Wheeler-DeWitt equation and the late gravitational collapse: effects of factor ordering and the tunneling scenario
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909308674899968 |
|---|---|
| author | Batic, Davide Nowakowski, Marek Kelkar, Neelima Govind |
| author_facet | Batic, Davide Nowakowski, Marek Kelkar, Neelima Govind |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_05077 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Wheeler-DeWitt equation and the late gravitational collapse: effects of factor ordering and the tunneling scenario Batic, Davide Nowakowski, Marek Kelkar, Neelima Govind General Relativity and Quantum Cosmology 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. |
| title | Wheeler-DeWitt equation and the late gravitational collapse: effects of factor ordering and the tunneling scenario |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2409.05077 |