Wheeler–DeWitt equation and the late gravitational collapse: Effects of factor ordering and the tunneling scenario

IF 3 3区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY Annals of Physics Pub Date : 2024-08-30 DOI:10.1016/j.aop.2024.169773
Davide Batic , M. Nowakowski , N.G. Kelkar
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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.

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惠勒-德威特方程和后期引力坍缩:因子排序和隧道方案的影响
我们建立了晚期引力坍缩的惠勒-德威特(WDW)方程。事实上,引力坍缩和宇宙的膨胀/坍缩都可以在罗伯逊-沃克度量的范围内描述,这使得坍缩物质的相应 WDW 方程成为一个永恒的薛定谔方程。我们探讨了这一方程的后果,发现密度可以用普朗克密度来量化。除此之外,作为 WDW 方程解的波函数表明,初始奇点是可以避免的。我们专注于方程动能项中的不同因子排序,并展示了在拆分指数解析之后,如何构建进入解的新多项式。这使我们能够得出结论:因子排序改变了求解和解释的细节,但总体而言,定性结果保持不变。我们还探究了正宇宙常数的影响。它为宇宙学视界的隧道情景提供了可能性。
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来源期刊
Annals of Physics
Annals of Physics 物理-物理:综合
CiteScore
5.30
自引率
3.30%
发文量
211
审稿时长
47 days
期刊介绍: Annals of Physics presents original work in all areas of basic theoretic physics research. Ideas are developed and fully explored, and thorough treatment is given to first principles and ultimate applications. Annals of Physics emphasizes clarity and intelligibility in the articles it publishes, thus making them as accessible as possible. Readers familiar with recent developments in the field are provided with sufficient detail and background to follow the arguments and understand their significance. The Editors of the journal cover all fields of theoretical physics. Articles published in the journal are typically longer than 20 pages.
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