Black Hole Universe: Construction and Analysis of Initial Data
  We numerically construct an one-parameter family of initial data of an
expanding inhomogeneous universe model which is composed of regularly aligned
black holes with an identical mass. They are initial data for vacuum solutions
of the Einstein equations. We call this universe model the "black hole
universe" and analyze the structure of these initial data. We study the
relation between the mean expansion rate of the 3-space, which corresponds to
the Hubble parameter, and the mass density of black holes. The result implies
that the same relation as that of the Einstein-de Sitter universe is realized
in the limit of the large separation between neighboring black holes. The
applicability of the cosmological Newtonian $N$-body simulation to the dark
matter composed of black holes is also discussed. The deviation of the spatial
metric of the cosmological Newtonian $N$-body system from that of the black
hole universe is found to be smaller than about 1% in a region distant from the
particles, if the separation length between neighboring particles is 20 times
larger than their gravitational radius. By contrast, the deviation of the
square of the Hubble parameter of the cosmological Newtonian $N$-body system
from that of the black hole universe is about 20% for the same separation
length.
