Cosmic censorship and spherical gravitational collapse with tangential pressure

We study the spherical gravitational collapse of a compact object under the approximation that the radial pressure is identically zero, and the tangential pressure is related to the density by a linear equation of state. It turns out that the Einstein equations can be reduced to the solution of an integral for the evolution of the area radius. We show that for positive pressure there is a finite region near the center which necessarily expands outwards, if collapse begins from rest. This region could be surrounded by an inward moving one which could collapse to a singularity - any such singularity will necessarily be covered by a horizon. For negative pressure the entire object collapses inwards, but any singularities that could arise are not naked. Thus the nature of the evolution is very different from that of dust, even when the ratio of pressure to density is infinitesimally small.Comment: 16 pages, Latex file, two figures, uses epsf.st

Spherical Universes with Anisotropic Pressure

Einstein's equations are solved for spherically symmetric universes composed of dust with tangential pressure provided by angular momentum, L(R), which differs from shell to shell. The metric is given in terms of the shell label, R, and the proper time, tau, experienced by the dust particles. The general solution contains four arbitrary functions of R - M(R), L(R), E(R) and r(0,R). The solution is described by quadratures, which are in general elliptic integrals. It provides a generalization of the Lemaitre-Tolman-Bondi solution. We present a discussion of the types of solution, and some examples. The relationship to Einstein clusters and the significance for gravitational collapse is also discussed.Comment: 24 pages, 11 figures, accepted for publication in Classical and Quantum Gravit

Methodology for estimating the ground heat absorption rate of Ground Heat Exchangers

In Ground Source Heat Pump systems, the heat exchange rate is an important factor with regard to the initial cost of the system. When the Ground Heat Exchanger (GHE) is installed in a lithology with high thermal properties in the presence of groundwater, the heat exchange rates are larger than in the cases with poor thermal response of the ground and no groundwater. This research, hence, focuses on a methodology of measuring and analyzing the thermal properties of the lithologies encountered in an area, which can be used for the prediction of heat injection rates of a GHE, depending on its characteristics, the installation area ground properties and groundwater flow. A tool was created with the use of FlexPDE software, and a study case was chosen in order to validate the results. Twenty-two, 100 m in depth, boreholes located in Lefkosia (Cyprus) were tested through simulation for their geothermal performance over time. Subsequently the estimated heat load for the boreholes, after 24 h of operation in cooling mode, was used with the help of Geographic Information System software for the compilation of a heat load per meter depth map that can be transferred to the ground by a GHE. A review of similar studies and Geographical Information System applications referring to other countries is also presented and their results are compared to the results of this study. The step by step procedure presented in this paper can be used by engineers handling geothermal projects as a useful guide for sizing GHEs and calculating the heat injection rates of any area

Gravastar Solutions with Continuous Pressures and Equation of State

We study the gravitational vacuum star (gravastar) configuration as proposed by other authors in a model where the interior de Sitter spacetime segment is continuously extended to the exterior Schwarzschild spacetime. The multilayered structure in previous papers is replaced by a continuous stress-energy tensor at the price of introducing anisotropy in the (fluid) model of the gravastar. Either with an ansatz for the equation of state connecting the radial $p_r$ and tangential $p_t$ pressure or with a calculated equation of state with non-homogeneous energy/fluid density, solutions are obtained which in all aspects satisfy the conditions expected for an anisotropic gravastar. Certain energy conditions have been shown to be obeyed and a polytropic equation of state has been derived. Stability of the solution with respect to possible axial perturbation is shown to hold.Comment: 19 pages, 9 figures. Latest version contains new and updated references along with some clarifying remarks in the stability analysi

Black holes vs. naked singularities formation in collapsing Einstein's clusters

Non-static, spherically symmetric clusters of counter-rotating particles, of the type first introduced by Einstein, are analysed here. The initial data space can be parameterized in terms of three arbitrary functions, namely; initial density, velocity and angular momentum profiles. The final state of collapse, black hole or naked singularity, turns out to depend on the order of the first non-vanishing derivatives of such functions at the centre. The work extends recent results by Harada, Iguchi and Nakao.Comment: 13 pages, LaTeX format. To appear in Physical Review

Bound states of spin-half particles in a static gravitational field close to the black hole field

We consider the bound-state energy levels of a spin-1/2 fermion in the gravitational field of a near-black hole object. In the limit that the metric of the body becomes singular, all binding energies tend to the rest-mass energy (i.e. total energy approaches zero). We present calculations of the ground state energy for three specific interior metrics (Florides, Soffel and Schwarzschild) for which the spectrum collapses and becomes quasi-continuous in the singular metric limit. The lack of zero or negative energy states prior to this limit being reached prevents particle pair production occurring. Therefore, in contrast to the Coulomb case, no pairs are produced in the non-singular static metric. For the Florides and Soffel metrics the singularity occurs in the black hole limit, while for the Schwarzschild interior metric it corresponds to infinite pressure at the centre. The behaviour of the energy level spectrum is discussed in the context of the semi-classical approximation and using general properties of the metric.Comment: 16 pages, 6 Figures. Submitted to General Relativity and Gravitatio

Effect of additional water supply during grain filling on protein composition and epitope characteristics of winter oats

Pure oats in gluten-free diets (GFD) represent important nutritional benefits for people suffering from celiac disease (CD). However, oat cultivars do not contain the typical CD-related wheat gliadin analog polypeptides. Emerging evidence suggests that oat cultivars containing gluten-like epitopes in avenin sequences may pose potential health risks for celiac patients in rare cases, depending on the individual’s susceptibility. Consequently, it is necessary to screen oats in terms of protein and epitope composition, to be able to select safe varieties for gluten-free applications. The overall aim of our study is to investigate the variation of oat protein composition directly related to health-related and techno-functional properties and to examine how the protein compositional parameters change due to irrigation during the grain-filling period as compared to the natural rain-fed grown, in a large winter oat population of different geographic origin. Elements of an oat sample population representing 164 winter oat varieties from 8 countries and the protein composition of resulting samples have been characterized. Size distribution of the total protein extracts has been analyzed by SE-HPLC, while the 70% ethanol extracted proteins were analyzed by RP-HPLC. Protein extracts are separated into 3 main groups of fractions on the SE-HPLC column; polymeric, avenin, and non-avenin monomeric protein groups, representing 59.17–80.87%, 12.89–31.03%, and 3.40–9.41% of total protein content, respectively. The ratio of polymeric to monomeric proteins varied between 1.71 and 6.07. 91 RP-HPLC-separated peaks have been differentiated from the ethanol extractable proteins of the entire population. The various parameters identified a lot of variation, confirming the significance of genotypic variation. In addition, it was also established that the additional water supply during grain filling significantly affected the various quantitative parameters of protein content, but not its qualitative structure. This environmental effect, however, was strongly genotype-dependent. Winter oat genotypes with low levels of epitope content were identified and it was proven that these characteristics were independent of the environmental factor of water availability. These genotypes are appropriate for initiating a specific breeding program to yield oat cultivars suitable for CD patients

How often does the Unruh-DeWitt detector click? Regularisation by a spatial profile

We analyse within first-order perturbation theory the instantaneous transition rate of an accelerated Unruh-DeWitt particle detector whose coupling to a massless scalar field on four-dimensional Minkowski space is regularised by a spatial profile. For the Lorentzian profile introduced by Schlicht, the zero size limit is computed explicitly and expressed as a manifestly finite integral formula that no longer involves regulators or limits. The same transition rate is obtained for an arbitrary profile of compact support under a modified definition of spatial smearing. Consequences for the asymptotic behaviour of the transition rate are discussed. A number of stationary and nonstationary trajectories are analysed, recovering in particular the Planckian spectrum for uniform acceleration.Comment: 30 pages, 1 figure. v3: Added references and minor clarification

Extension of the characteristic equation to absorption chillers with adiabatic absorbers

Various researchers have developed models of conventional H2O–LiBr absorption machines with the aim of predicting their performance. In this paper, the methodology of characteristic equations developed by Hellmann et al. (1998) is applied. This model is able to represent the capacity of single effect absorption chillers and heat pumps by means of simple algebraic equations. An extended characteristic equation based on a characteristic temperature difference has been obtained, considering the facility features. As a result, it is concluded that for adiabatic absorbers a subcooling temperature must be specified. The effect of evaporator overflow has been characterized. Its influence on cooling capacity has been included in the extended characteristic equation. Taking into account the particular design and operation features, a good agreement between experimental performance data and those obtained through the extended characteristic equation has been achieved at off-design operation. This allows its use for simulation and control purposes