Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Structure of Singularity in Spherical Inhomogeneous Dust Collapse   We study here the structure of singularity forming in gravitational collapse
of spherically symmetric inhomogeneous dust. Such a collapse is described by
the Tolman-Bondi-Lema{\^i}tre metric, which is a two-parameter family of
solutions to Einstein equations, characterized by two free functions of the
radial coordinate, namely the `mass function' F(r) and the `energy function'
f(r). The main new result here relates, in a general way, the formation of
black holes and naked shell-focusing singularities resulting as the final fate
of such a collapse to the generic form of regular initial data. Such a data is
characterized in terms of the density and velocity profiles of the matter,
specified on an initial time slice from which the collapse commences. Several
issues regarding the strength and stability of these singularities, when they
are naked, are examined with the help of the analysis developed here. In
particular, it is seen that strong curvature naked singularities can develop
from a generic form of initial data in terms of the initial density profiles
for the collapsing configuration. We also establish here that similar results
hold for black hole formation as well. We also discuss here the physical
constraints on the initial data for avoiding shell-crossing singularities; and
also the shell-focusing naked singularities, so that the collapse will
necessarily end as a black hole, preserving the cosmic censorship. These
results generalize several earlier works on inhomogeneous dust collapse as
special cases, and provide a clearer insight into the phenomena of black hole
and naked singularity formation in gravitational collapse.

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The categories of this paper are: q-fin
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The categories of this paper are: nucl-ex
2
The categories of this paper are: math
30
The categories of this paper are: q-alg
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The categories of this paper are: eess
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The categories of this paper are: acc-phys
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The categories of this paper are: stat
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The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
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The categories of this paper are: dg-ga
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The categories of this paper are: q-bio
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: physics
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The categories of this paper are: math-ph
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The categories of this paper are: cmp-lg