25,273 research outputs found
On the genericity of spacetime singularities
We consider here the genericity aspects of spacetime singularities that occur
in cosmology and in gravitational collapse. The singularity theorems (that
predict the occurrence of singularities in general relativity) allow the
singularities of gravitational collapse to be either visible to external
observers or covered by an event horizon of gravity. It is shown that the
visible singularities that develop as final states of spherical collapse are
generic. Some consequences of this fact are discussed.Comment: 19 pages, To be published in the Raychaudhuri Volume, eds. Naresh
Dadhich, Pankaj Joshi and Probir Ro
Turbofan aft duct suppressor study program listing and user's guide
A description of the structure of the Annular Flow Duct Program (AFDP) for the calculation of acoustic suppression due to treatment in a finite length annular duct carrying sheared flow is presented. Although most appropriate for engine exhaust ducts, this program can be used to study sound propagation in any duct that maintains annular geometry over a considerable length of the duct. The program is based on the modal analysis of sound propagation in ducts with axial segments of different wall impedances. For specified duct geometry, wall impedance, flow and acoustic conditions in the duct (including mode amplitude distribution of the source) and duct termination reflection characteristics, the program calculates the suppression due to the treatment in the duct. The presence of forward and backward traveling modes in the duct due to the reflection and redistribution of modes at segment interfaces and duct end terminations are taken into account in the calculations. The effects of thin wall boundary layers (with a linear or mean flow velocity profile) on the acoustic propagation are also included in the program. A functional description of the major subroutines is included and a sample run is provided with an explanation of the output
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Consultation and consequences: A view on the services experienced by some young people and six families
Reports the views of some young people and 6 families on services received from social care professionals. Summarises the main themes that emerged and emphasises the issue of professional reliability as articulated in these 2 small, but in depth, studies. The views of both sets of interviewees contributed to the creation of a course for front line managers drawing from user and worker consultations. Draws on the interviews to shed light on various aspects of professional relationships with services users and what they said they wanted. Discussion sets this in the context of policy agenda
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
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
Instability of black hole formation under small pressure perturbations
We investigate here the spectrum of gravitational collapse endstates when
arbitrarily small perfect fluid pressures are introduced in the classic black
hole formation scenario as described by Oppenheimer, Snyder and Datt (OSD) [1].
This extends a previous result on tangential pressures [2] to the more
physically realistic scenario of perfect fluid collapse. The existence of
classes of pressure perturbations is shown explicitly, which has the property
that injecting any smallest pressure changes the final fate of the dynamical
collapse from a black hole to a naked singularity. It is therefore seen that
any smallest neighborhood of the OSD model, in the space of initial data,
contains collapse evolutions that go to a naked singularity outcome. This gives
an intriguing insight on the nature of naked singularity formation in
gravitational collapse.Comment: 7 pages, 1 figure, several modifications to match published version
on GR
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 , the initial central density
of the massive body, and , the initial boundary. The collapse ends in a
black hole if the dimensionless quantity constructed out of this
initial data is greater than 0.0113, and it ends in a naked singularity if
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
A characterization of the central shell-focusing singularity in spherical gravitational collapse
We give a characterization of the central shell-focusing curvature
singularity that can form in the spherical gravitational collapse of a bounded
matter distribution obeying the dominant energy condition. This
characterization is based on the limiting behaviour of the mass function in the
neighbourhood of the singularity. Depending on the rate of growth of the mass
as a function of the area radius R, the singularity may be either covered or
naked. The singularity is naked if this growth rate is slower than R, covered
if it is faster than R, and either naked or covered if the growth rate is same
as R.Comment: 12 pages, Latex, significantly revised version, including change of
title. Revised version to appear in Classical and Quantum Gravit
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