Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Three dimensional stationary cyclic symmetric Einstein-Maxwell
  solutions; black holes   From a general metric for stationary cyclic symmetric gravitational fields
coupled to Maxwell electromagnetic fields within the $(2+1)$-dimensional
gravity the uniqueness of wide families of exact solutions is established,
among them, all uniform electromagnetic solutions possessing electromagnetic
fields with vanishing covariant derivatives, all fields having constant
electromagnetic invariants $F_{\mu\nu}\,F^{\mu\nu}$ and
$T_{\mu\nu}\,T^{\mu\nu}$, the whole classes of hybrid electromagnetic
solutions, and also wide classes of stationary solutions are derived for a
third order nonlinear key equations. Certain of these families can be thought
of as black hole solutions. For the most general set of Einstein-Maxwell
equations, reducible to three non-linear equations for the three unknown
functions, two new classes of solutions-having anti-de Sitter spinning metric
limit-are derived. The relationship of various families with those reported by
different authors' solutions has been established. Among the classes of
solutions with cosmological constant a relevant place occupy: the electrostatic
and magnetostatic Peldan solutions, the stationary uniform and spinning Clement
classes, the constant electromagnetic invariant branches with the particular
Kamata-Koikawa solution, the hybrid cyclic symmetric stationary black hole
fields, and the non-less important solutions generated via $SL(2,R)$
transformations where the Clement spinning charged solution, the
Martinez-Teitelboim-Zanelli black hole solution, and Dias-Lemos metric merit
mention.

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The categories of this paper are: adap-org
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The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
2
The categories of this paper are: math
32
The categories of this paper are: atom-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-th
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The categories of this paper are: q-alg
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: patt-sol
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The categories of this paper are: chao-dyn
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The categories of this paper are: cond-mat
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The categories of this paper are: chem-ph