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Gravitational collapse of a massless scalar field with the periodic boundarycondition in a cubic box is reported. This system can be regarded as a latticeuniverse model. We construct the initial data for a Gaussian like profile ofthe scalar field taking the integrability condition associated with theperiodic boundary condition into account. For a large initial amplitude, ablack hole is formed after a certain period of time. While the scalar fieldspreads out in the whole region for a small initial amplitude. It is shown thatthe expansion law in a late time approaches to that of the radiation dominateduniverse and the matter dominated universe for the small and large initialamplitude cases, respectively. For the large initial amplitude case, thehorizon is initially a past outer trapping horizon, whose area decreases withtime, and after a certain period of time, it turns to a future outer trappinghorizon with the increasing area.

Gravitational Collapse of a Massless Scalar Field in a Periodic Box