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We study the apparent horizon for two boosted black holes in theasymptotically de Sitter space-time by solving the initial data on a space withpunctures. We show that the apparent horizon enclosing both black holes is notformed if the conserved mass of the system (Abbott-Deser mass) is larger than acritical mass. The black hole with too large AD mass therefore cannot be formedin the asymptotically de Sitter space-time even though each black hole has anyinward momentum. We also discuss the dynamical meaning of AD mass by examiningthe electric part of the Weyl tensor (the tidal force) for various initialdata.Comment: 15 pages, accepted for publication in PR

Two boosted black holes in asymptotically de Sitter space-time: Relation between mass and apparent horizon formation