Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Constraint equations for 3 + 1 vacuum Einstein equations with a
  translational space-like Killing field in the asymptotically flat case II   We solve the Einstein constraint equations for a 3 + 1 dimensional vacuum
spacetime with a space-like translational Killing field in the asymptotically
flat case.. The presence of a space-like translational Killing field allows for
a reduction of the 3 + 1 dimensional problem to a 2+1 dimensional one. The aim
of this paper is to go further in the asymptotic expansion of the solutions
than in [14]. In particular the expansion we construct involves quantities
which are the 2-dimensional equivalent of the global charges.

20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
18
The categories of this paper are: econ