Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dynamical extensions for shell-crossing singularities   We derive global weak solutions of Einstein's equations for spherically
symmetric dust-filled space-times which admit shell-crossing singularities. In
the marginally bound case, the solutions are weak solutions of a conservation
law. In the non-marginally bound case, the equations are solved in a
generalized sense involving metric functions of bounded variation. The
solutions are not unique to the future of the shell-crossing singularity, which
is replaced by a shock wave in the present treatment; the metric is bounded but
not continuous.

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The categories of this paper are: cs
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The categories of this paper are: q-fin
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The categories of this paper are: math-ph
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The categories of this paper are: solv-int
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The categories of this paper are: q-alg
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The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
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The categories of this paper are: eess
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The categories of this paper are: quant-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: chem-ph
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The categories of this paper are: stat
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: comp-gas