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.

General relativistic cosmological N-body simulations. Part I. Time integration

“…Consequently, it cannot describe the correct (collisionless) dynamics at scales where shell-crossing occurs, which roughly coincides with the scales at which the dynamics become non-linear. One way of describing a cosmology with "granular" matter within NR, which has also received particular focus, are simulations of lattice black hole configurations [95][96][97][98][99][100][101][102][103], but the high degree of symmetry makes such solutions too idealized to describe realistic dark matter dynamics. The status quo naturally leads us to consider the potential advantages of an N -body NR approach, i.e.…”

Lie sphere geometry in lattice cosmology

“…But for completeness and comparison we note that the R 4 -distance X − Y and the intrinsic geodesic distance (compare (2)) Λ = Λ(X, Y ) := arccos(X · Y ) between two points X and Y on S 3 are simply related by X − Y = 2(1 − cos(Λ)) = 2 sin(Λ/2). This is the way the solution was recently presented and discussed in [3,12], with generalisation to nonvanishing cosmological constant in [13].…”

“…This linearity will be essential to the method used here. We refer to [3] for a recent comprehensive review of the expectations and achievements connected with lattice cosmology. More specifically, we refer to [11] for an instructive application to the backreaction problem, to [31] for an extensive study of redshifts and inregrated Sachs-Wolfe effects, and [4] for a general discussion of light-propagation in lattice cosmology.…”

Discrete cosmological models in the Brans–Dicke theory of gravity

“…[23] and reviewed in Ref. [21]. The work in Sections 3 and 4 of this paper provide the first (and currently only) steps to understand branches "2", "3" and "4" of this graph.…”