# Minimal Length Effects on Quantum Cosmology and Quantum Black Hole Models

## TL;DR

This paper explores how a modified quantization inspired by the Generalized Uncertainty Principle affects quantum cosmology and black hole models, leading to new potential wells and discrete spectra in the Wheeler-DeWitt equation.

## Contribution

It introduces a modified quantization scheme based on GUP into a Kantowski-Sachs model, revealing new potential wells and discrete energy spectra.

## Key findings

- Presence of a potential well in the Wheeler-DeWitt equation
- Emergence of wave functions with discrete energy levels
- Deviation from standard quantum cosmology results

## Abstract

A Kantowski-Sachs model with a modified quantization prescription is considered. Such quantization rules, inspired by the so-called Generalized Uncertainty Principle (GUP), 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.