Can we see naked singularities?

We study singularities which can form in a spherically symmetric gravitational collapse of a general matter field obeying weak energy condition. We show that no energy can reach an outside observer from a null naked singularity. That means they will not be a serious threat to the Cosmic Censorship Conjecture (CCC). For the timelike naked singularities, where only the central shell gets singular, the redshift is always finite and they can in principle, carry energy to a faraway observer. Hence for proving or disproving CCC the study of timelike naked singularities will be more important. Our results are very general and are independent of initial data and the form of the matter.Comment: 10 page

Spherical gravitational collapse: tangential pressure and related equations of state

We derive an equation for the acceleration of a fluid element in the spherical gravitational collapse of a bounded compact object made up of an imperfect fluid. We show that non-singular as well as singular solutions arise in the collapse of a fluid initially at rest and having only a tangential pressure. We obtain an exact solution of Einstein equations, in the form of an infinite series, for collapse under tangential pressure with a linear equation of state. We show that if a singularity forms in the tangential pressure model, the conditions for the singularity to be naked are exactly the same as in the model of dust collapse.Comment: Latex, 26 page

Small Black Holes on Branes: Is the horizon regular or singular ?

We investigate the following question: Consider a small mass, with $\epsilon$ (the ratio of the Schwarzschild radius and the bulk curvature length) much smaller than 1, that is confined to the TeV brane in the Randall-Sundrum I scenario. Does it form a black hole with a regular horizon, or a naked singularity? The metric is expanded in $\epsilon$ and the asymptotic form of the metric is given by the weak field approximation (linear in the mass). In first order of $\epsilon$ we show that the iteration of the weak field solution, which includes only integer powers of the mass, leads to a solution that has a singular horizon. We find a solution with a regular horizon but its asymptotic expansion in the mass also contains half integer powers.Comment: Accepted for publication in PR

Gravitational Collapse, Black Holes and Naked Singularities

This article gives an elementary review of gravitational collapse and the cosmic censorship hypothesis. Known models of collapse resulting in the formation of black holes and naked singularities are summarized. These models, when taken together, suggest that the censorship hypothesis may not hold in classical general relativity. The nature of the quantum processes that take place near a naked singularity, and their possible implication for observations, is briefly discussed.Comment: 17 pages, Latex File. Based on a talk given at the Discussion Workshop on Black Holes, Bangalore, 9-12 Dec. 1997, to appear in the Conference Proceeding

Reissner Nordstr\"{o}m Background Metric in Dynamical Co-ordinates: Exceptional Behaviour of Hadamard States

We cast the Reissner Nordstrom solution in a particular co-ordinate system which shows dynamical evolution from initial data. The initial data for the $E<M$ case is regular. This procedure enables us to treat the metric as a collapse to a singularity. It also implies that one may assume Wald axioms to be valid globally in the Cauchy development, especially when Hadamard states are chosen. We can thus compare the semiclassical behaviour with spherical dust case, looking upon the metric as well as state specific information as evolution from initial data. We first recover the divergence on the Cauchy horizon obtained earlier. We point out that the semiclassical domain extends right upto the Cauchy horizon. This is different from the spherical dust case where the quantum gravity domain sets in before. We also find that the backreaction is not negligible near the central singularity, unlike the dust case. Apart from these differences, the Reissner Nordstrom solution has a similarity with dust in that it is stable over a considerable period of time. The features appearing dust collapse mentioned above were suggested to be generally applicable within spherical symmetry. Reissner Nordstrom background (along with the quantum state) generated from initial data, is shown not to reproduce them

Mapping of forests based on biological diversity to identify conservation sites: A case study from Udupi and South Canara districts of Karnataka

Forest classification is traditionally based on the structure and composition of vegetation, which in tum is strongly linked with the climatic profile of the area. Forest maps thus prepared cannot appropriately meet the needs of the managers whose renewed mandate is to conserve the biological richness of the forests. The emerging need for protecting the forests is to understand the spatial distribution of the conservation value of the forests besides knowing their vegetation types. In other words, we need maps that depict the spatial distribution of biological diversity of the forests. In this paper, we rep011 on our attempt to develop such biodiversity maps for the forest ranges of Udupi and South Canara districts of Ka.rnataka state. Utilizing the data from the vegetation sampling of the Forest Survey of India, we developed a terrain view of the density and diversity of tree species and have attempted to identify the sites with the highest conservation value. We propose that such maps be developed for the entire country and discuss the potentialities and problems associated with this protocol

Learning with a Drifting Target Concept

We study the problem of learning in the presence of a drifting target concept. Specifically, we provide bounds on the error rate at a given time, given a learner with access to a history of independent samples labeled according to a target concept that can change on each round. One of our main contributions is a refinement of the best previous results for polynomial-time algorithms for the space of linear separators under a uniform distribution. We also provide general results for an algorithm capable of adapting to a variable rate of drift of the target concept. Some of the results also describe an active learning variant of this setting, and provide bounds on the number of queries for the labels of points in the sequence sufficient to obtain the stated bounds on the error rates

The Lemaitre-Schwarzschild Problem Revisited

The Lemaitre and Schwarzschild analytical solutions for a relativistic spherical body of constant density are linked together through the use of the Weyl quadratic invariant. The critical radius for gravitational collapse of an incompressible fluid is shown to vary continuously from 9/8 of the Schwarzschild radius to the Schwarzschild radius itself while the internal pressures become locally anisotropic.Comment: Final version as accepted by GR&G (to appear in vol. 34, september 2002

Method for Treating Cytokine Mediated Hepatic Injury

A method of modulating cytokine mediated hepatic injury by administering deltorphins to a mammal. Deltorphin I SEQ ID NO:1, deltorphin II SEQ ID NO:2 or combinations of deltorphins I SEQ ID NO:1 and II SEQ ID NO:2 may be administered. A deltorphin concentration in the range of about 0.5 mg/kg to about 20 mg/kg in a physiologically acceptable formulation blocks a cytokine cascade in a murine model of septic shock. A therapeutic method of modulating cytokine mediated acute inflammatory, trauma induced and toxin induced hepatic injury, particularly via tumor necrosis factor modulation, is thus disclosed

Method for Treating Cytokine Mediated Hepatic Injury

A method of modulating cytokine mediated hepatic injury by administering compound-D SEQ ID NO:1 to a mammal. A concentration of the compound in the range of about 0.5 mg/kg to about 20 mg/kg in a physiologically acceptable formulation blocks a cytokine cascade. A therapeutic method of modulating cytokine mediated acute inflammatory, trauma induced and toxin induced hepatic injury, particularly via tumor necrosis factor modulation, is thus disclosed