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Quantum-mechanical model of self-gravitating dust shell is considered. Toclarify the relation between classical and quantum spacetime which the shellcollapse form, we consider various time slicing on which quantum mechanics isdeveloped. By considering the static time slicing which corresponds to anobserver at a constant circumference radius, we obtain the wave functions ofthe shell motion and the discrete mass spectra which specify the globalstructures of spherically symmetric spacetime formed by the shell collapse. Itis found that wormhole states are forbidden when the rest mass is comparablewith Plank mass scale due to the zero-point quantum fluctuations.Comment: 10 pages in twocolumn, 8 figures, RevTeX 3.

Quantum formation of black holes and wormholes in the gravitational collapse of a dust shell