Unitary dynamics of spherical null gravitating shells
  The dynamics of a thin spherically symmetric shell of zero-rest-mass matter in its own gravitational field is studied. A form of action principle is used that enables the reformulation of the dynamics as motion on a fixed background manifold. A self-adjoint extension of the Hamiltonian is obtained via the group quantization method. Operators of position and of direction of motion are constructed. The shell is shown to avoid the singularity, to bounce and to re-expand to that asymptotic region from which it contracted; the dynamics is, therefore, truly unitary. If a wave packet is sufficiently narrow and/or energetic then an essential part of it can be concentrated under its Schwarzschild radius near the bounce point but no black hole forms. The quantum Schwarzschild horizon is a linear combination of a black and white hole apparent horizons rather than an event horizon. 
P. Hajicek