Partially locally rotationally symmetric perfect fluid cosmologies

We show that there are no new consistent cosmological perfect fluid solutions when in an open neighbourhood ${\cal U}$ of an event the fluid kinematical variables and the electric and magnetic Weyl curvature are all assumed rotationally symmetric about a common spatial axis, specialising the Weyl curvature tensor to algebraic Petrov type D. The consistent solutions of this kind are either locally rotationally symmetric, or are subcases of the Szekeres dust models. Parts of our results require the assumption of a barotropic equation of state. Additionally we demonstrate that local rotational symmetry of perfect fluid cosmologies follows from rotational symmetry of the Riemann curvature tensor and of its covariant derivatives only up to second order, thus strengthening a previous result.Comment: 20 pages, LaTeX2.09 (10pt), no figures; shortened revised version, new references; accepted for publication in Classical and Quantum Gravit

Fluid moment hierarchy equations derived from quantum kinetic theory

A set of quantum hydrodynamic equations are derived from the moments of the electrostatic mean-field Wigner kinetic equation. No assumptions are made on the particular local equilibrium or on the statistical ensemble wave functions. Quantum diffraction effects appear explicitly only in the transport equation for the heat flux triad, which is the third-order moment of the Wigner pseudo-distribution. The general linear dispersion relation is derived, from which a quantum modified Bohm-Gross relation is recovered in the long wave-length limit. Nonlinear, traveling wave solutions are numerically found in the one-dimensional case. The results shed light on the relation between quantum kinetic theory, the Bohm-de Broglie-Madelung eikonal approach, and quantum fluid transport around given equilibrium distribution functions.Comment: 5 pages, three figures, uses elsarticle.cl

Fluid moment hierarchy equations derived from gauge invariant quantum kinetic theory

The gauge invariant electromagnetic Wigner equation is taken as the basis for a fluid-like system describing quantum plasmas, derived from the moments of the gauge invariant Wigner function. The use of the standard, gauge dependent Wigner function is shown to produce inconsistencies, if a direct correspondence principle is applied. The propagation of linear transverse waves is considered and shown to be in agreement with the kinetic theory in the long wavelength approximation, provided an adequate closure is chosen for the macroscopic equations. A general recipe to solve the closure problem is suggested.Comment: 12 pages, 1 figur

Photon-graviton pair conversion

We consider the conversion of gravitons and photons as a four-wave mixing process. A nonlinear coupled systems of equations involving two gravitons and two photons is obtained, and the energy exchange between the different degrees of freedom is found. The scattering amplitudes are obtained, from which a crossection for incoherent processes can be found. An analytical example is given, and applications to the early Universe are discussed.Comment: 5 pages, slightly modified as compared to v1, to appear in Class. Quantum Grav. as a Letter to the Edito

Fermat's principle and variational analysis of an optical model for light propagation exhibiting a critical radius

Fermat's principle and variational analysis is used to analyze the trajectories of light propagating in a radially inhomogeneous medium with a singularity in the center. It is found that the light trajectories are similar to those around a black hole, in the sense that there exists a critical radius within which the light cannot escape, but spirals into the singularity.Comment: 5 pages from tex file + 3 figures (eps files

Axistationary perfect fluids -- a tetrad approach

Stationary axisymmetric perfect fluid space-times are investigated using the curvature description of geometries. Attention is focused on space-times with a vanishing electric part of the Weyl tensor. It is shown that the only incompressible axistationary magnetic perfect fluid is the interior Schwarzschild solution. The existence of a rigidly rotating perfect fluid, generalizing the interior Schwarzschild metric is proven. Theorems are stated on Petrov types and electric/magnetic Weyl tensors.Comment: 12 page

Oral Appliance Treatment for Obstructive Sleep Apnea: An Update

Oral appliances (OA) have emerged as an alternative to continuous positive airway pressure (CPAP) for obstructive sleep apnea (OSA) treatment. The most commonly used OA reduces upper airway collapse by advancing the mandible (OAm). There is a strong evidence base demonstrating OAm improve OSA in the majority of patients, including some with more severe disease. However OAm are not efficacious for all, with approximately one-third of patients experiencing no therapeutic benefit. OAm are generally well tolerated, although short-term adverse effects during acclimatization are common. Long-term dental changes do occur, but these are for the most part subclinical and do not preclude continued use. Patients often prefer OAm to gold-standard CPAP treatment. Head-to-head trials confirm CPAP is superior in reducing OSA parameters on polysomnography; however, this greater efficacy does not necessarily translate into better health outcomes in clinical practice. Comparable effectiveness of OAm and CPAP has been attributed to higher reported nightly use of OAm, suggesting that inferiority in reducing apneic events may be counteracted by greater treatment adherence. Recently, significant advances in commercially available OAm technologies have been made. Remotely controlled mandibular positioners have the potential to identify treatment responders and the level of therapeutic advancement required in single night titration polysomnography. Objective monitoring of OAm adherence using small embedded temperature sensing data loggers is now available and will enhance clinical practice and research. These technologies will further enhance efficacy and effectiveness of OAm treatment for OSA