  Everybody knows what the classical black holes are. In short, this is a
spacetime region beyond the so-called event horizon. The notion of the event
horizon is mathematically well defined. The situation with a definition of
quantum black hole is not so clear. The problem is that the classical event
horizon can be defined only globally, i.e. in order to be sure we have a black
hole we would need an infinite time interval. But, in classical physics we have
trajectories off all the particles and equations of motion for all the fields
and can, in principle, construct some ideal models for the gravitational
collapse and study the black hole formation under different conditions.
