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

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

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

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

Cellulose Acetate Binder-Based LOVA Gun Propellant for Tank Guns.

Cellulose acetate (CA) binder-based low vulnerability ammunition (LOYA) gun propellant formulations with varying percentages of fine RDX as energetic ingredient have been studied. RDX percentage varied from 76 to 80 in these formulations. An optimised composition with 78 per cent RDX was then studied exhaustively. Ballistic data determined by closed vessel (CV) evaluation and vulnerability aspects obtained by safety tests were then compared vis-a-vis the properties of standard triple base NQ composition. Theoretical prediction and CV test results indicated that the CA binder-based LOVA gun propellant Could satisfactorily meet the ballistic requirements for gun application

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

Acknowledging uncertainty in evolutionary reconstructions of ecological niches

Reconstructing ecological niche evolution can provide insight into the biogeography and diversification of evolving lineages. However, comparative phylogenetic methods may infer the history of ecological niche evolution inaccurately because (a) species' niches are often poorly characterized; and (b) phylogenetic comparative methods rely on niche summary statistics rather than full estimates of species' environmental tolerances. Here, we propose a new framework for coding ecological niches and reconstructing their evolution that explicitly acknowledges and incorporates the uncertainty introduced by incomplete niche characterization. Then, we modify existing ancestral state inference methods to leverage full estimates of environmental tolerances. We provide a worked empirical example of our method, investigating ecological niche evolution in the New World orioles (Aves: Passeriformes: Icterus spp.). Temperature and precipitation tolerances were generally broad and conserved among orioles, with niche reduction and specialization limited to a few terminal branches. Tools for performing these reconstructions are available in a new R package called nichevol

Acknowledging uncertainty in evolutionary reconstructions of ecological niches

Reconstructing ecological niche evolution can provide insight into the biogeography and diversification of evolving lineages. However, comparative phylogenetic methods may infer the history of ecological niche evolution inaccurately because (a) species' niches are often poorly characterized; and (b) phylogenetic comparative methods rely on niche summary statistics rather than full estimates of species' environmental tolerances. Here, we propose a new framework for coding ecological niches and reconstructing their evolution that explicitly acknowledges and incorporates the uncertainty introduced by incomplete niche characterization. Then, we modify existing ancestral state inference methods to leverage full estimates of environmental tolerances. We provide a worked empirical example of our method, investigating ecological niche evolution in the New World orioles (Aves: Passeriformes: Icterus spp.). Temperature and precipitation tolerances were generally broad and conserved among orioles, with niche reduction and specialization limited to a few terminal branches. Tools for performing these reconstructions are available in a new R package called nichevol

Physical aspects of naked singularity explosion - How does a naked singularity explode? --

The behaviors of quantum stress tensor for the scalar field on the classical background of spherical dust collapse is studied. In the previous works diverging flux of quantum radiation was predicted. We use the exact expressions in a 2D model formulated by Barve et al. Our present results show that the back reaction does not become important during the semiclassical phase. The appearance of the naked singularity would not be affected by this quantum field radiation. To predict whether the naked singularity explosion occurs or not we need the theory of quantum gravity. We depict the generation of the diverging flux inside the collapsing star. The quantum energy is gathered around the center positively. This would be converted to the diverging flux along the Cauchy horizon. The ingoing negative flux crosses the Cauchy horizon. The intensity of it is divergent only at the central naked singularity. This diverging negative ingoing flux is balanced with the outgoing positive diverging flux which propagates along the Cauchy horizon. After the replacement of the naked singularity to the practical high density region the instantaneous diverging radiation would change to more milder one with finite duration.Comment: 18 pages, 16 figure

Convergence to a self-similar solution in general relativistic gravitational collapse

We study the spherical collapse of a perfect fluid with an equation of state $P=k\rho$ by full general relativistic numerical simulations. For 0, it has been known that there exists a general relativistic counterpart of the Larson-Penston self-similar Newtonian solution. The numerical simulations strongly suggest that, in the neighborhood of the center, generic collapse converges to this solution in an approach to a singularity and that self-similar solutions other than this solution, including a ``critical solution'' in the black hole critical behavior, are relevant only when the parameters which parametrize initial data are fine-tuned. This result is supported by a mode analysis on the pertinent self-similar solutions. Since a naked singularity forms in the general relativistic Larson-Penston solution for 0, this will be the most serious known counterexample against cosmic censorship. It also provides strong evidence for the self-similarity hypothesis in general relativistic gravitational collapse. The direct consequence is that critical phenomena will be observed in the collapse of isothermal gas in Newton gravity, and the critical exponent $\gamma$ will be given by $\gamma\approx 0.11$, though the order parameter cannot be the black hole mass.Comment: 22 pages, 15 figures, accepted for publication in Physical Review D, reference added, typos correcte