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We examine the global structure of scalar field critical collapse spacetimesusing a characteristic double-null code. It can integrate past the horizonwithout any coordinate problems, due to the careful choice of constraintequations used in the evolution. The limiting sequence of sub- andsupercritical spacetimes presents an apparent paradox in the expected Penrosediagrams, which we address in this paper. We argue that the limiting spacetimeconverges pointwise to a unique limit for all r>0, but not uniformly. The r=0line is different in the two limits. We interpret that the two differentPenrose diagrams differ by a discontinuous gauge transformation. We concludethat the limiting spacetime possesses a singular event, with a future removablenaked singularity.Comment: RevTeX 4; 6 pages, 7 figure

Naked singularity in the global structure of critical collapse spacetimes