Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Phase Space Approach to the Conformal Construction of Non-Vacuum
  Initial Data Sets in General Relativity   We present a uniform (and unambiguous) procedure for scaling the matter
fields in implementing the conformal method to parameterize and construct
solutions of Einstein constraint equations with coupled matter sources. The
approach is based on a phase space representation of the space-time matter
fields after a careful $n+1$ decomposition into spatial fields $B$ and
conjugate momenta $\Pi_B$, which are specified directly and are conformally
invariant quantities. We show that if the Einstein-matter field theory is
specified by a Lagrangian which is diffeomorphism invariant and involves no
dependence on derivatives of the space-time metric in the matter portion of the
Lagrangian, then fixing $B$ and $\Pi_B$ results in conformal constraint
equations that, for constant-mean curvature initial data, semi-decouple just as
they do for the vacuum Einstein conformal constraint equations. We prove this
result by establishing a structural property of the Einstein momentum
constraint that is independent of the conformal method: For an Einstein-matter
field theory which satisfies the conditions just stated, if $B$ and $\Pi_B$
satisfy the matter Euler-Lagrange equations, then (in suitable form) the
right-hand side of the momentum constraint on each spatial slice depends only
on $B$ and $\Pi_B$ and is independent of the space-time metric. We discuss the
details of our construction in the special cases of the following models:
Einstein-Maxwell-charged scalar field, Einstein-Proca, Einstein-perfect fluid,
and Einstein-Maxwell-charged dust. In these examples we find that our technique
gives a theoretical basis for scaling rules, such as those for
electromagnetism, that have worked pragmatically in the past, but also
generates new equations with advantageous features for perfect fluids that
allow direct specification of total rest mass and total charge in any spatial
region.

4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int