Spherical Dust Collapse in Higher Dimensions

We consider here the question if it is possible to recover cosmic censorship when a transition is made to higher dimensional spacetimes, by studying the spherically symmetric dust collapse in an arbitrary higher spacetime dimension. It is pointed out that if only black holes are to result as end state of a continual gravitational collapse, several conditions must be imposed on the collapsing configuration, some of which may appear to be restrictive, and we need to study carefully if these can be suitably motivated physically in a realistic collapse scenario. It would appear that in a generic higher dimensional dust collapse, both black holes and naked singularities would develop as end states as indicated by the results here. The mathematical approach developed here generalizes and unifies the earlier available results on higher dimensional dust collapse as we point out. Further, the dependence of black hole or naked singularity end states as collapse outcomes, on the nature of the initial data from which the collapse develops, is brought out explicitly and in a transparent manner as we show here. Our method also allows us to consider here in some detail the genericity and stability aspects related to the occurrence of naked singularities in gravitational collapse.Comment: Revtex4, Title changed, To appear in Physical Review

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

Why do naked singularities form in gravitational collapse?

We investigate what are the key physical features that cause the development of a naked singularity, rather than a black hole, as the end-state of spherical gravitational collapse. We show that sufficiently strong shearing effects near the singularity delay the formation of the apparent horizon. This exposes the singularity to an external observer, in contrast to a black hole, which is hidden behind an event horizon due to the early formation of an apparent horizon.Comment: revised for clarity, new figure included; version accepted by Phys. Rev. D (RC

Higher dimensional radiation collapse and cosmic censorship

We study the occurrence of naked singularities in the spherically symmetric collapse of radiation shells in a higher dimensional spacetime. The necessary conditions for the formation of a naked singularity or a black hole are obtained. The naked singularities are found to be strong in the Tipler's sense and thus violating cosmic censorship conjecture.Comment: 4 pages, ReVTeX, Phys Rev D Vol 62 107502 (2000

Phase space reduction of the one-dimensional Fokker-Planck (Kramers) equation

A pointlike particle of finite mass m, moving in a one-dimensional viscous environment and biased by a spatially dependent force, is considered. We present a rigorous mapping of the Fokker-Planck equation, which determines evolution of the particle density in phase space, onto the spatial coordinate x. The result is the Smoluchowski equation, valid in the overdamped limit, m->0, with a series of corrections expanded in powers of m. They are determined unambiguously within the recurrence mapping procedure. The method and the results are interpreted on the simplest model with no field and on the damped harmonic oscillator.Comment: 13 pages, 1 figur

Electrostatic potential profiles of molecular conductors

The electrostatic potential across a short ballistic molecular conductor depends sensitively on the geometry of its environment, and can affect its conduction significantly by influencing its energy levels and wave functions. We illustrate some of the issues involved by evaluating the potential profiles for a conducting gold wire and an aromatic phenyl dithiol molecule in various geometries. The potential profile is obtained by solving Poisson's equation with boundary conditions set by the contact electrochemical potentials and coupling the result self-consistently with a nonequilibrium Green's function (NEGF) formulation of transport. The overall shape of the potential profile (ramp vs. flat) depends on the feasibility of transverse screening of electric fields. Accordingly, the screening is better for a thick wire, a multiwalled nanotube or a close-packed self-assembled monolayer (SAM), in comparison to a thin wire, a single-walled nanotube or an isolated molecular conductor. The electrostatic potential further governs the alignment or misalignment of intramolecular levels, which can strongly influence the molecular I-V characteristic. An external gate voltage can modify the overall potential profile, changing the current-voltage (I-V) characteristic from a resonant conducting to a saturating one. The degree of saturation and gate modulation depends on the metal-induced-gap states (MIGS) and on the electrostatic gate control parameter set by the ratio of the gate oxide thickness to the channel length.Comment: to be published in Phys. Rev. B 69, No.3, 0353XX (2004

Application of DSTATCOM for surplus power circulation in MV and LV distribution networks with single-phase distributed energy resources

Single-phase distributed energy resources (DERs), such as rooftop photovoltaic arrays, are usually installed based on the need and affordability of clients without any regard to the power demand of the connected phase of a three-phase system. It might so happen that the power generation in a particular phase is more than its load demand. This may cause a reverse power flow in a particular phase, especially in a three-phase, four-wire distribution system. If now the load demand in the other two phases is more than their respective generations, then these two phases will see a forward power flow, while there will be a reverse power flow in the third phase. This will create severe unbalance in the upstream network. In this paper, a distribution static compensator (DSTATCOM) is used to circulate the excess generation from one phase to the others such that a set of balanced currents flow from or into the upstream network. Two different topologies of DSTATCOM are proposed in this paper for the low and medium voltage feeders. Two different power circulation strategies are developed for this purpose. Furthermore, a suitable feedback scheme is developed for each topology for power converter control. The performance of the proposed topologies and the control schemes for the DSTATCOM is evaluated through computer simulation studies using PSCAD/EMTDC

Naked Singularity Formation In f(R) Gravity

We study the gravitational collapse of a star with barotropic equation of state $p=w\rho$ in the context of $f({\mathcal R})$ theories of gravity. Utilizing the metric formalism, we rewrite the field equations as those of Brans-Dicke theory with vanishing coupling parameter. By choosing the functionality of Ricci scalar as $f({\mathcal R})=\alpha{\mathcal R}^{m}$, we show that for an appropriate initial value of the energy density, if $\alpha$ and $m$ satisfy certain conditions, the resulting singularity would be naked, violating the cosmic censorship conjecture. These conditions are the ratio of the mass function to the area radius of the collapsing ball, negativity of the effective pressure, and the time behavior of the Kretschmann scalar. Also, as long as parameter $\alpha$ obeys certain conditions, the satisfaction of the weak energy condition is guaranteed by the collapsing configuration.Comment: 15 pages, 4 figures, to appear in GR

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.