Black-hole lattices as cosmological models

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