Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Invariants of the Kerr Vacuum   The Kerr vacuum has two independent invariants derivable from the Riemann
tensor without differentiation. Both of these invariants must be examined in
order to avoid an erroneous conclusion that the ring singularity of this
spacetime is "directional".

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The categories of this paper are: q-bio
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The categories of this paper are: q-alg
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The categories of this paper are: physics
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The categories of this paper are: alg-geom
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The categories of this paper are: atom-ph
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The categories of this paper are: nlin
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The categories of this paper are: econ
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The categories of this paper are: q-fin
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The categories of this paper are: chem-ph
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The categories of this paper are: math-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys