Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Local existence proofs for the boundary value problem for static
  spherically symmetric Einstein-Yang-Mills fields with compact gauge groups   We prove local existence and uniqueness of static spherically symmetric
solutions of the Einstein-Yang-Mills equations for an arbitrary compact
semisimple gauge group in the so-called regular case. By this we mean the
equations obtained when the rotation group acts on the principal bundle on
which the Yang-Mills connection takes its values in a particularly simple way
(the only one ever considered in the literature). The boundary value problem
that results for possible asymptotically flat soliton or black hole solutions
is very singular and just establishing that local power series solutions exist
at the center and asymptotic solutions at infinity amounts to a nontrivial
algebraic problem. We discuss the possible field equations obtained for
different group actions and solve the algebraic problem on how the local
solutions depend on initial data at the center and at infinity.

9
The categories of this paper are: nlin
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg