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

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

Energy Distribution of a Stringy Charged Black Hole

The energy distribution associated with a stringy charged black hole is studied using M{\o}ller's energy-momentum complex. Our result is reasonable and it differs from that known in literature using Einstein's energy-momentum complex.Comment: Latex, no figure

Rotating Relativistic Thin Disks

Two families of models of rotating relativistic disks based on Taub-NUT and Kerr metrics are constructed using the well-known "displace, cut and reflect" method. We find that for disks built from a generic stationary axially symmetric metric the "sound velocity", $(pressure/density)^{1/2}$, is equal to the geometric mean of the prograde and retrograde geodesic circular velocities of test particles moving on the disk. We also found that for generic disks we can have zones with heat flow. For the two families of models studied the boundaries that separate the zones with and without heat flow are not stable against radial perturbations (ring formation).Comment: 18 eps figures, to be published PR

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

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

Energy Distribution of a Stationary Beam of Light

Aguirregabiria et al showed that Einstein, Landau and Lifshitz, Papapetrou, and Weinberg energy-momentum complexes coincide for all Kerr-Schild metric. Bringely used their general expression of the Kerr-Schild class and found energy and momentum densities for the Bonnor metric. We obtain these results without using Aguirregabiria et al results and verify that Bringley's results are correct. This also supports Aguirregabiria et al results as well as Cooperstock hypothesis. Further, we obtain the energy distribution of the space-time under consideration.Comment: Latex, no figures [Admin note: substantial overlap with gr-qc/9910015 and hep-th/0308070

Predicting language learners' grades in the L1, L2, L3 and L4: the effect of some psychological and sociocognitive variables

This study of 89 Flemish high-school students' grades for L1 (Dutch), L2 (French), L3 (English) and L4 (German) investigates the effects of three higher-level personality dimensions (psychoticism, extraversion, neuroticism), one lower-level personality dimension (foreign language anxiety) and sociobiographical variables (gender, social class) on the participants' language grades. Analyses of variance revealed no significant effects of the higher-level personality dimensions on grades. Participants with high levels of foreign language anxiety obtained significantly lower grades in the L2 and L3. Gender and social class had no effect. Strong positive correlations between grades in the different languages could point to an underlying sociocognitive dimension. The implications of these findings are discussed

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

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