Black Hole Universe: Time Evolution

TL;DR

This study numerically simulates the time evolution of a black hole lattice universe and finds that its expansion behavior closely resembles that of a homogeneous Einstein-deSitter universe, despite extreme inhomogeneities.

Contribution

The paper presents a numerical simulation of a black hole lattice universe, demonstrating that local inhomogeneities have minimal impact on the global expansion law.

Findings

Effective scale factors match Einstein-deSitter universe behavior

Local inhomogeneities do not significantly alter global expansion

Numerical solutions of Einstein equations in a black hole lattice context

Abstract

Time evolution of a black hole lattice universe is simulated. The vacuum Einstein equations in a cubic box with a black hole at the origin are numerically solved with periodic boundary conditions on all pairs of opposite faces. Defining effective scale factors by using the area of a surface and the length of an edge of the cubic box, we compare them with that in the Einstein-deSitter universe. It is found that the behaviour of the effective scale factors is well approximated by that in the Einstein-deSitter universe. Our result suggests that local inhomogeneities do not significantly affect the global expansion law of the universe even if the inhomogeneity is extremely nonlinear.