In spherical symmetry, gravitational collapse of dust may give rise to the so-called shell-crossing singularities, beyond which spacetime can be extended using weak solutions to the integrated version of the equations of motion. We argue that the paradigm of weak solutions is ill suited for dynamical extension beyond shell crossings through shock waves, because it is based implicitly on the assumption that the Painlevé-Gullstrand time remains continuous across the shock, and leads to the unwanted prospect of shock waves of dust particles moving faster than light.

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• General relativity
• Quantum gravity