Black hole universe: Construction and analysis of initial data

Abstract

We numerically construct an one-parameter family of initial data of an expanding inhomogeneous universe model which is composed of regularly aligned black holes with an identical mass. They are initial data for vacuum solutions of the Einstein equations. We call this universe model the "black hole universe" and analyze the structure of these initial data. We study the relation between the mean expansion rate of the 3-space, which corresponds to the Hubble parameter, and the mass density of black holes. The result implies that the same relation as that of the Einstein-de Sitter universe is realized in the limit of the large separation between neighboring black holes. The applicability of the cosmological Newtonian N -body simulation to the dark matter composed of black holes is also discussed. The deviation of the spatial metric of the cosmological Newtonian N -body system from that of the black hole universe is found to be smaller than about 1% in a region distant from the particles, if the separation length between neighboring particles is 20 times larger than their gravitational radius. By contrast, the deviation of the square of the Hubble parameter of the cosmological Newtonian N -body system from that of the black hole universe is about 20% for the same separation length.

Black hole universe with a cosmological constant

“…We note that, differently from the Λ = 0 case in Ref. [3], the hypersurface may pass through the white hole region for a sufficiently large value of Λ. In this subsection, we only show the cases in which the hypersurface is passing through the white hole region, that is, the case (a) or (b).…”

“…The subscript "+" means outgoing and "−" means ingoing null expansion. If the initial hypersurface is passing through a black hole region as in the case Λ = 0 [3], there are two black hole horizons(future outer trapping horizons in terms of Ref. [17]).…”

“…Initial data for a black hole inside a cubic box with a periodic boundary condition have been constructed and analyzed in Refs. [3,8], and those time evolutions have been investigated in Refs. [2,7].…”

“…The black hole lattice universe is often used as one of tools to evaluate effects of local non-linear inhomogeneities on the global expansion. Recently, black hole lattice universe models have been revisited by several authors [2][3][4][5][6][7][8][9][10][11][12]. Time symmetric initial data for N-black hole systems on a virtual 3-sphere have been analyzed in Refs.…”

Piecewise silence in discrete cosmological models

“…The optical properties of these models have been studied in [17][18][19]. More recently numerical solutions to Einstein's equations have been found for these configurations in both the hyperspherical case [20] and the flat case [21][22][23]. Even taking into account their simplified nature, these lattice models are still more realistic in many aspects than the FLRW models: Firstly, they are locally inhomogeneous in a realistic non-perturbative manner; secondly, the matter content is discrete, rather than a fluid; and thirdly, they are vacuum models, as is the real Universe at almost all points.…”