title: Black-hole universe: time evolution.
abstract: Time evolution of a black hole lattice toy model 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 faces opposite to each other. 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-de Sitter universe. It is found that the behavior of the effective scale factors is well approximated by that in the Einstein-de Sitter universe. In our model, if the box size is sufficiently larger than the horizon radius, local inhomogeneities do not significantly affect the global expansion law of the Universe even though the inhomogeneity is extremely nonlinear.
authors.affiliation: Gravity and Particle Cosmology Group, Division of Particle and Astrophysical Science, Graduate School of Science, Nagoya University, Nagoya 464-8602, Japan and Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan.
authors.forename: Chul-Moon
authors.initials: CM
authors.lastname: Yoo
authors.forename: Hirotada
authors.initials: H
authors.lastname: Okawa
authors.forename: Ken-ichi
authors.initials: K
authors.lastname: Nakao