A Quasi-Static Approach to Structure Formation in Black Hole Universes

TL;DR

This paper introduces new exact initial data for inhomogeneous cosmological models with black hole clusters, exploring how structure formation impacts cosmological scales and interaction energies in a non-perturbative framework.

Contribution

It generalizes black hole lattice models to include clusters, allowing detailed study of structure formation effects on cosmology beyond perturbative methods.

Findings

Clustering significantly reduces the effective cosmological scale.

Interaction energies within and between clusters are substantial.

Large black hole clusters can be as small as 30% of Friedmann models with same mass.

Abstract

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.