Geometric algebra techniques for general relativity

Geometric (Clifford) algebra provides an efficient mathematical language for describing physical problems. We formulate general relativity in this language. The resulting formalism combines the efficiency of differential forms with the straightforwardness of coordinate methods. We focus our attention on orthonormal frames and the associated connection bivector, using them to find the Schwarzschild and Kerr solutions, along with a detailed exposition of the Petrov types for the Weyl tensor.     

Coordinates, observables and symmetry in relativity

We investigate the interplay and connections between symmetry properties of equations, the interpretation of coordinates, the construction of observables, and the existence of physical relativity principles in spacetime theories. Using the refined notion of an event as a “point-coincidence” between scalar fields that completely characterise a spacetime model, we also propose a natural generalisation of the relational local observables that does not require the existence of four everywhere invertible scalar fields. The collection of all point-coincidences forms in generic situations a four-dimensional manifold, which is naturally identified with the physical spacetime.     

Electroweak interactions between intense neutrino beams and dense electron-positron magnetoplasmas

The electroweak coupling between intense neutrino beams and strongly degenerate relativistic dense electron-positron magnetoplasmas is considered. The intense neutrino bursts interact with the plasma due to the weak Fermi interaction force, and their dynamics is governed by a kinetic equation. Our objective here is to develop a kinetic equation for a degenerate neutrino gas and to use that equation to derive relativistic magnetohydrodynamic equations. The latter are useful for studying numerous collective processes when intense neutrino beams nonlinearly interact with degenerate, relativistic, dense electron-positron plasmas in strong magnetic fields. If the number densities of the plasma particles are of the order of 10³³ cm^-3, the pair plasma becomes ultra-relativistic, which strongly affects the potential energy of the weak Fermi interaction. The new system of equations allows several neutrino-driven streaming instabilities involving new types of relativistic Alfvén-like waves. The relevance of our investigation to the early universe and supernova explosions is discussed. Received 11 September 2002 Published online 4 February 2003 RID="a" ID="a"Permanent address: Department of Physics, Tbilisi State University, Chavchavadze 3, Tbilisi 38028, Georgia. RID="b" ID="b"Also at the Department of Plasma Physics, Ume? University, 90187 Ume?, Sweden; and the Center for Interdisciplinary Plasma Science, Max-Planck Institut für Plasmaphysik und extraterrestrische Physik, Postfach 1312, 85741 Garching, Germany. e-mail: ps@tp4.ruhr-uni-bochum.de RID="c" ID="c"Permanent address: Department of Plasma Physics, Ume?University, 90187 Ume?, Sweden.     

EPR and photoacoustic studies on 30 kev H ion-implanted n-GaAs

Electron paramagnetic resonance (EPR) measurements are carried out on the 30 keV H⁺ion-implanted, Si-doped GaAs(1 0 0) for various doses from 10¹⁴ to 10¹⁷ cm⁻². The results are correlated with photoacoustic and photoluminescence measurements. All the measurements confirm the sign change of charge carrier at a dose of 10¹⁵ cm⁻².     

Air-coupled ultrasonic assessment of wood veneer

Air-coupled ultrasound (ACU) provides a tool to evaluate wood samples of small or moderate thickness (<30 mm) thereby avoiding direct contact or liquid coupling. Results of through-transmission ACU measurements on wood veneer samples and related products are reported with respect to a wide variety of quality aspects. Fluctuations in the averaged received signal levels appear to be correlated to the presence of natural or machine-induced thickness and density variations, flaws and grain damage, errors produced by the manufacturing process, insufficient bonding on a substrate, etc. In addition it is seen that the variability of the signal levels enables to distinguish between quarter and crown areas.     

Ultrasonic characterization of shrinkage microporosity in aluminum castings

Shrinkage microporosity in cast aluminum was characterized utilizing the frequency dependence of ultrasonic attenuation caused by scattering from the pores. Measurements were made with the plate specimen immersed in water, and, by using a focused transducer, spatial resolution of about 2 mm was obtained. An accurate measure of attenuation was obtained by comparing the specimen’s ultrasonic signal with that from a pore-free reference specimen. Although the attenuation could be fitted using a single spherical pore size, better fits were obtained by assuming a lognormal distribution of spheres. Pore volume fraction inferred from the lognormal fits overestimates the actual volume fraction, determined from density measurements, by the same factor for all volume fractions. The actual volume fraction is overestimated by more than 100%, due to the complicated, nonspherical pore shapes, and must be taken into account to obtain accurate values of porosity. The strong correlation (r²=0.97) between ultrasonic and density-derived volume fractions permits reliable, nondestructive laboratory measurements of porosity.     

Debye screening versus Gauss law in electrostatics: Finite size effects

We revisit the well-known topics of self- and induced-screening in an otherwise isotropic neutral plasma/colloid. It is pointed out that the standard Debye-Hückel (DH) theory (ignoring finite size effects) suffers from many ambiguities related to net ionic numbers, total charge of the system, role of the electrostatic Gauss law, short-distance behaviour of the potential and incorrectly normalized pair correlation functions. We give a new formulation (incorporating finite size effects) such that ionic numbers are maintained, the total charge of the system has physically correct value, the Gauss law boundary conditions are rigorously obeyed, short-distance behaviour of the potential is guaranteed automatically, and correlation functions are correctly normalized. Numerical differences between the two approaches show up if the screening length μ⁻¹ becomes comparable to the size R of the system.     

Electronic structure and electron dynamics at the GaSb(0 0 1) surface studied by femtosecond pump-and-probe pulsed laser photoemission spectroscopy

Transiently excited electron states at the GaSb(0 0 1) surface have been studied by means of time- and angle-resolved photoemission spectroscopy based on a femtosecond laser system. A normally unpopulated surface electron state has been found at ∼250 meV above the valence band maximum with a strong confinement at the center of the surface Brillouin zone. The lifetime of transiently excited carriers at the intergap surface states has been found to be ∼11 ps, associated with rapid carrier diffusion.     

Comment on `Five-Dimensional Cosmological Model with Variable

This comment corrects the small errors in the Letter of Baysal and Yilmaz [Chin. Phys. Lett. 24(2007)2185], where the case of n=1 was ignored. Meanwhile, the discussion in this comment on the case of n=-3 is novel, whichshows a potential reason why today the effect of the extra dimension has not been observed.