Appearance of the central singularity in spherical collapse

We analyze here the structure of non-radial nonspacelike geodesics terminating in the past at a naked singularity formed as the end state of inhomogeneous dust collapse. The spectrum of outgoing nonspacelike null geodesics is examined analytically. The local and global visibility of the singularity is also examined by integrating numerically the null geodesics equations. The possible implications of existence of such families towards the appearance of the star in late stages of gravitational collapse are considered. It is seen that the outgoing non-radial geodesics give an appearance to the naked central singularity as that of an expanding ball whose radius reaches a maximum before the star goes within its apparent horizon. The radiated energy (along the null geodesics) is shown to decay very sharply in the neighbourhood of the singularity. Thus the total energy escaping via non-radial null geodesics from the naked central singularity vanishes in the scenario considered here.Comment: 25 pages, 6 figure

Naked Singularity Explosion

It is known that the gravitational collapse of a dust ball results in naked singularity formation from an initial density profile which is physically reasonable. In this paper, we show that explosive radiation is emitted during the formation process of the naked singularity.Comment: 6 pages, 3 figures, Accepted for Publication in Phys. Rev. D as a Rapid Communicatio

Formation of a galaxy with a central black hole in the Lemaitre-Tolman model

We construct two models of the formation a galaxy with a central black hole, starting from a small initial fluctuation at recombination. This is an application of previously developed methods to find a Lemaitre-Tolman model that evolves from a given initial density or velocity profile to a given final density profile. We show that the black hole itself could be either a collapsed object, or a non-vacuum generalisation of a full Schwarzschild-Kruskal-Szekeres wormhole. Particular attention is paid to the black hole's apparent and event horizons.Comment: REVTeX, 22 pages including 11 figures (25 figure files). Replacement has minor changes in response to the referee, and editorial corrections. To appear in PR

Higher dimensional inhomogeneous dust collapse and cosmic censorship

We investigate the occurrence and nature of a naked singularity in the gravitational collapse of an inhomogeneous dust cloud described by higher dimensional Tolman-Bondi space-times. The naked singularities are found to be gravitationally strong in the sense of Tipler. Higher dimensions seem to favour black holes rather than naked singularities.Comment: 15 pages, LaTeX, 1 figure, 2 table

Higher dimensional dust collapse with a cosmological constant

The general solution of the Einstein equation for higher dimensional (HD) spherically symmetric collapse of inhomogeneous dust in presence of a cosmological term, i.e., exact interior solutions of the Einstein field equations is presented for the HD Tolman-Bondi metrics imbedded in a de Sitter background. The solution is then matched to exterior HD Scwarschild-de Sitter. A brief discussion on the causal structure singularities and horizons is provided. It turns out that the collapse proceed in the same way as in the Minkowski background, i.e., the strong curvature naked singularities form and that the higher dimensions seem to favor black holes rather than naked singularities.Comment: 7 Pages, no figure

Gravitational collapse of a Hagedorn fluid in Vaidya geometry

The gravitational collapse of a high-density null charged matter fluid, satisfying the Hagedorn equation of state, is considered in the framework of the Vaidya geometry. The general solution of the gravitational field equations can be obtained in an exact parametric form. The conditions for the formation of a naked singularity, as a result of the collapse of the compact object, are also investigated. For an appropriate choice of the arbitrary integration functions the null radial outgoing geodesic, originating from the shell focussing central singularity, admits one or more positive roots. Hence a collapsing Hagedorn fluid could end either as a black hole, or as a naked singularity. A possible astrophysical application of the model, to describe the energy source of gamma-ray bursts, is also considered.Comment: 14 pages, 2 figures, to appear in Phys. Rev.

Radial asymptotics of Lemaitre-Tolman-Bondi dust models

We examine the radial asymptotic behavior of spherically symmetric Lemaitre-Tolman-Bondi dust models by looking at their covariant scalars along radial rays, which are spacelike geodesics parametrized by proper length $\ell$, orthogonal to the 4-velocity and to the orbits of SO(3). By introducing quasi-local scalars defined as integral functions along the rays, we obtain a complete and covariant representation of the models, leading to an initial value parametrization in which all scalars can be given by scaling laws depending on two metric scale factors and two basic initial value functions. Considering regular "open" LTB models whose space slices allow for a diverging $\ell$, we provide the conditions on the radial coordinate so that its asymptotic limit corresponds to the limit as $\ell\to\infty$. The "asymptotic state" is then defined as this limit, together with asymptotic series expansion around it, evaluated for all metric functions, covariant scalars (local and quasi-local) and their fluctuations. By looking at different sets of initial conditions, we examine and classify the asymptotic states of parabolic, hyperbolic and open elliptic models admitting a symmetry center. We show that in the radial direction the models can be asymptotic to any one of the following spacetimes: FLRW dust cosmologies with zero or negative spatial curvature, sections of Minkowski flat space (including Milne's space), sections of the Schwarzschild--Kruskal manifold or self--similar dust solutions.Comment: 44 pages (including a long appendix), 3 figures, IOP LaTeX style. Typos corrected and an important reference added. Accepted for publication in General Relativity and Gravitatio

Proteomic Analysis Reveals Age-related Changes in Tendon Matrix Composition, with Age- and Injury-specific Matrix Fragmentation

Energy storing tendons, such as the human Achilles and equine superficial digital flexor tendon (SDFT), are highly prone to injury, the incidence of which increases with aging. The cellular and molecular mechanisms that result in increased injury in aged tendons are not well established but are thought to result in altered matrix turnover. However, little attempt has been made to fully characterize the tendon proteome nor determine how the abundance of specific tendon proteins changes with aging and/or injury. The aim of this study was, therefore, to assess the protein profile of normal SDFTs from young and old horses using label-free relative quantification to identify differentially abundant proteins and peptide fragments between age groups. The protein profile of injured SDFTs from young and old horses was also assessed. The results demonstrate distinct proteomic profiles in young and old tendon, with alterations in the levels of proteins involved in matrix organization and regulation of cell tension. Furthermore, we identified several new peptide fragments (neopeptides) present in aged tendons, suggesting that there are age-specific cleavage patterns within the SDFT. Proteomic profile also differed between young and old injured tendon, with a greater number of neopeptides identified in young injured tendon. This study has increased the knowledge of molecular events associated with tendon aging and injury, suggesting that maintenance and repair of tendon tissue may be reduced in aged individuals and may help to explain why the risk of injury increases with aging