Minimal length effects on quantum cosmology and quantum black hole models

A Kantowski–Sachs model with a modified quantization prescription is considered. Such quantization rules, inspired by the so-called generalized uncertainty principle, correspond to a modified commutation relation between minisuperspace variables and their conjugate momenta. For a wide range of the modification parameter, this approach differentiates from the standard results by the presence of a potential well in the corresponding Wheeler–DeWitt equation. This then produces the appearance of a set of wave functions, with corresponding discrete energy spectrum.