Wheeler-DeWitt equation and the late gravitational collapse: effects of factor ordering and the tunneling scenario

Abstract

We set up the Wheeler-DeWitt (WDW) equation for late gravitational collapse. The fact that the gravitational collapse and the expanding/ collapsing universe can be described within the realm of the Robertson-Walker metric renders the corresponding WDW equation for collapsing matter a timeless Schrödinger equation. We explore the consequences of such an equation and find the density to be quantized in terms of the Planck density. Apart from that, the wave function as a solution of the WDW equation shows that the initial singularity is avoided. We concentrate on different factor orderings in the kinetic term of the equation and show how after splitting off an exponential ansatz, new polynomials entering the solution can be constructed. This enables us to conclude that the factor ordering changes the details of the solution and interpretation, but overall on a qualitative level the results remain the same. We also probe into the effects of a positive cosmological constant. It offers the possibility of a tunneling scenario at the cosmological horizon.

22 pages, 5 figures

References in corpus (20)

• Making Sense of Non-Hermitian Hamiltonians
• The lifetime problem of evaporating black holes: mutiny or resignation
• Quantum Radiation from Quantum Gravitational Collapse
• Mutiny at the white-hole district
• An introduction to quantum gravity
• Quantum Non-Gravity and Stellar Collapse
• Quantum time scales in alpha tunneling
• Quantum reflection and dwell times of metastable states
• The strange equation of quantum gravity
• Is the Wheeler -- DeWitt equation more fundamental than the Schrödinger equation?
• No Time for Time from No-Time
• Reassessing the problem of time of quantum gravity
• Can degenerate bound states occur in one dimensional quantum mechanics?
• Wheeler-DeWitt equation and the applicability of crypto-Hermitian interaction representation in quantum cosmology
• Wheeler-DeWitt equation beyond the cosmological horizon: Annihilation to nothing, infinity avoidance, and loss of quantum coherence
• Extracting the Maxwell charge from the Wheeler-DeWitt equation
• On the possibility of Dark Energy from corrections to the Wheeler-De Witt equation
• Gravitational Collapse via Wheeler-DeWitt Equation
• Inflation of small true vacuum bubble by quantization of Einstein-Hilbert action
• Wheeler-DeWitt equation rejects quantum effects of grown-up universes as a candidate for dark energy