Static Ricci-flat 5-manifolds admitting the 2-sphere

We examine, in a purely geometrical way, static Ricci-flat 5-manifolds admitting the 2-sphere and an additional hypersurface-orthogonal Killing vector. These are widely studied in the literature, from different physical approaches, and known variously as the Kramer - Gross - Perry - Davidson - Owen solutions. The 2-fold infinity of cases that result are studied by way of new coordinates (which are in most cases global) and the cases likely to be of interest in any physical approach are distinguished on the basis of the nakedness and geometrical mass of their associated singularities. It is argued that the entire class of solutions has to be considered unstable about the exceptional solutions: the black string and soliton cases. Any physical theory which admits the non-exceptional solutions as the external vacuua of a collapsing object has to accept the possibility of collapse to zero volume leaving behind the weakest possible, albeit naked, geometrical singularities at the origin.Finally, it is pointed out that these types of solutions generalize, in a straightforward way, to higher dimensions.Comment: Generalize, in a straightforward way, to higher dimension

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

Hydrostatic equilibrium of insular, static, spherically symmetric, perfect fluid solutions in general relativity

An analysis of insular solutions of Einstein's field equations for static, spherically symmetric, source mass, on the basis of exterior Schwarzschild solution is presented. Following the analysis, we demonstrate that the {\em regular} solutions governed by a self-bound (that is, the surface density does not vanish together with pressure) equation of state (EOS) or density variation can not exist in the state of hydrostatic equilibrium, because the source mass which belongs to them, does not represent the `actual mass' appears in the exterior Schwarzschild solution. The only configuration which could exist in this regard is governed by the homogeneous density distribution (that is, the interior Schwarzschild solution). Other structures which naturally fulfill the requirement of the source mass, set up by exterior Schwarzschild solution (and, therefore, can exist in hydrostatic equilibrium) are either governed by gravitationally-bound regular solutions (that is, the surface density also vanishes together with pressure), or self-bound singular solutions (that is, the pressure and density both become infinity at the centre).Comment: 16 pages (including 1 table); added section 5; accepted for publication in Modern Physics Letters

An exact solution of the five-dimensional Einstein equations with four-dimensional de Sitter-like expansion

We present an exact solution to the Einstein field equations which is Ricci and Riemann flat in five dimensions, but in four dimensions is a good model for the early vacuum-dominated universe.Comment: 6 pages; to appear in Journal of Mathematical Physics; v2: reference 3 correcte

Gravitational Collapse of Dust with a Cosmological Constant

The recent analysis of Markovic and Shapiro on the effect of a cosmological constant on the evolution of a spherically symmetric homogeneous dust ball is extended to include the inhomogeneous and degenerate cases. The histories are shown by way of effective potential and Penrose-Carter diagrams.Comment: 2 pages, 2 figures (png), revtex. To appear in Phys. Rev.

Nanodiamond landmarks for subcellular multimodal optical and electron imaging.

There is a growing need for biolabels that can be used in both optical and electron microscopies, are non-cytotoxic, and do not photobleach. Such biolabels could enable targeted nanoscale imaging of sub-cellular structures, and help to establish correlations between conjugation-delivered biomolecules and function. Here we demonstrate a sub-cellular multi-modal imaging methodology that enables localization of inert particulate probes, consisting of nanodiamonds having fluorescent nitrogen-vacancy centers. These are functionalized to target specific structures, and are observable by both optical and electron microscopies. Nanodiamonds targeted to the nuclear pore complex are rapidly localized in electron-microscopy diffraction mode to enable "zooming-in" to regions of interest for detailed structural investigations. Optical microscopies reveal nanodiamonds for in-vitro tracking or uptake-confirmation. The approach is general, works down to the single nanodiamond level, and can leverage the unique capabilities of nanodiamonds, such as biocompatibility, sensitive magnetometry, and gene and drug delivery

Targeted Nanodiamonds for Identification of Subcellular Protein Assemblies in Mammalian Cells

Transmission electron microscopy (TEM) can be used to successfully determine the structures of proteins. However, such studies are typically done ex situ after extraction of the protein from the cellular environment. Here we describe an application for nanodiamonds as targeted intensity contrast labels in biological TEM, using the nuclear pore complex (NPC) as a model macroassembly. We demonstrate that delivery of antibody-conjugated nanodiamonds to live mammalian cells using maltotriose-conjugated polypropylenimine dendrimers results in efficient localization of nanodiamonds to the intended cellular target. We further identify signatures of nanodiamonds under TEM that allow for unambiguous identification of individual nanodiamonds from a resin-embedded, OsO4-stained environment. This is the first demonstration of nanodiamonds as labels for nanoscale TEM-based identification of subcellular protein assemblies. These results, combined with the unique fluorescence properties and biocompatibility of nanodiamonds, represent an important step toward the use of nanodiamonds as markers for correlated optical/electron bioimaging.Comment: 38 pages, 6 figures, SI section with 3 figure