Gravitational energy and cosmic acceleration

Cosmic acceleration is explained quantitatively, as an apparent effect due to gravitational energy differences that arise in the decoupling of bound systems from the global expansion of the universe. "Dark energy" is a misidentification of those aspects of gravitational energy which by virtue of the equivalence principle cannot be localised, namely gradients in the energy due to the expansion of space and spatial curvature variations in an inhomogeneous universe. A new scheme for cosmological averaging is proposed which solves the Sandage-de Vaucouleurs paradox. Concordance parameters fit supernovae luminosity distances, the angular scale of the sound horizon in the CMB anisotropies, and the effective comoving baryon acoustic oscillation scale seen in galaxy clustering statistics. Key observational anomalies are potentially resolved, and unique predictions made, including a quantifiable variance in the Hubble flow below the scale of apparent homogeneity.Comment: 9 pages, 2 figures. An essay which received Honorable Mention in the 2007 GRF Essay Competition. To appear in a special issue of Int. J. Mod. Phys.

Imaging the Near Field

In an earlier paper we introduced the concept of the perfect lens which focuses both near and far electromagnetic fields, hence attaining perfect resolution. Here we consider refinements of the original prescription designed to overcome the limitations of imperfect materials. In particular we show that a multi-layer stack of positive and negative refractive media is less sensitive to imperfections. It has the novel property of behaving like a fibre-optic bundle but one that acts on the near field, not just the radiative component. The effects of retardation are included and minimized by making the slabs thinner. Absorption then dominates image resolution in the near-field. The deleterious effects of absorption in the metal are reduced for thinner layers.Comment: RevTeX, (9 pages, 8 figures

Robertson-Walker fluid sources endowed with rotation characterised by quadratic terms in angular velocity parameter

Einstein's equations for a Robertson-Walker fluid source endowed with rotation Einstein's equations for a Robertson-Walker fluid source endowed with rotation are presented upto and including quadratic terms in angular velocity parameter. A family of analytic solutions are obtained for the case in which the source angular velocity is purely time-dependent. A subclass of solutions is presented which merge smoothly to homogeneous rotating and non-rotating central sources. The particular solution for dust endowed with rotation is presented. In all cases explicit expressions, depending sinusoidally on polar angle, are given for the density and internal supporting pressure of the rotating source. In addition to the non-zero axial velocity of the fluid particles it is shown that there is also a radial component of velocity which vanishes only at the poles. The velocity four-vector has a zero component between poles

Dynamical coherent states and physical solutions of quantum cosmological bounces

A new model is studied which describes the quantum behavior of transitions through an isotropic quantum cosmological bounce in loop quantum cosmology sourced by a free and massless scalar field. As an exactly solvable model even at the quantum level, it illustrates properties of dynamical coherent states and provides the basis for a systematic perturbation theory of loop quantum gravity. The detailed analysis is remarkably different from what is known for harmonic oscillator coherent states. Results are evaluated with regard to their implications in cosmology, including a demonstration that in general quantum fluctuations before and after the bounce are unrelated. Thus, even within this solvable model the condition of classicality at late times does not imply classicality at early times before the bounce without further assumptions. Nevertheless, the quantum state does evolve deterministically through the bounce.Comment: 30 pages, 3 figure

Asymptotic properties of black hole solutions in dimensionally reduced Einstein-Gauss-Bonnet gravity

We study the asymptotic behavior of the spherically symmetric solutions of the system obtained from the dimensional reduction of the six-dimensional Einstein- Gauss-Bonnet action. We show that in general the scalar field that parametrizes the size of the internal space is not trivial, but nevertheless the solutions depend on a single parameter. In analogy with other models containing Gauss-Bonnet terms, naked singularities are avoided if a minimal radius for the horizon is assumed.Comment: 9 pages, plain Te

A DC magnetic metamaterial

Electromagnetic metamaterials are a class of materials which have been artificially structured on a subwavelength scale. They are currently the focus of a great deal of interest because they allow access to previously unrealisable properties like a negative refractive index. Most metamaterial designs have so far been based on resonant elements, like split rings, and research has concentrated on microwave frequencies and above. In this work, we present the first experimental realisation of a non-resonant metamaterial designed to operate at zero frequency. Our samples are based on a recently-proposed template for an anisotropic magnetic metamaterial consisting of an array of superconducting plates. Magnetometry experiments show a strong, adjustable diamagnetic response when a field is applied perpendicular to the plates. We have calculated the corresponding effective permeability, which agrees well with theoretical predictions. Applications for this metamaterial may include non-intrusive screening of weak DC magnetic fields.Comment: 6 pages, 3 figure

Slowly, rotating non-stationary, fluid solutions of Einstein's equations and their match to Kerr empty space-time

A general class of solutions of Einstein's equation for a slowly rotating fluid source, with supporting internal pressure, is matched using Lichnerowicz junction conditions, to the Kerr metric up to and including first order terms in angular speed parameter. It is shown that the match applies to any previously known non-rotating fluid source made to rotate slowly for which a zero pressure boundary surface exists. The method is applied to the dust source of Robertson-Walker and in outline to an interior solution due to McVittie describing gravitational collapse. The applicability of the method to additional examples is transparent. The differential angular velocity of the rotating systems is determined and the induced rotation of local inertial frame is exhibited

Entropy of Lovelock Black Holes

A general formula for the entropy of stationary black holes in Lovelock gravity theories is obtained by integrating the first law of black hole mechanics, which is derived by Hamiltonian methods. The entropy is not simply one quarter of the surface area of the horizon, but also includes a sum of intrinsic curvature invariants integrated over a cross section of the horizon.Comment: 15 pages, plain Latex, NSF-ITP-93-4