A Quasi-Static Approach to Structure Formation in Black Hole Universes
  Motivated by the existence of hierarchies of structure in the Universe, we
present four new families of exact initial data for inhomogeneous cosmological
models at their maximum of expansion. These data generalise existing black hole
lattice models to situations that contain clusters of masses, and hence allow
the consequences of cosmological structures to be considered in a well-defined
and non-perturbative fashion. The degree of clustering is controlled by a
parameter $\lambda$, in such a way that for $\lambda \sim 0$ or $1$ we have
very tightly clustered masses, whilst for $\lambda \sim 0.5$ all masses are
separated by cosmological distance scales. We study the consequences of
structure formation on the total net mass in each of our clusters, as well as
calculating the cosmological consequences of the interaction energies both
within and between clusters. The locations of the shared horizons that appear
around groups of black holes, when they are brought sufficiently close
together, are also identified and studied. We find that clustering can have
surprisingly large effects on the scale of the cosmology, with models that
contain thousands of black holes sometimes being as little as 30% of the size
of comparable Friedmann models with the same total proper mass. This deficit is
comparable to what might be expected to occur from neglecting gravitational
interaction energies in Friedmann cosmology, and suggests that these quantities
may have a significant influence on the properties of the large-scale
cosmology.
