Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Vacuum Einstein Equations via Holonomy around Closed Loops on
  Characteristic Surfaces   We reformulate the standard local equations of general relativity for
asymptotically flat spacetimes in terms of two non-local quantities, the
holonomy $H$ around certain closed null loops on characteristic surfaces and
the light cone cut function $Z$, which describes the intersection of the future
null cones from arbitrary spacetime points, with future null infinity. We
obtain a set of differential equations for $H$ and $Z$ equivalent to the vacuum
Einstein equations. By finding an algebraic relation between $H$ and $Z$ this
set of equations is reduced to just two coupled equations: an
integro-differential equation for $Z$ which yields the conformal structure of
the underlying spacetime and a linear differential equation for the ``vacuum''
conformal factor. These equations, which apply to all vacuum asymptotically
flat spacetimes, are however lengthy and complicated and we do not yet know of
any solution generating technique. They nevertheless are amenable to an
attractive perturbative scheme which has Minkowski space as a zeroth order
solution.

13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th