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

TL;DR

This paper formulates the Wheeler-DeWitt equation for late gravitational collapse, investigates the effects of factor ordering and a cosmological constant, and finds that quantum effects can avoid singularities and enable tunneling scenarios.

Contribution

It introduces a detailed analysis of the Wheeler-DeWitt equation in gravitational collapse, highlighting the impact of factor ordering and cosmological constant on quantum solutions.

Findings

Density quantization in terms of Planck density

Initial singularity avoidance in wave function solutions

Potential tunneling at the cosmological horizon

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 Schr\"odinger 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.