Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Integration in the GHP formalism II: An operator approach for spacetimes
  with killing vectors, with applications to twisting type n spaces   Held has proposed a coordinate- and gauge-free integration procedure within
the GHP formalism built around four functionally independent zero-weighted
scalars constructed from the spin coefficients and the Riemann tensor
components. Unfortunately, a spacetime with Killing vectors will be unable to
supply the full quota of four scalars of this type. However, for such a
spacetime additional scalars are supplied by the components of the Killing
vectors; by using these alongside the spin coefficients and the Riemann tensor
components we have the possibility of constructing the full quota of four
functionally independent zero-weighted scalars, and of exploiting Held's
procedure.
  As an illustration we investigate the vacuum Type N spaces admitting a
Killing vector and a homothetic Killing vector. In a direct manner, we reduce
the problem to a pair of ordinary differential operator `master equations',
making use of a new zero-weighted GHP operator. By first rewriting the master
equations as a closed set of complex first order equations, we reduce the
problem to one real third order operator differential equation for a complex
function of a real variable --- but with still the freedom to choose explicitly
our fourth coordinate. An alternative, more algorithmic approach, using a
closed chain of real first order equations for real functions, reduces the
problem to the same order, but in a more natural and much more concise form. It
is also outlined how the various other third order differential equations,
which have been derived previously by other workers on this problem, can be
deduced from our master equations.

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The categories of this paper are: eess
37
The categories of this paper are: supr-con
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The categories of this paper are: bayes-an
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The categories of this paper are: physics
0
The categories of this paper are: hep-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ex
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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: nucl-th
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The categories of this paper are: nlin
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The categories of this paper are: q-alg
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The categories of this paper are: cond-mat
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The categories of this paper are: cs
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The categories of this paper are: stat
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The categories of this paper are: funct-an