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

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

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

Synthesis and Antifungal Activity of Some New Guanidines

The synthesis of some N-subsituted -N'-aryl-N"-ethyl/benzyl guanidines (II) and (III) and their precurser thiocarbamides (I) has been carried out. All these compounds have been screened in vitro for their antifungal activity against Helminthosporium oryzae, Drechlere papendor fii and Alternaria alternata. In general, N-substituted-N'aryl-N"benzyl guanidines except N-(p-pyrolidinopropoxyphenyl)-N'-p-tolyl-N"-benzyl guanidine possess high antifungal activity against all the test fungi at concentration 2% and comparatively less at 0.2% None of these compounds exhibit fungicidal activity at lower concentrations (0.02 and 0.002%)