Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spherically Symmetric Black Hole Formation in Painlev\'e-Gullstrand
  Coordinates   We perform a numerical study of black hole formation from the spherically
symmetric collapse of a massless scalar field. The calculations are done in
Painlev\'e-Gullstrand (PG) coordinates that extend across apparent horizons and
allow the numerical evolution to proceed until the onset of singularity
formation. We generate spacetime maps of the collapse and illustrate the
evolution of apparent horizons and trapping surfaces for various initial data.
We also study the critical behaviour and find the expected Choptuik scaling
with universal values for the critical exponent and echoing period consistent
with the accepted values of $\gamma=0.374$ and $\Delta = 3.44$, respectively.
The subcritical curvature scaling exhibits the expected oscillatory behaviour
but the form of the periodic oscillations in the supercritical mass scaling
relation, while universal with respect to initial PG data, is non-standard: it
is non-sinusoidal with large amplitude cusps.

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The categories of this paper are: stat
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The categories of this paper are: chao-dyn
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The categories of this paper are: cmp-lg
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The categories of this paper are: eess
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The categories of this paper are: cs
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The categories of this paper are: math-ph
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The categories of this paper are: nlin
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The categories of this paper are: quant-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: funct-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con
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The categories of this paper are: hep-lat
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The categories of this paper are: q-alg