A Tolman-Bondi-Lemaitre Cell-Model for the Universe and Gravitational Collapse

A piecewise Tolman-Bondi-Lemaitre (TBL) cell-model for the universe incorporating local collapsing and expanding inhomogeneities is presented here. The cell-model is made up of TBL underdense and overdense spherical regions surrounded by an intermediate region of TBL shells embedded in an expanding universe. The cell-model generalizes the Friedmann as well as Einstein-Straus swiss-cheese models and presents a number of advantages over other models, and in particular the time evolution of the cosmological inhomogeneities is now incorporated within the scheme. Important problem of gravitational collapse of a massive dust cloud, such as a cluster of galaxies or even a massive star, in such a cosmological background is examined. It is shown that the collapsing local inhomogeneities in an expanding universe could result in either a black hole, or a naked singularity, depending on the nature of the set of initial data which consists of the matter distribution and the velocities of the collapsing shells in the cloud at the initial epoch from which the collapse commences.Comment: 14 pages, 3 figure

Initial data and the end state of spherically symmetric gravitational collapse

Generalizing earlier results on the initial data and the final fate of dust collapse, we study here the relevance of the initial state of a spherically symmetric matter cloud towards determining its end state in the course of a continuing gravitational collapse. It is shown that given an arbitrary regular distribution of matter at the initial epoch, there always exists an evolution from this initial data which would result either in a black hole or a naked singularity depending on the allowed choice of free functions available in the solution. It follows that given any initial density and pressure profiles for the cloud, there is a non-zero measure set of configurations leading either to black holes or naked singularities, subject to the usual energy conditions ensuring the positivity of energy density. We also characterize here wide new families of black hole solutions resulting from spherically symmetric collapse without requiring the cosmic censorship assumption.Comment: Ordinary Tex file, 31 pages no figure

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

Relativistic Static Thin Disks: The Counter-Rotating Model

A detailed study of the Counter-Rotating Model (CRM) for generic finite static axially symmetric thin disks with nonzero radial pressure is presented. We find a general constraint over the counter-rotating tangential velocities needed to cast the surface energy-momentum tensor of the disk as the superposition of two counter-rotating perfect fluids. We also found expressions for the energy density and pressure of the counter-rotating fluids. Then we shown that, in general, there is not possible to take the two counter-rotating fluids as circulating along geodesics neither take the two counter-rotating tangential velocities as equal and opposite. An specific example is studied where we obtain some CRM with well defined counter-rotating tangential velocities and stable against radial perturbations. The CRM obtained are in agree with the strong energy condition, but there are regions of the disks with negative energy density, in violation of the weak energy condition.Comment: 19 pages, 6 figures. Submitted to Physical Review

Relativistic Static Thin Disks with Radial Stress Suport

New solutions for static non-rotating thin disks of finite radius with nonzero radial stress are studied. A method to introduce either radial pressure or radial tension is presented. The method is based on the use of conformal transformations.Comment: 19 pages, LaTeX, 7 figures, submitted to Class. Quan. Gra

Investigation of the relevant kinetic processes in the initial stage of a double-arcing instability in oxygen plasmas

A numerical investigation of the kinetic processes in the initial (nanosecond range) stage of the double-arcing instability was developed. The plasma-sheath boundary region of an oxygen-operated cutting torch was considered. The energy balance and chemistry processes in the discharge were described. It is shown that the double-arcing instability is a sudden transition from a diffuse (glow-like) discharge to a constricted (arc-like) discharge in the plasma-sheath boundary region arising from a field-emission instability. A critical electric field value of ∼10^7 V/m was found at the cathodic part of the nozzle wall under the conditions considered. The field-emission instability drives in turn a fast electronic-to-translational energy relaxation mechanism, giving rise to a very fast gas heating rate of at least ∼10^9 K/s, mainly due to reactions of preliminary dissociation of oxygen molecules via the highly excited electronic state O2(B^3) populated by electron impact. It is expected that this fast oxygen heating rate further stimulates the discharge contraction through the thermal instability mechanism.Fil: Mancinelli, Beatriz Rosa. Universidad Tecnológica Nacional. Facultad Regional Venado Tuerto; ArgentinaFil: Prevosto, Leandro. Universidad Tecnológica Nacional. Facultad Regional Venado Tuerto; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe; ArgentinaFil: Chamorro Garcés, Juan Camilo. Universidad Tecnológica Nacional. Facultad Regional Venado Tuerto; ArgentinaFil: Minotti, Fernando Oscar. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Kelly, Hector Juan. Universidad Tecnológica Nacional. Facultad Regional Venado Tuerto; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe; Argentin

Gravitational Collapse and Cosmological Constant

We consider here the effects of a non-vanishing cosmological term on the final fate of a spherical inhomogeneous collapsing dust cloud. It is shown that depending on the nature of the initial data from which the collapse evolves, and for a positive value of the cosmological constant, we can have a globally regular evolution where a bounce develops within the cloud. We characterize precisely the initial data causing such a bounce in terms of the initial density and velocity profiles for the collapsing cloud. In the cases otherwise, the result of collapse is either formation of a black hole or a naked singularity resulting as the end state of collapse. We also show here that a positive cosmological term can cover a part of the singularity spectrum which is visible in the corresponding dust collapse models for the same initial data.Comment: 18 pages, no figure

Naked singularities and Seifert's conjecture

It is shown that for a general nonstatic spherically symmetric metric of the Kerr-Schild class several energy-momentum complexes give the same energy distribution as in the Penrose prescription, obtained by Tod. This result is useful for investigating the Seifert conjecture for naked singularities. The naked singularity forming in the Vaidya null dust collapse supports the Seifert conjecture. Further, an example and a counterexample to this conjecture are presented in the Einstein massless scalar theory.Comment: RevTex, no figures, new results included, published in Physical Review D 60, 104041 (1999

Comparison of bulk milk antibody and youngstock serology screens for determining herd status for Bovine Viral Diarrhoea Virus

BACKGROUND: This paper examines the use of Bulk Milk antibody (BM Ab), Youngstock (YS) serology (Check Tests) and Bulk Milk PCR (BM PCR) for determining the presence or absence of animals persistently infected (PI) with Bovine Viral Diarrhoea Virus (BVDV) within a herd. Data is presented from 26 herds where average herd sizes were 343 and 98 animals for dairy and beef units respectively. Seventeen herds had sufficient data to analyse using Receiver Operating Characteristic (ROC) and probability curves enabling calculation of the sensitivity and specificity of BM Ab and YS Check tests for determining the presence of PI animals within herds in this dataset. RESULTS: Using BM Ab to screen a herd for the presence of PI animals, achieved a herd level sensitivity and specificity of 80.00 % (44.39–97.48 %) and 85.71 % (42.13–99.64 %) respectively (95 % confidence intervals quoted). Sensitivity and specificity of YS Check Tests at a cut off of 3/10 Ab positive YS were 81.82 % (48.22–97.72 %) and 66.67 % (22.28–95.67 %) respectively (95 % confidence interval). These results were achieved by comparing the screening tests to whole herd PI searches that took place 1–19 months after the initial screen with a mean interval of 8 months. Removal of this delay by taking BM samples on the day of a whole herd test and simulating a YS Check Test from the herd test data produced improvements in the reliability of the Check Tests. BM Ab sensitivity and specificity remained unchanged. However, the Check Test sensitivity and specificity improved to 90.9 % (58.72–99.77 %) and 100 % (54.07–100 %) respectively (95 % confidence interval) at a cut of off 2.5/10 Ab positive animals. Our limited BM PCR results identified 5/23 dairy farms with a positive BM PCR result; two contained milking PIs, two had non-milking PIs and another had no PIs identified. CONCLUSIONS: Delaying a PI search following an initial herd screen decreased the diagnostic accuracy and relevance of our results. With careful interpretation, longitudinal surveillance using a combination of the techniques discussed can successfully determine farm status and therefore allow changes in BVDV status to be detected early, thus enabling prompt action in the event of a BVDV incursion