Quantum theory of gravitational collapse (lecture notes on quantum conchology)

These notes consist of three parts. The first one contains the review of previous work on a gauge-invariant Hamiltonian dynamics of generally covariant models. The method is based on the exclusive use of gauge-invariant variables, the so-called Dirac observables, and on privileged dynamical symmetries such as the asymptotic time translation. The second part applies the method to the model of spherically symmetric thin shell of light-like substance in its own gravitational field following a paper by C. Kiefer and myself. A natural set of Dirac observables is chosen and the Hamiltonian defined by the time translation symmetry is calculated. In the third part, my construction of a version of quantum mechanics for the model is reviewed. The quantum evolution is unitary in spite of the classical theory containing black and white holes and singularities. The wave packet describing the quantum shell contracts, bounces and reexpands. The state of the quantum horizon is a linear combination of the "white" and "black" (past and future) apparent horizons.