Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Applications of theorems of Jean Leray to the Einstein-scalar field
  equations   The Einstein-scalar field theory can be used to model gravitational physics
with scalar field matter sources. We discuss the initial value formulation of
this field theory, and show that the ideas of Leray can be used to show that
the Einstein-scalar field system of partial differential equations is
well-posed as an evolutionary system. We also show that one can generate
solutions of the Einstein-scalar field constraint equations using conformal
methods.

10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci