MG13 - Talk detail

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We numerically construct an one-parameter family of initial data sets of an expanding inhomogeneous universe which is composed of regularly aligned black holes with an identical mass. They are initial data of vacuum solutions for the Einstein equations. We call this universe model the "black hole universe" and analyze the structure of these initial data sets by searching for the trapped surfaces. Giving definitions of an effective Hubble parameter and an effective energy density, we show that these quantities asymptotically satisfy the Hubble equation for the Einstein-de Sitter universe in the limit of a large separation between neighboring black holes, although the energy density is always larger than that estimated from the mass of the black hole only. The accuracy of the cosmological Newtonian approximation is also discussed.

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