Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: General framework of higher order gauge invariant perturbation theory   Based on the gauge invariant variables proposed in [K. Nakamura, Prog. Theor.
Phys. vol.110 (2003), 723.], general framework of the second order gauge
invariant perturbation theory on arbitrary background spacetime is considered.
We derived formulae of the perturbative Einstein tensor of each order, which
have the similar form to the definitions of gauge invariant variables for
arbitrary perturbative fields. As a result, each order Einstein equation is
necessarily given in terms of gauge invariant variables.

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The categories of this paper are: atom-ph
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-th
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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: mtrl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
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The categories of this paper are: ao-sci
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The categories of this paper are: bayes-an
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The categories of this paper are: supr-con
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The categories of this paper are: adap-org
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The categories of this paper are: funct-an
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The categories of this paper are: patt-sol
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The categories of this paper are: physics
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The categories of this paper are: eess