The singularity problem and phase-space noncanonical noncommutativity

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.

4 pages, revtex4

References in corpus (6)

• Weyl-Wigner Formulation of Noncommutative Quantum Mechanics
• Towards Quantum Noncommutative $\kappa$-deformed Field Theory
• Towards Noncommutative Quantum Black Holes
• Black Holes and Phase Space Noncommutativity
• Towards a Noncommutative Astrophysics
• Noncommutative Quantum Mechanics and Quantum Cosmology

Cited by in corpus (25)

• Aspects of Phase-Space Noncommutative Quantum Mechanics
• Phase-Space Noncommutativity and the Dirac Equation
• New bounds for Tsallis parameter in a noncommutative phase-space entropic gravity and nonextensive Friedmann equations
• Black Holes and Phase Space Noncommutativity
• Hořava-Lifshitz Quantum Cosmology
• Probing phase-space noncommutativity through quantum beating, missing information and the thermodynamic limit
• Noncommutative Graphene
• Entanglement due to noncommutativity in the phase-space
• Phase-space noncommutative formulation of Ozawa's uncertainty principle
• Non-Canonical Phase-Space Noncommutativity and the Kantowski-Sachs singularity for Black Holes
• Probing phase-space noncommutativity through quantum mechanics and thermodynamics of free particles and quantum rotors
• Violation of the Robertson-Schrödinger uncertainty principle and non-commutative quantum mechanics
• A Deformation Quantization Theory for Non-Commutative Quantum Mechanics
• Phase-space noncommutative extension of the Robertson-Schroedinger formulation of Ozawa's uncertainty principle
• Bell operator and Gaussian squeezed states in noncommutative quantum mechanics
• Modified entropies, their corresponding Newtonian forces, potentials, and temperatures
• Static and Dynamic Phases for Vortex Matter with Attractive Interactions
• Phase diagrams of vortex matter with multi-scale inter-vortex interactions in layered superconductors
• Non-commutative Quantum Mechanics in Three Dimensions and Rotational Symmetry
• Coherent quantum squeezing due to the phase space noncommutativity
• Noncommutative Black Holes and the Singularity Problem
• Collapsing Shells and Black Holes: a quantum analysis
• Uncertainty relations for a non-canonical phase-space noncommutative algebra
• A Phase-Space Noncommutative Picture of Nuclear Matter
• Emergent time crystals from phase-space noncommutative quantum mechanics