Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Existence of Static Metric Extensions in General Relativity   Motivated by problems related to quasi-local mass in general relativity, we
study the static metric extension conjecture proposed by R. Bartnik
\cite{Bartnik_energy}. We show that, for any metric on $\bar{B}_1$ that is
close enough to the Euclidean metric and has reflection invariant boundary
data, there always exists an asymptotically flat and scalar flat {\em static}
metric extension in $M = \R^3 \setminus B_1$ such that it satisfies Bartnik's
geometric boundary condition \cite{Bartnik_energy} on $\partial B_1$.

35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an