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 conside red. To clarify the relation between classical and quantum spacetime w hich the shell collapse forms, we consider various time slicings on wh ich quantum mechanics is developed. By considering the static time sli cing which corresponds to an observer at a constant circumference radi us, we obtain the wave functions of the shell motion and the discrete mass spectra which specify the global structures of spherically symmet ric spacetime formed by the shell collapse. It is found that wormhole states are forbidden when the rest mass is comparable to the Planck ma ss scale due to the zero-point quantum fluctuations.