Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Perturbative Solutions of the Extended Constraint Equations in General
  Relativity   The extended constraint equations arise as a special case of the conformal
constraint equations that are satisfied by an initial data hypersurface $Z$ in
an asymptotically simple spacetime satisfying the vacuum conformal Einstein
equations developed by H. Friedrich. The extended constraint equations consist
of a quasi-linear system of partial differential equations for the induced
metric, the second fundamental form and two other tensorial quantities defined
on $Z$, and are equivalent to the usual constraint equations that $Z$ satisfies
as a spacelike hypersurface in a spacetime satisfying Einstein's vacuum
equation. This article develops a method for finding perturbative,
asymptotically flat solutions of the extended constraint equations in a
neighbourhood of the flat solution on Euclidean space. This method is
fundamentally different from the `classical' method of Lichnerowicz and York
that is used to solve the usual constraint equations.

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The categories of this paper are: physics
25
The categories of this paper are: patt-sol
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The categories of this paper are: hep-lat
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: quant-ph
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The categories of this paper are: cs
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The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an