Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stability Analysis in N dimensional Gravitational collapse with equation
  of state   We study stability of occurrence of black holes and naked singularities that
arise as a final state for a complete gravitational collapse of type I matter
field in a spherically symmetric $N$ dimensional spacetime with equation of
state $p = k \rho$, $0 \leq k \leq 1$. We prove that for a regular initial data
comprising of pressure (or density) profiles at an initial surface $t = t_{i}$,
from which the collapse evolves, there exists a large class of the velocity
functions and classes of solutions of Einstein equations, such that the
spacetime evolution goes to a final state which is either a black hole or a
naked singularity. We further prove that in an infinite dimensional separable
Banach space, the set of regular initial data leading the collapse to a black
hole or a naked singularity, forms an open subset of the set of all regular
initial data. In this sense, the gravitational collapse leading to either a
black hole or a naked singularity is stable. These results are discussed and
analyzed in the light of the cosmic censorship hypothesis in black hole
physics.

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The categories of this paper are: plasm-ph
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The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
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The categories of this paper are: cmp-lg
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The categories of this paper are: stat
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
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The categories of this paper are: supr-con
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The categories of this paper are: bayes-an
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The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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The categories of this paper are: math-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin