Quantum general relativity and Hawking radiation

In a previous paper we have set up the Wheeler-DeWitt equation which describes the quantum general relativistic collapse of a spherical dust cloud. In the present paper we specialize this equation to the case of matter perturbations around a black hole, and show that in the WKB approximation, the wave-functional describes an eternal black hole in equilibrium with a thermal bath at Hawking temperature.Comment: 13 pages, minor revisions in: (i) para 5 of Introduction, (ii) para following Eqn. (10). Revised version to appear in Phys. Rev.

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

Isotope Exchange Reaction Between As(V) & As(III) In Acid Medium

100-10

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

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

Do Ecological Niche Model Predictions Reflect the Adaptive Landscape of Species?: A Test Using Myristica malabarica Lam., an Endemic Tree in the Western Ghats, India

Ecological niche models (ENM) have become a popular tool to define and predict the “ecological niche” of a species. An implicit assumption of the ENMs is that the predicted ecological niche of a species actually reflects the adaptive landscape of the species. Thus in sites predicted to be highly suitable, species would have maximum fitness compared to in sites predicted to be poorly suitable. As yet there are very few attempts to address this assumption. Here we evaluate this assumption. We used Bioclim (DIVA GIS version 7.3) and Maxent (version 3.3.2) to predict the habitat suitability of Myristica malabarica Lam., an economically important tree occurring in the Western Ghats, India. We located populations of the trees naturally occurring in different habitat suitability regimes (from highly suitable to poorly suitable) and evaluated them for their regeneration ability and genetic diversity. We also evaluated them for two plant functional traits, fluctuating asymmetry – an index of genetic homeostasis, and specific leaf weight – an index of primary productivity, often assumed to be good surrogates of fitness. We show a significant positive correlation between the predicted habitat quality and plant functional traits, regeneration index and genetic diversity of populations. Populations at sites predicted to be highly suitable had a higher regeneration and gene diversity compared to populations in sites predicted to be poor or unsuitable. Further, individuals in the highly suitable sites exhibited significantly less fluctuating asymmetry and significantly higher specific leaf weight compared to individuals in the poorly suitable habitats. These results for the first time provide an explicit test of the ENM with respect to the plant functional traits, regeneration ability and genetic diversity of populations along a habitat suitability gradient. We discuss the implication of these resultsfor designing viable species conservation and restoration programs

In vitro regeneration of Momordica dioica (Roxb.)

Momordica dioica, Roxb. (Family: Cucurbitaceae) commonly called as Kartoli, is an important medicinal plant, which has remained unexplored from the commercial point of view. Considering its scarce availability and the medicinal importance, in vitro cultures were established. Traditionally, M. dioica has been propagated mainly through its tuberous roots and less commonly by seeds. Germination through seeds is very difficult or impossible because of hard seed coat. As an alternative to traditional methods tissue culture offers an efficient method for propagation of M. dioica. Mature seeds were used for the regeneration of M. dioica. The decoated seeds of M. dioica were cultured on Murashige and Skoog basal medium (MS medium) supplemented with various combinations of Auxins (á – naphthaleneacetic acid) and Cytokinins (N6 - benzyl adenine). MS basal medium supplemented with 4.44 µM and 8.88 µM N6 - benzyl adenine (BA) gave rise to maximum number of shoots in 7-8 weeks. In vitro grown shoots were sub cultured on MS medium supplemented with different concentrations of indole-3-butyric acid (IBA) for root initiation. MS medium with 0.049mM indole-3-butyric acid (IBA) showed rooting in 45 days. The regenerated plantlets were successfully hardened in vermiculite

Quantum Radiation from Black Holes and Naked Singularities in Spherical Dust Collapse

A sufficiently massive collapsing star will end its life as a spacetime singularity. The nature of the Hawking radiation emitted during collapse depends critically on whether the star's boundary conditions are such as would lead to the eventual formation of a black hole or, alternatively, to the formation of a naked singularity. This latter possibility is not excluded by the singularity theorems. We discuss the nature of the Hawking radiation emitted in each case. We justify the use of Bogoliubov transforms in the presence of a Cauchy horizon and show that if spacetime is assumed to terminate at the Cauchy horizon, the resulting spectrum is thermal, but with a temperature different from the Hawking temperature.Comment: PHYZZX macros, 27 pages, 3 figure

Can Naked Singularities Yield Gamma Ray Bursts?

Gamma-ray bursts are believed to be the most luminous objects in the Universe. There has been some suggestion that these arise from quantum processes around naked singularities. The main problem with this suggestion is that all known examples of naked singularities are massless and hence there is effectively no source of energy. It is argued that a globally naked singularity coupled with quantum processes operating within a distance of the order of Planck length of the singularity will probably yield energy burst of the order of M_pc^2\approx2\times 10^{16} ergs, where M_p is the Planck mass.Comment: 4 pages, TeX, no figure

Gravitational Collapse of Inhomogeneous Dust in (2+1) Dimensions

We examine the gravitational collapse of spherically symmetric inhomogeneous dust in (2+1) dimensions, with cosmological constant. We obtain the analytical expressions for the interior metric. We match the solution to a vacuum exterior. We discuss the nature of the singularity formed by analyzing the outgoing radial null geodesics. We examine the formation of trapped surfaces during the collapse.Comment: Accepted for publication in CQ