Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Bach equations in Spin-Coefficient form   Conformal gravity theories are defined by field equations that determine only
the conformal structure of the spacetime manifold. The Bach equations represent
an early example of such a theory, we present them here in component form in
terms of spin- and boost-weighted spin-coefficients using the compacted
spin-coefficient formalism. These equations can be used as an efficient
alternative to the standard tensor form. As a simple application we solve the
Bach equations for pp-wave and static spherically symmetric spacetimes.

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The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
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The categories of this paper are: cs
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The categories of this paper are: ao-sci
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The categories of this paper are: adap-org
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The categories of this paper are: cond-mat
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The categories of this paper are: funct-an
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The categories of this paper are: math
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The categories of this paper are: mtrl-th
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The categories of this paper are: nlin
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: math-ph