Quantization of the Schwarzschild geometry

摘要: The conditional symmetries of the reduced Einstein-Hilbert action emerging from a static, spherically symmetric geometry are used as supplementary conditions on wave function. Based their integrability conditions, only one three existing can be consistently imposed, while unique Casimir invariant, being product remaining two symmetries, is calculated possible second condition This quadratic integral motion identified with reparametrization generator, an implication uniqueness dynamical evolution, by fixing suitable parametrization r-lapse In this parametrization, determinant supermetric plays role mesure. combined Wheeler – DeWitt and linear symmetry equations analytically solved. solutions obtained depend "scale factors".