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On the Role of Initial Data in the Gravitational Collapse of Inhomogeneous Dust

We consider here the gravitational collapse of a spherically symmetric inhomogeneous dust cloud described by the Tolman-Bondi models. By studying a general class of these models, we find that the end state of the collapse is either a black hole or a naked singularity, depending on the parameters of the initial density distribution, which are $\rho_{c}$, the initial central density of the massive body, and $R_0$, the initial boundary. The collapse ends in a black hole if the dimensionless quantity $\beta$ constructed out of this initial data is greater than 0.0113, and it ends in a naked singularity if $\beta$ is less than this number. A simple interpretation of this result can be given in terms of the strength of the gravitational potential at the starting epoch of the collapse.Comment: Original title changed, numerical range of naked singularity corrected. Plain Tex File. 14 pages. To appear in Physical Review

Quantum evaporation of a naked singularity

We investigate here quantum effects in gravitational collapse of a scalar field model which classically leads to a naked singularity. We show that non-perturbative semi-classical modifications near the singularity, based on loop quantum gravity, give rise to a strong outward flux of energy. This leads to the dissolution of the collapsing cloud before the singularity can form. Quantum gravitational effects thus censor naked singularities by avoiding their formation. Further, quantum gravity induced mass flux has a distinct feature which may lead to a novel observable signature in astrophysical bursts.Comment: 4 pages, 2 figures. Minor changes to match published version in Physical Review Letter

Gravitational collapse of an isentropic perfect fluid with a linear equation of state

We investigate here the gravitational collapse end states for a spherically symmetric perfect fluid with an equation of state $p=k\rho$. It is shown that given a regular initial data in terms of the density and pressure profiles at the initial epoch from which the collapse develops, the black hole or naked singularity outcomes depend on the choice of rest of the free functions available, such as the velocities of the collapsing shells, and the dynamical evolutions as allowed by Einstein equations. This clarifies the role that equation of state and initial data play towards determining the final fate of gravitational collapse.Comment: 7 Pages, Revtex4, To appear in Classical and Quantum Gravit

The Linearly Independent Non Orthogonal yet Energy Preserving (LINOEP) vectors

It is well known that, in any inner product space, a set of linearly independent (LI) vectors can be transformed to a set of orthogonal vectors, spanning the same space, by the Gram-Schmidt Orthogonalization Method (GSOM). In this paper, we propose a transformation from a set of LI vectors to a set of LI non orthogonal yet energy (square of the norm) preserving (LINOEP) vectors in an inner product space and we refer it as LINOEP method. We also show that there are various solutions to preserve the square of the norm.Comment: 6 pages, 2 figure

The Final Fate of Spherical Inhomogeneous Dust Collapse

We examine the role of the initial density and velocity distribution in the gravitational collapse of a spherical inhomogeneous dust cloud. Such a collapse is described by the Tolman-Bondi metric which has two free functions: the `mass-function' and the `energy function', which are determined by the initial density and velocity profile of the cloud. The collapse can end in a black-hole or a naked singularity, depending on the initial parameters characterizing these profiles. In the marginally bound case, we find that the collapse ends in a naked singularity if the leading non-vanishing derivative of the density at the center is either the first one or the second one. If the first two derivatives are zero, and the third derivative non-zero, the singularity could either be naked or covered, depending on a quantity determined by the third derivative and the central density. If the first three derivatives are zero, the collapse ends in a black hole. In particular, the classic result of Oppenheimer and Snyder, that homogeneous dust collapse leads to a black hole, is recovered as a special case. Analogous results are found when the cloud is not marginally bound, and also for the case of a cloud starting from rest. We also show how the strength of the naked singularity depends on the density and velocity distribution. Our analysis generalizes and simplifies the earlier work of Christodoulou and Newman [4,5] by dropping the assumption of evenness of density functions. It turns out that relaxing this assumption allows for a smooth transition from the naked singularity phase to the black-hole phase, and also allows for the occurrence of strong curvature naked singularities.Comment: 23 pages; Plain Tex; TIFR-TAP preprin

Mappings preserving locations of movable poles: a new extension of the truncation method to ordinary differential equations

The truncation method is a collective name for techniques that arise from truncating a Laurent series expansion (with leading term) of generic solutions of nonlinear partial differential equations (PDEs). Despite its utility in finding Backlund transformations and other remarkable properties of integrable PDEs, it has not been generally extended to ordinary differential equations (ODEs). Here we give a new general method that provides such an extension and show how to apply it to the classical nonlinear ODEs called the Painleve equations. Our main new idea is to consider mappings that preserve the locations of a natural subset of the movable poles admitted by the equation. In this way we are able to recover all known fundamental Backlund transformations for the equations considered. We are also able to derive Backlund transformations onto other ODEs in the Painleve classification.Comment: To appear in Nonlinearity (22 pages

Views and attitudes towards blood donation: a qualitative investigation of Indian non-donors living in England

OBJECTIVE: To explore the views and attitudes of Indians living in England on blood donation. BACKGROUND: In light of the predicted shortages in blood supply, it is vital to consider ways in which to maximise donation rates. These include addressing the issue of lower donation rates among ethnic minorities, including Indians. However research specifically among minority ethnicities in UK is sparse. SETTING: General practice in North London. PARTICIPANTS: A convenience sample of 12 non-donor Indians living in England. METHODS: This is a qualitative investigation involving semistructured interviews. Themes derived were analysed using thematic framework analysis. RESULTS: Five key themes emerged from the data, and these concerned participants’ perspectives regarding attitudes towards blood, blood donation as a ‘good thing’, donation disincentives, the recipient matters and the donor matters. CONCLUSION: A variety of attitudes were presented, but were generally positive, and blood was conceptualised in a manner previously found to be consistent with donation. However, lack of awareness and accessibility were prominent barriers, indicating the need for improvement in these capacities. In contrast to this, blood was also greatly associated with family and acted as a symbol of kinship: this ‘emotional charge’ often acted to dissuade participants from separating with their blood through donation. Possibly due to this, there was also a strong preference for donated blood to be distributed within the family, as opposed to strangers. This presents a potential barrier to blood donation for some Indians within the current system in which donations are given to unknown recipients

Preparation, characterization, and electrical properties of epitaxial NbO2 thin film lateral devices

Epitaxial NbO2 (110) films, 20 nm thick, were grown by pulsed laser deposition on Al2O3 (0001) substrates. The Ar/O2 total pressure during growth was varied to demonstrate the gradual transformation between NbO2 and Nb2O5 phases, which was verified using x-ray diffraction, x-ray photoelectron spectroscopy, and optical absorption measurements. Electric resistance threshold switching characteristics were studied in a lateral geometry using interdigitated Pt top electrodes in order to preserve the epitaxial crystalline quality of the films. Volatile and reversible transitions between high and low resistance states were observed in epitaxial NbO2 films, while irreversible transitions were found in case of Nb2O5 phase. Electric field pulsed current measurements confirmed thermally-induced threshold switching.Comment: This is an author-created, un-copyedited version of an article accepted for publication in Journal of Physics D: Applied Physics. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at http://dx.doi.org/10.1088/0022-3727/48/33/33530

Study of spur dikes

In order to study the variables governing the depth of scour around obstructions such as spur dikes, tests were carried out. The salient features of these tests are summarized herein