The Final Fate of Spherical Inhomogeneous Dust Collapse

We examine the role of the initial density and velocity distribution in the gravitational collapse of a spherical inhomogeneous dust cloud. Such a collapse is described by the Tolman-Bondi metric which has two free functions: the `mass-function' and the `energy function', which are determined by the initial density and velocity profile of the cloud. The collapse can end in a black-hole or a naked singularity, depending on the initial parameters characterizing these profiles. In the marginally bound case, we find that the collapse ends in a naked singularity if the leading non-vanishing derivative of the density at the center is either the first one or the second one. If the first two derivatives are zero, and the third derivative non-zero, the singularity could either be naked or covered, depending on a quantity determined by the third derivative and the central density. If the first three derivatives are zero, the collapse ends in a black hole. In particular, the classic result of Oppenheimer and Snyder, that homogeneous dust collapse leads to a black hole, is recovered as a special case. Analogous results are found when the cloud is not marginally bound, and also for the case of a cloud starting from rest. We also show how the strength of the naked singularity depends on the density and velocity distribution. Our analysis generalizes and simplifies the earlier work of Christodoulou and Newman [4,5] by dropping the assumption of evenness of density functions. It turns out that relaxing this assumption allows for a smooth transition from the naked singularity phase to the black-hole phase, and also allows for the occurrence of strong curvature naked singularities.Comment: 23 pages; Plain Tex; TIFR-TAP preprin

Genericity aspects in gravitational collapse to black holes and naked singularities

We investigate here the genericity and stability aspects for naked singularities and black holes that arise as the final states for a complete gravitational collapse of a spherical massive matter cloud. The form of the matter considered is a general Type I matter field, which includes most of the physically reasonable matter fields such as dust, perfect fluids and such other physically interesting forms of matter widely used in gravitation theory. We first study here in some detail the effects of small pressure perturbations in an otherwise pressure-free collapse scenario, and examine how a collapse evolution that was going to the black hole endstate would be modified and go to a naked singularity, once small pressures are introduced in the initial data. This allows us to understand the distribution of black holes and naked singularities in the initial data space. Collapse is examined in terms of the evolutions allowed by Einstein equations, under suitable physical conditions and as evolving from a regular initial data. We then show that both black holes and naked singularities are generic outcomes of a complete collapse, when genericity is defined in a suitable sense in an appropriate space.Comment: 24 pages, 6 figures, some changes in text and figures to match the version accepted for publication by IJMP

Electronic reconstruction and enhanced superconductivity at La1.6−x_{1.6-x}Nd0.4_{0.4}Srx_{x}CuO4_{4}/La1.55_{1.55}Sr0.45_{0.45}CuO4_{4} bilayer interface

We report enhanced superconductivity in bilayer thin films consisting of superconducting La$_{1.6-x}$Nd$_{0.4}$Sr$_{x}$CuO$_{4}$ with 0.06 $\leq x<$ 0.20 and metallic but non-superconducting La$_{1.55}$Sr$_{0.45}$CuO$_{4}$. These bilayers show a maximum increase in superconducting transition temperature ($T_c$) of more than 200% for $x$ = 0.06 while no change in $T_c$ is observed for the bilayers with $x\geq$ 0.20. The analysis of the critical current and kinetic inductance data suggests 2-3 unit cells thick interfacial layer electronically perturbed to have a higher $T_c$. A simple charge transfer model with cation intermixing explains the observed $T_c$ in bilayers. Still the unusually large thickness of interfacial superconducting layers can not be explained in terms of this model. We believe the stripe relaxation as well as the proximity effect also influence the superconductivity of the interface

On the genericity of spacetime singularities

We consider here the genericity aspects of spacetime singularities that occur in cosmology and in gravitational collapse. The singularity theorems (that predict the occurrence of singularities in general relativity) allow the singularities of gravitational collapse to be either visible to external observers or covered by an event horizon of gravity. It is shown that the visible singularities that develop as final states of spherical collapse are generic. Some consequences of this fact are discussed.Comment: 19 pages, To be published in the Raychaudhuri Volume, eds. Naresh Dadhich, Pankaj Joshi and Probir Ro

