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

Stability of Naked Singularity arising in gravitational collapse of Type I matter fields

Considering gravitational collapse of Type I matter fields, we prove that, given an arbitrary $C^{2}$- mass function $\textit{M}(r,v)$ and a $C^{1}$- function $h(r,v)$ (through the corresponding $C^{1}$- metric function $\nu(t,r)$), there exist infinitely many choices of energy distribution function $b(r)$ such that the `true' initial data ($\textit{M},h(r,v)$) leads the collapse to the formation of naked singularity. We further prove that the occurrence of such a naked singularity is stable with respect to small changes in the initial data. We remark that though the initial data leading to both black hole and naked singularity form a "big" subset of the true initial data set, their occurrence is not generic. The terms `stability' and `genericity' are appropriately defined following the theory of dynamical systems. The particular case of radial pressure $p_{r}(r)$ has been illustrated in details to get clear picture of how naked singularity is formed and how, it is stable with respect to initial data.Comment: 16 pages, no figure, Latex, submitted to Praman

Spatiotemporal analyses of soil moisture from point to footprint scale in two different hydroclimatic regions

This paper presents time stability analyses of soil moisture at different spatial measurement support scales (point scale and airborne remote sensing (RS) footprint scale 800 m × 800 m) in two different hydroclimatic regions. The data used in the analyses consist of in situ and passive microwave remotely sensed soil moisture data from the Southern Great Plains Hydrology Experiments 1997 and 1999 (SGP97 and SGP99) conducted in the Little Washita (LW) watershed, Oklahoma, and the Soil Moisture Experiments 2002 and 2005 (SMEX02 and SMEX05) in the Walnut Creek (WC) watershed, Iowa. Results show that in both the regions soil properties (i.e., percent silt, percent sand, and soil texture) and topography (elevation and slope) are significant physical controls jointly affecting the spatiotemporal evolution and time stability of soil moisture at both point and footprint scales. In Iowa, using point‐scale soil moisture measurements, the WC11 field was found to be more time stable (TS) than the WC12 field. The common TS points using data across the 3 year period (2002–2005) were mostly located at moderate to high elevations in both the fields. Furthermore, the soil texture at these locations consists of either loam or clay loam soil. Drainage features and cropping practices also affected the field‐scale soil moisture variability in the WC fields. In Oklahoma, the field having a flat topography (LW21) showed the worst TS features compared to the fields having gently rolling topography (LW03 and LW13). The LW13 field (silt loam) exhibited better time stability than the LW03 field (sandy loam) and the LW21 field (silt loam). At the RS footprint scale, in Iowa, the analysis of variance (ANOVA) tests show that the percent clay and percent sand are better able to discern the TS features of the footprints compared to the soil texture. The best soil indicator of soil moisture time stability is the loam soil texture. Furthermore, the hilltops (slope ∼0%–0.45%) exhibited the best TS characteristics in Iowa. On the other hand, in Oklahoma, ANOVA results show that the footprints with sandy loam and loam soil texture are better indicators of the time stability phenomena. In terms of the hillslope position, footprints with mild slope (0.93%–1.85%) are the best indicators of TS footprints. Also, at both point and footprint scales in both the regions, land use–land cover type does not influence soil moisture time stability

Evaluations of a Mechanistic Hypothesis for the Influence of Extracellular Ions on Electroporation Due to High-Intensity, Nanosecond Pulsing

The effect of ions present in the extracellular medium on electroporation by high-intensity, short-duration pulsing is studied through molecular dynamic simulations. Our simulation results indicate that mobile ions in the medium might play a role in creating stronger local electric fields across membranes that then reinforce and strengthen electroporation. Much faster pore formation is predicted in higher conductivity media. However, the impact of extracellular conductivity on cellular inflows, which depend on transport processes such as electrophoresis, could be different as discussed here. Our simulation results also show that interactions between cations (Na+ in this case) and the carbonyl oxygen of the lipid headgroups could impede pore resealing