Optical scalars in spherical spacetimes

Consider a spherically symmetric spacelike slice through a spherically symmetric spacetime. One can derive a universal bound for the optical scalars on any such slice. The only requirement is that the matter sources satisfy the dominant energy condition and that the slice be asymptotically flat and regular at the origin. This bound can be used to derive new conditions for the formation of apparent horizons. The bounds hold even when the matter has a distribution on a shell or blows up at the origin so as to give a conical singularity

The Jang equation, apparent horizons, and the Penrose inequality

The Jang equation in the spherically symmetric case reduces to a first order equation. This permits an easy analysis of the role apparent horizons play in the (non)existence of solutions. We demonstrate that the proposed derivation of the Penrose inequality based on the Jang equation cannot work in the spherically symmetric case. Thus it is fruitless to apply this method, as it stands, to the general case. We show also that those analytic criteria for the formation of horizons that are based on the use of the Jang equation are of limited validity for the proof of the trapped surface conjecture.Comment: minor misprints correcte

First constraint on cosmological variation of the proton-to-electron mass ratio from two independent telescopes

A high signal-to-noise spectrum covering the largest number of hydrogen lines (90 H2 lines and 6 HD lines) in a high redshift object was analyzed from an observation along the sight-line to the bright quasar source J2123$-$005 with the UVES spectrograph on the ESO Very Large Telescope (Paranal, Chile). This delivers a constraint on a possible variation of the proton-to-electron mass ratio of Dmu/mu = (8.5 \pm 3.6_{stat} \pm 2.2_{syst}) x 10^{-6} at redshift z=2.059$, which agrees well with a recently published result on the same system observed at the Keck telescope yielding Dmu/mu = (5.6 \pm 5.5_{stat} \pm 2.9_{syst}) x 10^{-6}. Both analyses used the same robust absorption line fitting procedures with detailed consideration of systematic errors.Comment: Accepte

Maxillary sinus septa: prevalence, morphology, diagnostics and implantological implications. Systematic review

Background: The purpose of this review is to indicate the prevalence of septa, illustrate the most adequate diagnostic method and further discuss pre-operative considerations and implantological implications.Materials and methods: On June 30th, 2013, a comprehensive database search was executed using PubMed (Medline) and Google Scholar. No time frames were applied. Only publications in English, Polish and German in peer-reviewed journals were considered.Results: The final number of articles was 55: 7 articles were found to describe the possible aetiology of sinus septa, 34 articles describing the prevalence, 21 including information on classification, 19 showed methods of diagnosis and 24 articles included practical information about the influence of the septa in pre- and implantation surgery. One article could be found in more than one category.Conclusions: Septa can be found in 9% to 70% patients (mean prevalence: about 36%) in every age group — young dentate patients as primary septa and old edentate or edentulous patients as primary or secondary septa more frequentin edentate or edentulous patients. When planning any surgical procedures, septa incidence should be taken into consideration. Precise information about the septa can be obtained from computed tomography (CT) or cone-beam CT. With development of the knowledge and surgical technique, septa appearance has simply become another option for treatment as any form of disadvantage

Global solutions of a free boundary problem for selfgravitating scalar fields

The weak cosmic censorship hypothesis can be understood as a statement that there exists a global Cauchy evolution of a selfgravitating system outside an event horizon. The resulting Cauchy problem has a free null-like inner boundary. We study a selfgravitating spherically symmetric nonlinear scalar field. We show the global existence of a spacetime with a null inner boundary that initially is located outside the Schwarzschild radius or, more generally, outside an apparent horizon. The global existence of a patch of a spacetime that is exterior to an event horizon is obtained as a limiting case.Comment: 31 pages, revtex, to appear in the Classical and Quantum Gravit

Waves in Schwarzschild spacetimes: How strong can imprints of the spacetime curvature be

Misprints corrected, two references added. To appear in the Phys. Rev. D

Necessary Conditions for Apparent Horizons and Singularities in Spherically Symmetric Initial Data

We establish necessary conditions for the appearance of both apparent horizons and singularities in the initial data of spherically symmetric general relativity when spacetime is foliated extrinsically. When the dominant energy condition is satisfied these conditions assume a particularly simple form. Let $\rho_{Max}$ be the maximum value of the energy density and $\ell$ the radial measure of its support. If $\rho_{Max}\ell^2$ is bounded from above by some numerical constant, the initial data cannot possess an apparent horizon. This constant does not depend sensitively on the gauge. An analogous inequality is obtained for singularities with some larger constant. The derivation exploits Poincar\'e type inequalities to bound integrals over certain spatial scalars. A novel approach to the construction of analogous necessary conditions for general initial data is suggested.Comment: 15 pages, revtex, to appear in Phys. Rev.

On the Penrose Inequality for general horizons

For asymptotically flat initial data of Einstein's equations satisfying an energy condition, we show that the Penrose inequality holds between the ADM mass and the area of an outermost apparent horizon, if the data are restricted suitably. We prove this by generalizing Geroch's proof of monotonicity of the Hawking mass under a smooth inverse mean curvature flow, for data with non-negative Ricci scalar. Unlike Geroch we need not confine ourselves to minimal surfaces as horizons. Modulo smoothness issues we also show that our restrictions on the data can locally be fulfilled by a suitable choice of the initial surface in a given spacetime.Comment: 4 pages, revtex, no figures. Some comments added. No essential changes. To be published in Phys. Rev. Let

THE EFFECT OF SPACE CHARGE ON PARTIAL DISCHARGES INCEPTION VOLTAGE IN AIR GAPS WITHIN HIGH DENSITY POLYETHYLENE

Partial discharges (PDs) which can occur in embedded voids in solid dielectrics depend on many factors, among them space charge which can seem to be one of the most relevant. As a matter of fact, under certain high voltage operating conditions, trapped or low-mobility electrically charged species within the insulation can give rise to space charge build up. These charges may have been the product of earlier PD events but they can also be the result of charge transport from the electrodes towards defect which can be contained within the insulation. This paper deals with the relation between space charge and partial discharges phenomena due to electrical stresses. Both simulation and experimental evidences of relations between partial discharge inception voltage (PDIV) and charge accumulation are investigated. PDs in trapped air-filled gaps between two adjacent insulated tapes made of high density polyethylene (HDPE) were measured. An amount of space charge is introduced on the cavity surface by negative direct current application (DC). An alternative current of increasing magnitude was then applied until PDs were initiated and observed. The voltages at which PDs initiate are measured for samples with and without space charge. It was shown that the larger the amount of space charge, the lower PDIV. Simulation results are in good agreement with those obtained from experiment