Role of initial data in spherical collapse

We bring out here the role of initial data in causing the black hole and naked singularity phases as the final end state of a continual gravitational collapse. The collapse of a type I general matter field is considered, which includes most of the known physical forms of matter. It is shown that given the distribution of the density and pressure profiles at the initial surface from which the collapse evolves, there is a freedom in choosing rest of the free functions, such as the velocities of the collapsing shells, so that the end state could be either a black hole or a naked singularity depending on this choice. It is thus seen that it is the initial data that determines the end state of spherical collapse in terms of these outcomes, and we get a good picture of how these phases come about.Comment: 5 pages, Revtex4, Revised version, To appear in Physical Review

Interface driven reentrant superconductivity in HoNi5_5-NbN-HoNi5_5 nanostructures

Superconductivity (S) and ferromagnetism (F) are probed through transport and magnetization measurements in nanometer scale HoNi$_5$-NbN (F-S) bilayers and HoNi$_5$-NbN-HoNi$_5$ (F-S-F) trilayers. The choice of materials has been made on the basis of their comparable ordering temperatures and strong magnetic anisotropy in HoNi$_5$. We observe the normal state reentrant behavior in resistance vs. temperature plots of the F-S-F structures just below the superconducting transition in the limited range of HoNi$_5$ layer thickness d$_{HN}$ (20 nm $<$ d$_{HN}$ $<$ 80 nm) when d$_{NbN}$ is fixed at $\simeq$ 10 nm. The reentrance is quenched by increasing the out-of-plane (H$_{\perp}$) magnetic field and transport current where as in-plane (H$_{\parallel}$) field of $\leq$ 1500 Oe has no effect on the reentrance. The thermally activated flux flow characteristics of the S, F-S and F-S-F layers reveal a transition from collective pinning to single vortex pinning as we place F layers on both sides of the S film. The origin of the reentrant behavior seen here in the range of 0.74 $\leq$ T$_{Curie}$/T$_C$ $\leq$ 0.92 is attribute to a delicate balance between the magnetic exchange energy and the condensation energy in the interfacial regions of the trilayer.Comment: 13 pages and 5 figure

Quality Comparison of Vegetables Dehydrated in Solar Drier and Electrical Oven

Ascorbic acid, sugars, dehydration ratio and moisture were determined in the vegetables dehydrated separately in solar drier and in electrical oven under similar conditions by standard methods. Vegetables examined were cabbage, cauliflower, tomato, radish, turnip, lahi, methi and palak. It was revealed that in each case, contents of ascorbic acid were higher in solar-dried vegetables in comparison to oven-dried stuffs. This finding indicated superiority of solar driers over electrical ovens, both in reference to quality of the dehydrated vegetables and its overall cost of operation

On the Role of Initial Data in the Gravitational Collapse of Inhomogeneous Dust

We consider here the gravitational collapse of a spherically symmetric inhomogeneous dust cloud described by the Tolman-Bondi models. By studying a general class of these models, we find that the end state of the collapse is either a black hole or a naked singularity, depending on the parameters of the initial density distribution, which are $\rho_{c}$, the initial central density of the massive body, and $R_0$, the initial boundary. The collapse ends in a black hole if the dimensionless quantity $\beta$ constructed out of this initial data is greater than 0.0113, and it ends in a naked singularity if $\beta$ is less than this number. A simple interpretation of this result can be given in terms of the strength of the gravitational potential at the starting epoch of the collapse.Comment: Original title changed, numerical range of naked singularity corrected. Plain Tex File. 14 pages. To appear in Physical Review

On the global visibility of singularity in quasi-spherical collapse

We analyze here the issue of local versus the global visibility of a singularity that forms in gravitational collapse of a dust cloud, which has important implications for the weak and strong versions of the cosmic censorship hypothesis. We find conditions as to when a singularity will be only locally naked, rather than being globally visible, thus preseving the weak censorship hypothesis. The conditions for formation of a black hole or naked singularity in the Szekeres quasi-spherical collapse models are worked out. The causal behaviour of the singularity curve is studied by examining the outgoing radial null geodesics, and the final outcome of collapse is related to the nature of the regular initial data specified on an initial hypersurface from which the collapse evolves. An interesting feature that emerges is the singularity in Szekeres spacetimes can be ``directionally naked''.Comment: Latex file, 32 pages, 12 postscript figures. To appear in the Journal of General Relativity and Gravitatio