Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Convergence to a self-similar solution in general relativistic
  gravitational collapse   We study the spherical collapse of a perfect fluid with an equation of state
$P=k\rho$ by full general relativistic numerical simulations. For $0<k\alt
0.036$, it has been known that there exists a general relativistic counterpart
of the Larson-Penston self-similar Newtonian solution. The numerical
simulations strongly suggest that, in the neighborhood of the center, generic
collapse converges to this solution in an approach to a singularity and that
self-similar solutions other than this solution, including a ``critical
solution'' in the black hole critical behavior, are relevant only when the
parameters which parametrize initial data are fine-tuned. This result is
supported by a mode analysis on the pertinent self-similar solutions. Since a
naked singularity forms in the general relativistic Larson-Penston solution for
$0<k\alt0.0105$, this will be the most serious known counterexample against
cosmic censorship. It also provides strong evidence for the self-similarity
hypothesis in general relativistic gravitational collapse. The direct
consequence is that critical phenomena will be observed in the collapse of
isothermal gas in Newton gravity, and the critical exponent $\gamma$ will be
given by $\gamma\approx 0.11$, though the order parameter cannot be the black
hole mass.

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The categories of this paper are: math-ph
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The categories of this paper are: eess
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The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
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The categories of this paper are: supr-con
2
The categories of this paper are: math
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
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The categories of this paper are: comp-gas
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The categories of this paper are: adap-org
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The categories of this paper are: chao-dyn
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The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph