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Given spherically symmetric characteristic initial data for theEinstein-scalar field system with a positive cosmological constant, we providea criterion, in terms of the dimensionless size and dimensionless renormalizedmass content of an annular region of the data, for the formation of a futuretrapped surface. This corresponds to an extension of Christodoulou's classicalcriterion by the inclusion of the cosmological term.

The formation of trapped surfaces in the gravitational collapse of spherically symmetric scalar fields with a positive cosmological constant