Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Irrotational dust with Div H=0   For irrotational dust the shear tensor is consistently diagonalizable with
its covariant time derivative: $\sigma_{ab}=0=\dot{\sigma}_{ab},\; a\neq b$, if
and only if the divergence of the magnetic part of the Weyl tensor vanishes:
$div~H = 0$. We show here that in that case, the consistency of the Ricci
constraints requires that the magnetic part of the Weyl tensor itself vanishes:
$H_{ab}=0$.

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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-th
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ex
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The categories of this paper are: math-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: math
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The categories of this paper are: cmp-lg
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-th
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The categories of this paper are: patt-sol