Abstract:
Most recently, experimental determinations of the spectrometric characteristics and internal structural velocities of galaxies have suggested the presence of massive central black holes. In the present work, we examine whether conditions existed in the early universe, that could have led to the formation of gravitational structures possessing such unusual characteristics. We propose an early-time pressure-fluctuation model, which would have generated a radiation based energy distribution possessing the characteristic of a centrally collapsed zone isolated from its surrounding environment and thereby manifesting such a black hole behavior. Einstein's gravitational equations are assumed to apply within the radiation-dominated hole-core spatial domain and, with utilization of a spherically symmetric isotropic metric, are used in order to calculate the evolutionary time expansion characteristics. Birth times for the radiation structures are uniquely correlated with the size of the spheres and are primarily determined from the early time energy densities and the apparent curvatures presented by the gravitational equations. The model displays an early time pressure fluctuation collapse, tentatively interpreted to be the formation of a galaxy hole, and therein provides a theoretical basis for the experimental data.

Abstract:
We use direct products of Einstein Metrics to construct new solutions to Einstein's Equations with cosmological constant. We illustrate the technique with three families of solutions having the geometries Kerr/de Sitter X de Sitter, Kerr/anti-de Sitter X anti-de Sitter and Kerr X Kerr.

Abstract:
Classical determinations of galaxy distances and galaxy recessional velocities have been generated from luminosity and emission spectrometric data. The analyses of these galactic spectrometric electromagnetic frequency shifts have resulted in the Hubble law and are understood as a Doppler effect stemming from an expansion of space. In the present work, a galaxy-core expansion model with a time evolving matter and radiation distribution is put forth, leading to a supplementary treatment of the optical redshift measurements. Einstein's gravitational equations are assumed to apply within a galaxy-core spatial domain and, with utilization of a generalized Robertson-Walker-Schwarzschild metric, are used in order to calculate the evolutionary expansion characteristics. The galaxy-core model is described as a flat metric, matter plus radiation, sigma = 1/3, energy distribution. It predicts an early time density fluctuation collapse, understood to be the formation of a galaxy hole, and provides an interpretational basis for the experimental data.

Abstract:
We present a practical application of parallel symbolic computation in General Relativity: the calculation of curvature invariants for large dimension. We discuss the structure of the calculations, an implementation of the technique and scaling of the computation with spacetime dimension for various invariants.

Abstract:
We present exact solutions describing rotating, inhomogeneous dust with generic initial data in 2+1 dimensional AdS spacetime and show how they are smoothly matched to the Banados-Teitelboim-Zanelli (BTZ) solution in the exterior. The metrics, which are the rotational analogues of the 2+1 dimensional LeMaitre-Tolman-Bondi (LTB) family, are described by their angular momentum and one additional constant which, together with the angular momentum, determines the energy density of the dust cloud. The weak energy condition gives a constraint on the angular momentum profile inside the cloud. Solutions can be stationary or time dependent, but only the time dependent solutions can be matched consistently to a BTZ exterior. No singularity is formed in either the stationary or the time dependent cases.

Abstract:
Quantum fields propagating on a curved spacetime are investigated in terms of microlocal analysis. We discuss a condition on the wave front set for the corresponding n-point distributions, called ``microlocal spectrum condition'' ($\mu$SC). On Minkowski space, this condition is satisfied as a consequence of the usual spectrum condition. Based on Radzikowski's determination of the wave front set of the two-point function of a free scalar field, satisfying the Hadamard condition in the Kay and Wald sense, we construct in the second part of this paper all Wick polynomials including the energy-momentum tensor for this field as operator valued distributions on the manifold and prove that they satisfy our microlocal spectrum condition.

Abstract:
Using speckle-interferometry we have carried out repeated measurements of relative positions for the components of 34 T Tauri binary systems. The projected separation of these components is low enough that orbital motion is expected to be observable within a few years. In most cases orbital motion has indeed been detected. The observational data is discussed in a manner similar to Ghez et al. (1995). However, we extend their study to a larger number of objects and a much longer timespan. The database presented in this paper is valuable for future visible orbit determinations. It will yield empirical masses for T Tauri stars that now are only poorly known. The available data is however not sufficient to do this at the present time. Instead, we use short series of orbital data and statistical distributions of orbital parameters to derive an average system mass that is independent of theoretical assumptions about the physics of PMS stars. For our sample this mass is 2.0 solar masses and thus in the order of magnitude one expects for the mass sum of two T Tauri stars. It is also comparable to mass estimates obtained for the same systems using theoretical PMS evolutionary models.

Abstract:
Biological filaments such as DNA or bacterial flagella are typically curved in their natural states. To elucidate the interplay of viscous drag, twisting, and bending in the overdamped dynamics of such filaments, we compute the steady-state torsional stress and shape of a rotating rod with a kink. Drag deforms the rod, ultimately extending or folding it depending on the kink angle. For certain kink angles and kink locations, both states are possible at high rotation rates. The agreement between our macroscopic experiments and the theory is good, with no adjustable parameters.

Abstract:
Strategies and concepts for the design of THz emitters based on the quantum cascade scheme are analyzed and modeled in terms of a fully three-dimensional Monte Carlo approach; this allows for a proper inclusion of both carrier-carrier and carrier-phonon scattering mechanisms. Starting from the simulation of previously published far-infrared emitters, where no population inversion is achieved, two innovative designs are proposed. The first one follows the well-established chirped-superlattice scheme whereas the second one employs a double-quantum well superlattice to allow energy relaxation through optical phonon emission. For both cases a significant population inversion is predicted at temperatures up to 80 K.

Abstract:
Mid-IR (8 - 13 micron) interferometric data of four oxygen-rich AGB stars (R Aql, R Aqr, R Hya, and W Hya) and one carbon-rich AGB star (V Hya) were obtained with MIDI/VLTI between April 2007 and September 2009. The spectrally dispersed visibility data are analyzed by fitting a circular fully limb-darkened disk (FDD). Results. The FDD diameter as function of wavelength is similar for all oxygen-rich stars. The apparent size is almost constant between 8 and 10 micron and gradually increases at wavelengths longer than 10 micron. The apparent FDD diameter in the carbon-rich star V Hya essentially decreases from 8 to 12 micron. The FDD diameters are about 2.2 times larger than the photospheric diameters estimated from K-band observations found in the literature. The silicate dust shells of R Aql, R Hya and W Hya are located fairly far away from the star, while the silicate dust shell of R Aqr and the amorphous carbon (AMC) and SiC dust shell of V Hya are found to be closer to the star at around 8 photospheric radii. Phase-to-phase variations of the diameters of the oxygen-rich stars could be measured and are on the order of 15% but with large uncertainties. From a comparison of the diameter trend with the trends in RR Sco and S Ori it can be concluded that in oxygen-rich stars the overall larger diameter originates from a warm molecular layer of H2O, and the gradual increase longward of 10 micron can be most likely attributed to the contribution of a close Al2O3 dust shell. The chromatic trend of the Gaussian FWHM in V Hya can be explained with the presence of AMC and SiC dust. The observations suggest that the formation of amorphous Al2O3 in oxygen- rich stars occurs mainly around or after visual minimum. However, no firm conclusions can be drawn concerning the mass-loss mechanism.