The singularity problem and phase-space noncanonical noncommutativity

TL;DR

This paper explores a noncanonical noncommutative extension of quantum cosmology for black holes, demonstrating that the wave function vanishes near the singularity, suggesting potential singularity resolution.

Contribution

It introduces a novel noncanonical noncommutative framework for the Wheeler-DeWitt equation in black hole models, analyzing its implications for singularity behavior.

Findings

Wave function is normalizable using asymptotic analysis.

Probability vanishes near the black hole singularity.

Noncommutative extension affects singularity structure.

Abstract

The Wheeler-DeWitt equation arising from a Kantowski-Sachs model is considered for a Schwarzschild black hole under the assumption that the scale factors and the associated momenta satisfy a noncanonical noncommutative extension of the Heisenberg-Weyl algebra. An integral of motion is used to factorize the wave function into an oscillatory part and a function of a configuration space variable. The latter is shown to be normalizable using asymptotic arguments. It is then shown that on the hypersufaces of constant value of the argument of the wave function's oscillatory piece, the probability vanishes in the vicinity of the black hole singularity.