Abstrakt
Canonical quantization of spacetimes leads to numerous problems some of which are already present on classical level and the others emerge from the used quantization process. We will present a quantization of spherically symmetric spacetimes with a massless scalar-field source and a brief examination of the constraint algebra which plays an important part in the problem of operator ordering.
On this type of spacetime will be then applied Dirac's method of canonical quantization, leading to Wheeler-DeWitt equations. We will attempt to solve these equations generally for above-mentioned spacetimes but so far with only partial success.
Additional demand of staticity of the spacetimes will help us find a solution to the Wheeler-DeWitt equations, at least for this restricted class of spacetimes. The solution, its nature and remaining problems will be then briefly examined.