Black-Hole Lattices as Cosmological Models

Abstract

The search for solutions of Einstein's equations representing relativistic cosmological models with a discrete matter content has been remarkably fruitful in the last decade. In this review we discuss the progress made in the study of a specific subclass of discrete cosmologies, Black-Hole Lattice models. In particular, we illustrate the techniques used for the construction of these spacetimes, and examine their resulting physical properties. This includes their large-scale dynamics, the dressing of mass due to the interaction between individual black holes, along with features of direct observational interest such as the distance-to-redshift relation. This collection of results provides a novel perspective on the physical effects of averaging in General Relativity, as well as on the emergence of gravitational structures from solutions with isolated objects.

54 pages, 16 figures, review prepared for the CQG Special Focus Issue "Computational issues in mathematical cosmology"

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• Cosmology using numerical relativity
• Gauss-Bonnet-Chern approach to the averaged Universe
• The effect of dark matter discreteness on light propagation
• Cosmic expansion from spinning black holes
• Perturbatively constructed cosmological model with periodically distributed dust inhomogeneities
• Einstein clusters as models of inhomogeneous spacetimes
• Structure formation and quasi-spherical collapse from initial curvature perturbations with numerical relativity simulations
• Sound waves from primordial black hole formations
• On the intrinsically flat cosmological models in a lattice
• Intrinsically symmetric cosmological model in the presence of dissipative fluids
• Lie sphere-geometry in lattice cosmology
• Construction of the cosmological model with periodically distributed inhomogeneities with growing amplitude
• Discrete Cosmological Models in the Brans-Dicke Theory of Gravity
• Analytic Analysis of Irregular Discrete Universes
• A Gravitational Wave Background from Primordial Black Hole Lattices in Matter Dominated Era