Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the existence of initial data containing isolated black holes   We present a general construction of initial data for Einstein's equations
containing an arbitrary number of black holes, each of which is instantaneously
in equilibrium. Each black hole is taken to be a marginally trapped surface and
plays the role of the inner boundary of the Cauchy surface. The black hole is
taken to be instantaneously isolated if its outgoing null rays are shear-free.
Starting from the choice of a conformal metric and the freely specifiable part
of the extrinsic curvature in the bulk, we give a prescription for choosing the
shape of the inner boundaries and the boundary conditions that must be imposed
there. We show rigorously that with these choices, the resulting non-linear
elliptic system always admits solutions.

35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs