Letter: A Potential for the Radiative Part of the Lienard Wiechert Field

We show a superpotential totally non-local whichgenerates the radiative part of the Maxwell tensor ofLienard-Wiechert.     

LETTER: A Note on the Algebraic Symmetries of the Riemann and Lanczos Tensors

The usual algebraic symmetries of the Riemanntensor involve four convenient relations. It is shownthat these can be encompassed in three, two or just onerelation. Similar results are shown for the Lanczos tensor.     

Chronostructures of Special Relativity Theory

The class of all theoretically admissiblegeometric structures describing relative rates at whichmoving clocks work (the so called chronostructures) isconsidered. The transformations of space-timecoordinates of events implied by the choice of thechronostructure are determined. It is shown that thechronostructure is invariant with respect to thetransformations which it determines if, and only if, itis correlated with the Lorentz chronostructure. Thischronostructure is the simplest one in the class ofinvariant chronostructures.     

Hamiltonian Formulation of FRW Equations of Cosmology

We give a general Hamiltonian formulation of the Friedmann-Robertson-Walker (FRW) fundamental equations of a homogeneous and isotropic universe in the Standard Cosmological model. It gives some interesting insight on the 3-curvature of the universe, which is found to be obtained in terms of the scale factor (also termed radius of the universe) and its first derivative. It also leads to an easy determination of the Schrödinger equation for the (R) wave function of the universe, in the radiative era.     

Sparling Two-Forms, the Conformal Factor and the Gravitational Energy Density of the Teleparallel Equivalent of General Relativity

It has been shown recently that within the framework of the teleparallel equivalent of general relativity (TEGR) it is possible to define the energy density of the gravitational field in a unique way. The tegr amounts to an alternative formulation of Einstein's general relativity, not to an alternative gravity theory. The localizability of the gravitational energy has been investigated in a number of spacetimes with distinct topologies, and the outcome of these analyses agree with previously known results regarding the exact expression of the gravitational energy, and/or with the specific properties of the spacetime manifold. In this article we establish a relationship between the expression of the gravitational energy density of the TEGR and the Sparling two-forms, which are known to be closely connected with the gravitational energy. We will also show that our expression of energy yields the correct value of gravitational mass contained in the conformal factor of the metric field.     

Testing the Equivalence Principle in the Quantum Regime

We consider possible tests of the Einstein Equivalence Principle for physical systems in which quantum-mechanical vacuum energies cannot be neglected. Specific tests include a search for the manifestation of non-metric effects in Lamb-shift transitions of hydrogenic atoms and in anomalous magnetic moments of massive leptons. We discuss how current experiments already set bounds on the violation of the equivalence principle in this sector and how new (high-precision) measurements of these quantities could provide further information to this end.     

A Closed Contour of Integration in Regge Calculus

The analytic structure of the Regge action on a cone in d dimensions over a boundary of arbitrary topology is determined in simplicial minisuperspace. The minisuperspace is defined by the assignment of a single internal edge length to all 1-simplices emanating from the cone vertex, and a single boundary edge length to all 1-simplices lying on the boundary. The Regge action is analyzed in the space of complex edge lengths, and it is shown that there are three finite branch points in this complex plane. A closed contour of integration encircling the branch points is shown to yield a convergent real wave function. This closed contour can be deformed to a steepest descent contour for all sizes of the bounding universe. In general, the contour yields an oscillating wave function for universes of size greater than a critical value which depends on the topology of the bounding universe. For values less than the critical value the wave function exhibits exponential behaviour. It is shown that the critical value is positive for spherical topology in arbitrary dimensions. In three dimensions we compute the critical value for a boundary universe of arbitrary genus, while in four and five dimensions we study examples of product manifolds and connected sums.     

Tensor Expressions for Solving Einstein's Equations by the Method of Sequential Approximation

The main aim of this paper is to develop a mathematical tool for General Relativity (GR). For this purpose useful tensor expressions have been worked out, which considerably ease various calculations using the sequential approximation in Einstein's GR. Based upon these expressions, compact and explicit formulae have been worked out for the covariant and contravariant components of the metric tensor and its determinant.     

Repulsive Gravitation in the Kerr-Newman Field

It is shown that uncharged test particles, released from rest at infinity in the Kerr-Newman field, stop and rebound when the radial coordinate r takes the value r₀ = Q²/(2M). This expression corresponds to the position of a stationary source of the Kerr-Newman field found by the author. It represents the surface of a massive oblate ellipsoid of revolution undergoing rigid rotation. Besides, the magnitude of r₀ guarantees that no violation of causality occurs throughout spacetime. Although the test particles' angular momenta are always zero, they acquire a rotational motion as a consequence of the dragging of inertial frames.     

On a Static Solution of the Einstein Equation with Incoming and Outgoing Radiation

The Einstein equation with T = k k + where k, l are null is considered with spherical symmetry and staticity. The solution has a naked singularity and is not asymptotically flat. However, it may be interpreted as an envelope for any static spherical body making it more massive. Such an interpretation and some of its implications are detailed.     

Theorems on Shear-Free Perfect Fluids with Their Newtonian Analogues

In this paper we provide fully covariant proofs of some theorems on shear-free perfect fluids. In particular, we explicitly show that any shear-free perfect fluid with the acceleration proportional to the vorticity vector (including the simpler case of vanishing acceleration) must be either non-expanding or non-rotating. We also show that these results are not necessarily true in the Newtonian case, and present an explicit comparison of shear-free dust in Newtonian and relativistic theories in order to see where and why the differences appear.     

Addendum to the paper “Closed Spaces in Cosmology”

A few corrections and comments are made upon a previously published paper, on the subject of cosmological models with compact spatial sections.     

How Is the Local-scale Gravitational Instability Influenced by the Surrounding Large-scale Structure Formation?

