Analytic Analysis of Irregular Discrete Universes

TL;DR

This paper explores the complex dynamics of irregularly distributed black holes in cosmological models with spherical topology, revealing richer behaviors than regular models and differences from isotropic dust models.

Contribution

It introduces a novel method for analyzing irregular black hole distributions in cosmology using tessellation and LRS conditions, expanding understanding beyond regular arrangements.

Findings

Irregular black hole models exhibit richer dynamics than regular ones.

The initial geometry differs significantly from regular models in approaching isotropy.

Randomized distributions can be unbiased or clustered, affecting evolution.

Abstract

In this work we investigate the dynamics of cosmological models with spherical topology containing up to 600 Schwarzschild black holes arranged in an irregular manner. We solve the field equations by tessellating the 3-sphere into eight identical cells, each having a single edge which is shared by all cells. The shared edge is enforced to be locally rotationally symmetric (LRS), thereby allowing for solving the dynamics to high accuracy along this edge. Each cell will then carry an identical (up to parity) configuration which can however have an arbitrarily random distribution. The dynamics of such models is compared to that of previous works on regularly distributed black holes as well as with the standard isotropic dust models of the FLRW type. The irregular models are shown to have richer dynamics than that of the regular models. The randomization of the distribution of the black holes is done both without bias and also with a certain clustering bias. The geometry of the initial configuration of our models is shown to be qualitatively different from the regular case in the way it approaches the isotropic model