large this is not so; the physics in $(4 + n)$ does explicitly depend on $m$, as well as on the nature of the singularities in high dimensions, and the mass of the effective matter distribution (with the exception of wormhole-like distributions) is bigger than the Schwarzshild mass. These results may be relevant to observations for an experimental/observational test of the theory.Comment: A typo in Eq. (24) is fixe

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

SCNet: Learning Semantic Correspondence

This paper addresses the problem of establishing semantic correspondences between images depicting different instances of the same object or scene category. Previous approaches focus on either combining a spatial regularizer with hand-crafted features, or learning a correspondence model for appearance only. We propose instead a convolutional neural network architecture, called SCNet, for learning a geometrically plausible model for semantic correspondence. SCNet uses region proposals as matching primitives, and explicitly incorporates geometric consistency in its loss function. It is trained on image pairs obtained from the PASCAL VOC 2007 keypoint dataset, and a comparative evaluation on several standard benchmarks demonstrates that the proposed approach substantially outperforms both recent deep learning architectures and previous methods based on hand-crafted features.Comment: ICCV 201

Steady-state stabilization due to random delays in maps with self-feedback loops and in globally delayed-coupled maps

We study the stability of the fixed-point solution of an array of mutually coupled logistic maps, focusing on the influence of the delay times, $\tau_{ij}$, of the interaction between the $i$th and $j$th maps. Two of us recently reported [Phys. Rev. Lett. {\bf 94}, 134102 (2005)] that if $\tau_{ij}$ are random enough the array synchronizes in a spatially homogeneous steady state. Here we study this behavior by comparing the dynamics of a map of an array of $N$ delayed-coupled maps with the dynamics of a map with $N$ self-feedback delayed loops. If $N$ is sufficiently large, the dynamics of a map of the array is similar to the dynamics of a map with self-feedback loops with the same delay times. Several delayed loops stabilize the fixed point, when the delays are not the same; however, the distribution of delays plays a key role: if the delays are all odd a periodic orbit (and not the fixed point) is stabilized. We present a linear stability analysis and apply some mathematical theorems that explain the numerical results.Comment: 14 pages, 13 figures, important changes (title changed, discussion, figures, and references added