Dark Energy and the mass of galaxy clusters

Up to now, Dark Energy evidences are based on the dynamics of the universe on very large scales, above 1 Gpc. Assuming it continues to behave like a cosmological constant $\Lambda$ on much smaller scales, I discuss its effects on the motion of non-relativistic test-particles in a weak gravitational field and I propose a way to detect evidences of $\Lambda \neq 0$ at the scale of about 1 Mpc: the main ingredient is the measurement of galaxy cluster masses.Comment: 5 pages, no figures, references adde

Gravitational Collapse with a Cosmological Constant

We consider the effect of a positive cosmological constant on spherical gravitational collapse to a black hole for a few simple, analytic cases. We construct the complete Oppenheimer-Snyder-deSitter (OSdS) spacetime, the generalization of the Oppenheimer-Snyder solution for collapse from rest of a homogeneous dust ball in an exterior vacuum. In OSdS collapse, the cosmological constant may affect the onset of collapse and decelerate the implosion initially, but it plays a diminishing role as the collapse proceeds. We also construct spacetimes in which a collapsing dust ball can bounce, or hover in unstable equilibrium, due to the repulsive force of the cosmological constant. We explore the causal structure of the different spacetimes and identify any cosmological and black hole event horizons which may be present.Comment: 7 pages, 10 figures; To appear in Phys. Rev.

Maximally extended, explicit and regular coverings of the Schwarzschild - de Sitter vacua in arbitrary dimension

Maximally extended, explicit and regular coverings of the Schwarzschild - de Sitter family of vacua are given, first in spacetime (generalizing a result due to Israel) and then for all dimensions $D$ (assuming a $D-2$ sphere). It is shown that these coordinates offer important advantages over the well known Kruskal - Szekeres procedure.Comment: 12 pages revtex4 5 figures in color. Higher resolution version at http://www.astro.queensu.ca/~lake/regularcoordinates.pd

Global properties of warped solutions in General Relativity

Assuming the four-dimensional space-time to be a general warped product of two surfaces we reduce the four-dimensional Einstein equations to a two-dimensional problem which can be solved. All global vacuum solutions are explicitly constructed and analysed. The classification of the solutions includes the Schwarzschild, the (anti-)de Sitter, and other well-known solutions but also many exact ones whose detailed global properties to our knowledge have not been discussed before. They have a natural physical interpretation describing single or several wormholes, domain walls of curvature singularities, cosmic strings, cosmic strings surrounded by domain walls, solutions with closed timelike curves, etc.Comment: 35 pages, 5 eps figures, minor change

A dynamic deep sleep stage in Drosophila

Howmight one determine whether simple animals such as flies sleep in stages? Sleep inmammalsis a dynamic process involving different stages of sleep intensity, and these are typically associated with measurable changes in brain activity (Blake and Gerard, 1937; Rechtschaffen and Kales, 1968; Webb and Agnew, 1971). Evidence for different sleep stages in invertebrates remains elusive, even though it has been well established that many invertebrate species require sleep (Campbell and Tobler, 1984; Hendricks et al., 2000; Shaw et al., 2000; Sauer et al., 2003). Here we used electrophysiology and arousal-testing paradigms to show that the fruit fly, Drosophila melanogaster, transitions between deeper and lighter sleep within extended bouts of inactivity, with deeper sleep intensities after15 and30 min of inactivity. As in mammals, the timing and intensity of these dynamic sleep processes in flies is homeostatically regulated and modulated by behavioral experience. Two molecules linked to synaptic plasticity regulate the intensity of the first deep sleep stage. Optogenetic upregulation of cyclic adenosine monophosphate during the day increases sleep intensity at night, whereas loss of function of a molecule involved in synaptic pruning, the fragile-X mental retardation protein, increases sleep intensity during the day. Our results show that sleep is not homogenous in insects, and suggest that waking behavior and the associated synaptic plasticity mechanisms determine the timing and intensity of deep sleep stages in Drosophila

