Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Automorphisms and a Cartography of the Solution Space for Vacuum Bianchi
  Cosmologies: The Type III Case   The theory of symmetries of systems of coupled, ordinary differential
equations (ODE's) is used to develop a concise algorithm for cartographing the
space of solutions to vacuum Bianchi Einstein's Field Equations (EFE). The
symmetries used are the well known automorphisms of the Lie algebra for the
corresponding isometry group of each Bianchi Type, as well as the scaling and
the time eparameterization symmetry. Application of the method to Type III
results in: a) the recovery of all known solutions without prior assumption of
any extra symmetry, b) the enclosure of the entire unknown part of the solution
space into a single, second order ODE in terms of one dependent variable and c)
a partial solution to this ODE. It is also worth-mentioning the fact that the
solution space is seen to be naturally partitioned into three distinct,
disconnected pieces: one consisting of the known Siklos (pp-wave) solution,
another occupied by the Type III member of the known Ellis-MacCallum family and
the third described by the aforementioned ODE in which an one parameter
subfamily of the known Kinnersley geometries resides. Lastly, preliminary
results reported show that the unknown part of the solution space for other
Bianchi Types is described by a strikingly similar ODE, pointing to a natural
operational unification as far as the problem of solving the cosmological EFE's
is concerned.

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The categories of this paper are: bayes-an
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
2
The categories of this paper are: math
13
The categories of this paper are: quant-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
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The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: comp-gas
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The categories of this paper are: q-alg
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The categories of this paper are: math-ph
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The categories of this paper are: stat
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The categories of this paper are: chao-dyn
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The categories of this paper are: eess