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

A quantum-mechanical model of a self-gravitating dust shell is considered. To clarify the relation between classical and quantum spacetime which the shell collapse forms, we consider various time slicings on which quantum mechanics is developed. By considering the static time slicing which corresponds to an observer at a constant circumference radius, we obtain the wave functions of the shell motion and the discrete mass spectra which specify the global structures of spherically symmetric spacetime formed by the shell collapse. It is found that wormhole states are forbidden when the rest mass is comparable to the Planck mass scale due to the zero-point quantum fluctuations.