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The naked singularity in the global structure of critical collapse spacetimes

Andrei V. Frolov·Ue-Li Pen
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Abstract

We examine the global structure of scalar field critical collapse spacetimes using a characteristic double-null code. It can integrate past the horizon without any coordinate problems, due to the careful choice of constraint equations used in the evolution. The limiting sequence of sub- and supercritical spacetimes presents an apparent paradox in the expected Penrose diagrams, which we address in this paper. We argue that the limiting spacetime converges pointwise to a unique limit for all r>0, but not uniformly. The r=0 line is different in the two limits. We interpret that the two different Penrose diagrams differ by a discontinuous gauge transformation. We conclude that the limiting spacetime possesses a singular event, with a future removable naked singularity.

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Andrei V. Frolov, Ue-Li Pen. 2003-07-17. The naked singularity in the global structure of critical collapse spacetimes. https://doi.org/10.1103/physrevd.68.124024

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