Spherical symmetric gravitational collapse of a dust cloud: Polymerized dynamics in reduced phase space
Spherical symmetric gravitational collapse of a dust cloud: Polymerized dynamics in reduced phase space
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DOI：
10.1103/physrevd.107.044047
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发表时间：
2022-12
影响因子：
5
通讯作者：
K. Giesel;Muxin Han;Bao-Fei Li;Hongguang Liu;Parampreet Singh
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文献类型：
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作者：
K. Giesel;Muxin Han;Bao-Fei Li;Hongguang Liu;Parampreet Singh
基于圈量子引力（LQG）约化相空间中球对称约化模型的$bar mu格式的有效动力学，研究了均匀尘埃云的引力坍缩，高斯尘埃既是参考场又是引力坍缩源.从所考虑的均匀尘埃云模型的有效动力学精确地减少到圈量子宇宙学（LQC）与外部曲率为基础的K-量子化的有效动力学，表明LQC有效动力学的生活作为一个子部门的模型在这里。在有效动力学中，在临界束缚和束缚两种情况下，奇点都被解决并被反弹所取代。虽然空间曲率的量子几何修正不直接包含在K量子化中，但它确实影响了坍缩尘埃云的定性动力学，一方面对于边缘约束的情况，尘埃云在固定的最大能量密度下反弹一次，另一方面对于约束的情况，尘埃云经历无限的收缩和膨胀循环，其能量密度取决于尘埃质量。最后，在每一种情况下的捕获面的形成的质量阈值被发现和内部塌陷时空和一个有效的外部静态解决方案之间的匹配条件进行了讨论。
Based on the effective dynamics in the $\bar \mu$ scheme of the spherical symmetry reduced model in the reduced phase space formulation of loop quantum gravity (LQG), we investigate the gravitational collapse of a homogeneous dust cloud, with Gaussian dust serving as both the reference field and the source of the gravitational collapse. The effective dynamics from the considered model for a homogeneous dust cloud reduces precisely to the effective dynamics of loop quantum cosmology (LQC) with extrinsic curvature based K-quantization, indicating that the LQC effective dynamics lives as a subsector of the model presented here. In both the marginally bound and the bound cases of the collapse in effective dynamics, the singularity is resolved and replaced by a bounce. Though quantum geometric modification from spatial curvature is not directly included in the K-quantization it does affect the qualitative dynamics of the collapsing dust cloud in the sense that on the one hand for the marginally bound case, the dust cloud bounces once at fixed maximum energy density and on the other hand for the bound case, the dust cloud undergoes infinite cycles of contraction and expansion at energy densities dependent on the dust mass. Finally, the mass threshold for the formation of a trapped surface in each case is found and the matching conditions between the interior collapsing spacetime and an effective exterior static solution are discussed.