Analytic derivation of the map of null rays passing near a naked singularity

Recently the energy emission from a naked singularity forming in spherical dust collapse has been investigated. This radiation is due to the particle creation in a curved spacetime. In this discussion, the central role is played by the mapping formula between the incoming and the outgoing null coordinates. For the self-similar model, this mapping formula has been derived analytically. But for the model with $C^{\infty}$ density profile, the mapping formula has been obtained only numerically. In the present paper, we argue that the singular nature of the mapping is determined by the local geometry around the point at which the singularity is first formed. If this is the case, it would be natural to expect that the mapping formula can be derived analytically. In the present paper, we analytically rederive the same mapping formula for the model with $C^{\infty}$ density profile that has been earlier derived using a numerical technique.Comment: 4 pages, submitted to Phys. Rev.

Are naked singularites forbidden by the second law of thermodynamics?

By now, many examples of naked singularities in classical general relativity are known. It may however be that a physical principle over and above the general theory prevents the occurrence of such singularities in nature. Assuming the validity of the Weyl curvature hypothesis, we propose that naked singularities are forbidden by the second law of thermodynamics.Comment: 6 pages, Latex file. This essay was selected for honorable mention by the Gravity Research Foundatio

Divergence of the Quantum Stress Tensor on the Cauchy Horizon in 2-d Dust Collapse

We prove that the quantum stress tensor for a massless scalar field in two dimensional non-selfsimilar Tolman Bondi dust collapse and Vaidya radiation collapse models diverges on the Cauchy horizon, if the latter exists. The two dimensional model is obtained by suppressing angular co-ordinates in the corresponding four dimensional spherical model.Comment: 16 pages, no figures, LaTeX fil

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

Climatic niche and flowering and fruiting phenology of an epiphytic plant

Species have geographic distributions constrained by combinations of abiotic factors, biotic factors and dispersal-related factors. Abiotic requirements vary across the life stages for a species; for plant species, a particularly important life stage is when the plant flowers and develops seeds. A previous year-long experiment showed that ambient temperature of 5–35 °C, relative humidity of >50 % and ≤15 consecutive rainless days are crucial abiotic conditions for Spanish moss (Tillandsia usneoides L.). Here, we explore whether these optimal physiological intervals relate to the timing of the flowering and fruiting periods of Spanish moss across its range. As Spanish moss has a broad geographic range, we examined herbarium specimens to detect and characterize flowering/fruiting periods for the species across the Americas; we used high-temporal-resolution climatic data to assess the availability of optimal conditions for Spanish moss populations during each population's flowering period. We explored how long populations experience suboptimal conditions and found that most populations experience suboptimal conditions in at least one environmental dimension. Flowering and fruiting periods of Spanish moss populations are either being optimized for one or a few parameters or may be adjusted such that all parameters are suboptimal. Spanish moss populations appear to be constrained most closely by minimum temperature during this period