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