Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Monodromy transform approach to solution of the Ernst equations in
  General Relativity   The approach, referred to as "monodromy transform", provides some general
base for solution of all known integrable space - time symmetry reductions of
Einstein equations for the case of pure vacuum gravitational fields, in the
presence of gravitationally interacting massless fields, as well as for some
string theory induced gravity models. In this communication we present the key
points of this approach, applied to Einstein equations for vacuum and to
Einstein - Maxwell equations for electrovacuum fields in the cases, reducible
to the known Ernst equations. Definition of the monodromy data, formulation and
solution of the direct and inverse problems of the monodromy transform, a proof
of existence and uniqueness of their solutions, the structure of the basic
linear singular integral equations and their regularizations, which lead to the
equations of (quasi-)Fredholm type are also discussed. A construction of
general local solution of these equations is given in terms of homogeneously
convergent functional series.

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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: comp-gas
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The categories of this paper are: plasm-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
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The categories of this paper are: astro-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: chem-ph
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The categories of this paper are: supr-con
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The categories of this paper are: eess
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The categories of this paper are: q-fin
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The categories of this paper are: mtrl-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