A Cosmological No-Hair Theorem

A generalisation of Price's theorem is given for application to Inflationary Cosmologies. Namely, we show that on a Schwarzschild--de Sitter background there are no static solutions to the wave or gravitational perturbation equations for modes with angular momentum greater than their intrinsic spin.Comment: 9 pages, NCL94 -TP4, (Revtex

Combined assessment (aspiration cytology and mammography) of clinically suspicious breast masses

We examined the safety and utility of the combined assessment of aspiration cytology and mammography in 705 women who had clinically suspicious or malignant palpable breast masses. Histological assessment confirmed 176 benign and 529 malignant lesions. There were no incorrect (false positive) diagnoses made in the 176 benign masses when combined assessment was used (specificity 1,0; predictive value 0,86); in isolation, however, there was a false positive cytological diagnosis («papillary carcinoma») and 3 false positive mammographic diagnoses. Benign disease (false negative) was incorrectly diagnosed by combined assessment in 4 of the 529 malignant masses (sensitivity 0,99; predictive value 0,98): cytological diagnoses were of fat necrosis (2) and benign cells on cytospin (1) and aspiration biopsy (1); mammographic diagnoses were of benign disease (2) and normality (2). Indeterminate («atypical», «suspicious») diagnoses were problematic and frequent (overall 223 (31,6%), malignant masses 137 (25,9%), benign masses 86 (48,9%); cytology 117 (16,6%), mammography 141 (20%). Thus, with the combined assessment of mammography and cytology in clinically suspicious breast masses, a decisive diagnosis was made in about two-thirds of cases allowing the safe commencement of therapy; the balance of patients required cone or excision biopsy

Ernst equation and spheroidal coordinates with a cosmological constant term

We discuss solution generating techniques treating stationary and axially symmetric metrics in the presence of a cosmological constant. Using the recently found extended form of Ernst's complex equation, which takes into account the cosmological constant term, we propose an extension of spheroidal coordinates adapted to asymptotically de-Sitter and anti de-Sitter static spacetimes. In the absence of a cosmological constant we show in addition that any higher dimensional metric parametrised by a single angular momentum can be given by a 4 dimensional solution and Weyl potentials parametrising the extra Killing directions. We explicitly show how a stationary, and a static axially symmetric spacetime solution in 4 dimensions, can be {\it added} together to give a 5 dimensional stationary and axisymmetric solution.Comment: 9 pages, no figures, some additional results to gr-qc/0610091. Prepared for 12th Conference on Recent Developments in Gravity (NEB XII), Nafplio, Greece, 29 Jun - 2 Jul 200

Maxwell's theory on a post-Riemannian spacetime and the equivalence principle

The form of Maxwell's theory is well known in the framework of general relativity, a fact that is related to the applicability of the principle of equivalence to electromagnetic phenomena. We pose the question whether this form changes if torsion and/or nonmetricity fields are allowed for in spacetime. Starting from the conservation laws of electric charge and magnetic flux, we recognize that the Maxwell equations themselves remain the same, but the constitutive law must depend on the metric and, additionally, may depend on quantities related to torsion and/or nonmetricity. We illustrate our results by putting an electric charge on top of a spherically symmetric exact solution of the metric-affine gauge theory of gravity (comprising torsion and nonmetricity). All this is compared to the recent results of Vandyck.Comment: 9 pages, REVTeX, no figures; minor changes, version to be published in Class. Quantum Gra

The geodesic structure of the Schwarzschild Anti-de Sitter black hole

In the present work we found the geodesic structure of an AdS black hole. By means of a detailed analyze of the corresponding effective potentials for particles and photon, we found all the possible motions which are allowed by the energy levels. Radial and non radial trajectories were exactly evaluated for both geodesics. The founded orbits were plotted in order to have a direct visualization of the allowed motions. We show that the geodesic structure of this black hole presents new type of motions not allowed by the Schwarzschild spacetime.Comment: 17 pages, 11 figure