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It is well-known that Birkhoff's theorem is no longer valid in theories with more than four dimensions.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

Nodal Liquid Theory of the Pseudo-Gap Phase of High-Tc Superconductors

We introduce and study the nodal liquid, a novel zero-temperature quantum phase obtained by quantum-disordering a d-wave superconductor. It has numerous remarkable properties which lead us to suggest it as an explanation of the pseudo-gap state in underdoped high-temperature superconductors. In the absence of impurities, these include power-law magnetic order, a T-linear spin susceptibility, non-trivial thermal conductivity, and two- and one-particle charge gaps, the latter evidenced, e.g. in transport and electron photoemission (which exhibits pronounced fourfold anisotropy inherited from the d-wave quasiparticles). We use a 2+1-dimensional duality transformation to derive an effective field theory for this phase. The theory is comprised of gapless neutral Dirac particles living at the former d-wave nodes, weakly coupled to the fluctuating gauge field of a dual Ginzburg-Landau theory. The nodal liquid interpolates naturally between the d-wave superconductor and the insulating antiferromagnet, and our effective field theory is powerful enough to permit a detailed analysis of a panoply of interesting phenomena, including charge ordering, antiferromagnetism, and d-wave superconductivity. We also discuss the zero-temperature quantum phase transitions which separate the nodal liquid from various ordered phases.Comment: 19 pages, 4 figure

Bistability in sine-Gordon: the ideal switch

The sine-Gordon equation, used as the representative nonlinear wave equation, presents a bistable behavior resulting from nonlinearity and generating hysteresis properties. We show that the process can be understood in a comprehensive analytical formulation and that it is a generic property of nonlinear systems possessing a natural band gap. The approach allows to discover that sine-Gordon can work as an it ideal switch by reaching a transmissive regime with vanishing driving amplitude.Comment: Phys. Rev. E, (to be published, May 2005

Extra symmetry in the field equations in 5D with spatial spherical symmetry

We point out that the field equations in 5D, with spatial spherical symmetry, possess an extra symmetry that leaves them invariant. This symmetry corresponds to certain simultaneous interchange of coordinates and metric coefficients. As a consequence a single solution in 5D can generate very different scenarios in 4D, ranging from static configurations to cosmological situations. A new perspective emanates from our work. Namely, that different astrophysical and cosmological scenarios in 4D might correspond to the same physics in 5D. We present explicit examples that illustrate this point of view.Comment: Typos corrected. Accepted for publication in Classical and Quantum Gravit

Memristive excitable cellular automata

The memristor is a device whose resistance changes depending on the polarity and magnitude of a voltage applied to the device's terminals. We design a minimalistic model of a regular network of memristors using structurally-dynamic cellular automata. Each cell gets info about states of its closest neighbours via incoming links. A link can be one 'conductive' or 'non-conductive' states. States of every link are updated depending on states of cells the link connects. Every cell of a memristive automaton takes three states: resting, excited (analog of positive polarity) and refractory (analog of negative polarity). A cell updates its state depending on states of its closest neighbours which are connected to the cell via 'conductive' links. We study behaviour of memristive automata in response to point-wise and spatially extended perturbations, structure of localised excitations coupled with topological defects, interfacial mobile excitations and growth of information pathways.Comment: Accepted to Int J Bifurcation and Chaos (2011

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

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

Bistable light detectors with nonlinear waveguide arrays

Bistability induced by nonlinear Kerr effect in arrays of coupled waveguides is studied and shown to be a means to conceive light detectors that switch under excitation by a weak signal. The detector is obtained by coupling two single 1D waveguide to an array of coupled waveguides with adjusted indices and coupling. The process is understood by analytical description in the conservative and continuous case and illustrated by numerical simulations of the model with attenuation.Comment: Phys. Rev. Lett., v.94, (2005, to be published