论文标题
弹跳紧凑的对象。第二部分:脉动普朗克恒星的有效理论
Bouncing compact objects. Part II: Effective theory of a pulsating Planck star
论文作者
论文摘要
本文介绍了精确的Oppenheimer-Snyder(OS)崩溃的有效量子扩展,其中使用空间闭合环量子宇宙学的有效动力学对奇异性分辨率进行了建模。施加最小的连接条件,即以色列 - 达拉姆岛的条件,我们将这种弹跳的LQC几何形状粘在经典的真空外部Schwarzschild几何形状上,跨过时间样的薄壳。结构的一致性导致与经典OS塌陷模型的几个重大偏差。首先,没有被困的区域可以形成,弹跳始终发生在上方,或最多在Schwarzschild Radius。其次,此处讨论的弹跳恒星承认IR截止值,此外还与紫外线切断相对应,因此对应于脉动紧凑型物体。第三,量子重力效应变得不可忽略的规模是在量子理论的紫外线截止与IR截止的比例中编码的,而IR截止的比例又代表了恒星倒塌之前的恒星的最小能量密度$ρ_{\ text {min}} $。这种能量密度不再像经典的OS模型那样由质量和最大半径固定,但现在是模型的自由参数。最后,尽管本模型无法描述普朗克星模型最初建议的黑白孔反弹,但它提供了基于LQC技术的脉动紧凑型物体的具体实现。该模型的一致性表明,其适用性限制在Planckian文物中,而宏观恒星对象则被排除在外。第一个最小的结构应作为进一步研究的平台,以探索在环量子宇宙学框架内弹跳紧凑物体的物理。
This article presents an effective quantum extension of the seminal Oppenheimer-Snyder (OS) collapse in which the singularity resolution is modeled using the effective dynamics of the spatially closed loop quantum cosmology. Imposing the minimal junction conditions, namely the Israel-Darmois conditions, we glue this bouncing LQC geometry to the classical vacuum exterior Schwarzschild geometry across a time-like thin-shell. Consistency of the construction leads to several major deviations from the classical OS collapse model. Firstly, no trapped region can form and the bounce occurs always above, or at most at the Schwarzschild radius. Secondly, the bouncing star discussed here admits an IR cut-off, additionally to the UV cut-off and corresponds therefore to a pulsating compact object. Thirdly, the scale at which quantum gravity effects become non-negligible is encoded in the ratio between the UV cut-off of the quantum theory and the IR cut-off, which in turn, encodes the minimal energy density $ρ_{\text{min}}$ of the star prior to collapse. This energy density is no more fixed by the mass and maximal radius as in the classical OS model, but is now a free parameter of the model. In the end, while the present model cannot describe a black-to-white hole bounce as initially suggested by the Planck star model, it provides a concrete realization of a pulsating compact object based on LQC techniques. Consistency of the model shows that its regime of applicability is restricted to Planckian relics while macroscopic stellar objects are excluded. This first minimal construction should serve as a platform for further investigations in order to explore the physics of bouncing compact objects within the framework of loop quantum cosmology.