Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Lanczos potential for the Weyl curvature tensor: existence, wave
  equation and algorithms   In the last few years renewed interest in the 3-tensor potential $L_{abc} $
proposed by Lanczos for the Weyl curvature tensor has not only clarified and
corrected Lanczos's original work, but generalised the concept in a number of
ways. In this paper we carefully summarise and extend some aspects of these
results, and clarify some misunderstandings in the literature. We also clarify
some comments in a recent paper by Dolan and Kim; in addition, we correct some
internal inconsistencies in their paper and extend their results.
  The following new results are also presented. The (computer checked)
complicated second order partial differential equation for the 3-potential, in
arbitrary gauge, for Weyl candidates satisfying Bianchi-type equations is given
-- in those $n $-dimensional spaces (with arbitrary signature) for which the
potential exists; this is easily specialised to Lanczos potentials for the Weyl
curvature tensor. It is found that it is {\it only} in 4-dimensional spaces
(with arbitrary signature and gauge), that the non-linear terms disappear and
that the awkward second order derivative terms cancel; for 4-dimensional
spacetimes (with Lorentz signature), this remarkably simple form was originally
found by Illge, using spinor methods. It is also shown that, for most
4-dimensional vacuum spacetimes, any 3-potential in the Lanczos gauges which
satisfies a simple homogeneous wave equation must be a Lanczos potential for
the Weyl curvature tensor of the background vacuum spacetime. This result is
used to prove that the form of a {\it possible} Lanczos potential proposed by
Dolan and Kim for a class of vacuum spacetimes is in fact a genuine Lanczos
potential for these spacetimes.

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The categories of this paper are: cond-mat
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The categories of this paper are: math
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-th
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The categories of this paper are: econ
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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: q-fin
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The categories of this paper are: q-alg
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: physics
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The categories of this paper are: quant-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: stat
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The categories of this paper are: nlin