We develop the formalism to investigate therelation between the evolution of the large-scale(quasi) linear structure and that of the small-scalenonlinear structure in Newtonian cosmology within theLagrangian framework. In doing so, we first derive thestandard Friedmann expansion law using the averagingprocedure over the present horizon scale. Then thelarge-scale (quasi) linear flow is defined by averaging the full trajectory field over a large-scaledomain, but much smaller then the horizon scale. Therest of the full trajectory field is supposed todescribe small-scale nonlinear dynamics. We obtain the evolution equations for the large-scale andsmall-scale part of the trajectory field. These arecoupled each other in most general situations. It isshown that if the shear deformation of fluid elements is ignored in the averaged large-scaledynamics, the small-scale dynamics is described byNewtonian dynamics in an effectiveFriedmann-Robertson-Walker (FRW) background with a localscale factor. The local scale factor is defined by the sum of theglobal scale factor and the expansion deformation of theaveraged large-scale displacement field. This means thatthe evolution of small-scale fluctuations is influenced by the surrounding large-scale structurethrough the modification of FRW scale factor. The effectmight play an important role in the structure formationscenario.     

The Quantum Corrections to the Entropy of Stationary Axisymmetric Einstein-Maxwell-Dilaton-Axion Black Holes

By using 't Hooft's brick wall model, thecorrections for a massless quantum scalar field to theblack hole entropy are studied in a stationaryaxisymmetric Einstein-Maxwell-dilaton-axion black holespace-time. The free energy and entropy for this case arecalculated; in Hartle-Hawking states, the derivedquantum entropy is composed of the part that has ageometric feature and the part that is logarithmically divergent, and it turns out that thelogarithmic part is related to the characteristicquantities of a black hole.     

The Klein-Gordon and the Dirac Oscillators in a Noncommutative Space

We study the Dirac and the Klein-Gordon oscillators in a noncommutative space. It is shown that the Klein-Gordon oscillator in a noncommutative space has a similar behaviour to the dynamics of a particle in a commutative space and in a constant magnetic field. The Dirac oscillator in a noncommutative space has a similar equation to the equation of motion for a relativistic fermion in a commutative space and in a magnetic field, however a new exotic term appears, which implies that a charged fermion in a noncommutative space has an electric dipole moment.     

The Dynamics of Pendulums on Surfaces of Constant Curvature

We define the notion of a pendulum on a surface of constant curvature and study the motion of a mass at a fixed distance from a pivot. We consider some special cases: first a pivot that moves with constant speed along a geodesic, and then a pivot that undergoes acceleration along a fixed geodesic.      

Direct measurement of group dispersion of optical components using white-light spectral interferometry

We present a simple white-light spectral interferometric technique employing a low-resolution spectrometer for a direct measurement of the group dispersion of optical components over a wide wavelength range. The technique utilizes an unbalanced Mach-Zehnder interferometer with a component under test inserted in one arm and the other arm with adjustable path length. We record a series of spectral interferograms to measure the equalization wavelength as a function of the path length difference. We measure the absolute group refractive index as a function of wavelength for a quartz crystal of known thickness and the relative one for optical fiber. In the latter case we use a microscope objective in front and a lens behind the fiber and subtract their group dispersion, which is measured by a technique of tandem interferometry including also a Michelson interferometer.     

Measuring Light Field of Light Source with High Directional Resolution Using Mirrored Ball and Pinhole Camera

This paper presents a method of measuring a light field of a light source with high directional resolution using a mirrored ball and a pinhole camera. The light field describes a spatial and directional distribution of radiances from the light source. The directional distribution is expanded by a reflection on the mirrored ball, and the radiances are measured by a charge-coupled device (CCD) camera with a pinhole lens. The light source is laterally moved by a robot arm to measure the directionally expanded light field, and each pixel on a CCD can obtain the radiances from the light source through the pinhole lens with high directional resolution. The light field is estimated from the pixel value and the position of each pixel using a ray tracing technique. The light field of a krypton lamp was experimentally measured by the proposed method, and the accuracy of the measurement was evaluated against the irradiances measured by a spectro-radiometer at sample points.     

Lognormal Modes of Dielectric Optical Waveguides

It is shown that, at a critical point where the effective refractive index of a mode coincides with the bulk index of a cladding region, optical waveguide modes exhibiting a lognormal feature are supportable for a hyperlongrange refractive-index profile. As a typical example of waveguides that support lognormal modes a parabolic-index core surrounded by a depressed-index cladding is presented.     

Reconstruction of the acoustic impedance profile in a plate using an inverse spectral procedure

An inverse spectral procedure was applied to reconstruct the acoustic impedance profile along the thickness direction of a plate using its thickness resonance frequencies, density and thickness. For a successful reconstruction, the material-property profile must be symmetric about the mid-plane of the plate. Several cases of numerical simulations, including plates with a few layers and with a high number of layers are described. The calculated resonance frequencies were used to reconstruct the acoustic impedance profile, a process that was successful for all cases. We assume that a plate with a high number of layers, each with a different but constant acoustic impedance, simulates a plate with a smoothly varying acoustic impedance profile. It can be concluded that such a plate, which generates small, virtually undetectable, internally reflected waves, can also be reconstructed. In the special case of a plate of unknown thickness and unknown but constant density, the method is still useful, because a relative variation of the material property can be reconstructed using only the resonance frequencies. An experiment using a resonance-mode electromagnetic acoustic transducer (resonance-mode EMAT) is also described. EMAT is a non-contact ultrasonic method that can measure thickness resonance frequencies, making it appropriate for this method. Some examples of applications are measurement of the temperature profile inside a rolled metal sheet, measurement of a clad metal plate, and monitoring of a metal casting.