Quantum Propagators for Geodesic Congruences

Using the Raychaudhuri equation, we show that a quantum probability amplitude (Feynman propagator) can be univocally associated to any timelike or null affinely parametrized geodesic congruence.

Modified Equation of Impulse for Solitons in an Open Water Channel

On the basis of the certain form of write of an impulse equation the modeling of the solitary waves in the water channel is examined at action of gravitation forces. It is shown that as against an existing method of modelling where the waves propagating from left to right turn out from the equation of an impulse, and from right to left from the continuity equation in the offered technique both waves turn out from the equation of impulse. It is marked that the given method is physically more correct. Calculation of a solitary wave, its velocity and geometrical characteristics is submitted.

A Conceptual Model to Explain Dark Matter and Dark Energy

This paper considers a conceptual model that attempts to explain ‘Dark Matter’ and ‘Dark Energy’. The model is based on considering a gravitational field to be the result of a mass (a Higgs field) scattering pre-existing cosmic background space-time waves or ‘Uber-waves’. The term ‘Uber’ is used to denote an outstanding or supreme example of a particular kind of gravitational wave with cosmic-scale wavelengths that are far in excess of those associated with the gravitational waves generated by accelerating masses. Such waves are taken to be the very lowest frequency components associated with the spectrum of space-time waves generated by the ‘Big Bang’ and are supported by the expanding fabric of space-time produced at the point of the big bang, i.e. the lowest frequency components of a cosmological spectrum whose bandwidth is the a Planck frequency (～10∧43 Hz). Like electromagnetic waves, Uber waves are taken to propagate with an upper velocity consistent with the speed of light and interact with, and are scattered by, a Higgs field. This interaction produces the effect of a mass locally curving space-time, an idea that is contrary to the conventional model associated with General Relativity where mass is taken to curve space-time directly which otherwise remains ‘flat’. By assuming the pre-existence of background Uber waves, we consider the concave curvature of such waves to generate an apparent attractive gravitational force. This interaction produces the effect of a mass locally curving space-time, an idea that is contrary to the conventional model associated with General Relativity where mass is taken to curve space-time directly which otherwise remains ‘flat’. By assuming the pre-existence of background Uber waves, we consider the concave curvature of such waves to generate an apparent attractive gravitational force. This attractive force is taken to govern the formation of large scale structures of matter (galaxies and super-clusters of galaxies, for example) in the conventional sense but surrounded by a residual background gravitational field. It is this residual field that gives rise to the effect known as dark matter where more gravity (as an attractive only force) appears to be available than that which can be accounted for by the observed (luminous) mass, a luminosity that is generated primarily by nuclear fusion in stars. The convex curvature of Uber waves is considered to account for cosmic voids within which gravity is a repulsive force and where large scale structures of matter can therefore not be formed. This is considered to explain the super-large cosmic voids or super voids that are observed. These are regions of the universe where there is an absence of rich super clusters of matter. In these anti-gravity zones, only relatively small structures of matter can be formed by electrostatic forces alone which are then repelled from each other when their mass becomes significant enough for the force of anti-gravity to become significant. In such regions of an Uber wave, the matter generated from electrostatic forces builds up to produce a weak gravitational repulsive field due to the low mass density within a void. However, due to the immense size of these cosmic voids, they are taken to generate a net repulsive force which is considered to be the reason for the acceleration associated with the expansion of the universe; the effect of dark energy. This effect also accounts for the cosmic web structure in which luminescent matter appears to exist in relatively thin connective filaments. The purpose of this paper is to provide a conceptual model and not to investigate the ideas proposed in any significant mathematical detail. This is accomplished by building up the ideas on a case-by-case basis, coupled with a series of thought experiments but without resorting to specific physical scales or the physical parameters associated with these scales other than, by default, the speed of light and Newton’s gravitational constant.

Eikonal Equations for Null Radial Geodesics in the Schwarzschild Metric

We study the eikonal function φ corresponding to outgoing and ingoing radial null geodesics (light rays in the short wave length limit) in the Schwarzschild spacetime. Contrary to the behavior of the expansion scalar θ at the singularities (past and future), φ turns out to be finite at r = 0 (except for light travelling along the horizons) and inversely proportional to M, the mass of the black hole, and so proportional to the Hawking temperature.

Antipodal Identification in the Schwarzschild Spacetime

"Through a Möbius transformation, we study aspects like topology, ligth cones, horizons, curvature singularity, lines of constant Schwarzschild coordinates r and t, null geodesics, and transformed metric, of the spacetime (SKS/2)^' that results from: i) the antipode identification in the Schwarzschild-Kruskal-Szekeres (SKS) spacetime, and ii) the suppression of the consequent conical singularity. In particular, one obtains a non simply-connected topology: (SKS/2)^' = R^2* ×S^2 and, as expected, bending light cones."

Interaction of Electromagnetic Wave and Metamaterial with Inductive Type Chiral Inclusions

The principle of calculation of a plate from a metamaterial with inductive type chiral inclusions is submitted. It is shown that distribution of an electromagnetic wave in such substance can be investigated with the help of using of a chiral parameter and on the basis of a detailed method of calculation. By comparison of two methods the dependence of chiral parameter from frequency of electromagnetic radiation falling on a plate is found. With the help of a detailed method the nonlinear differential equation for potential on the chiral plate is found. It is shown that this equation has solutions as traveling solitary waves and standing waves but not traveling sine waves. The analysis of the received solutions of the nonlinear equation is carried out. Transition from the multiwave solution to the solution as standing waves is graphically shown at reduction of distance between the chiral elements.