Based on modifications inspired from loop quantum gravity (LQG), spherically symmetric models have recently been explored to understand the resolution of classical singularities and the fate of the spacetime beyond. While such phenomenological studies have provided useful insights, questions remain on whether such models exhibit some of the desired properties such as consistent LTB conditions, covariance, and compatibility with the improved dynamics of loop quantum cosmology in the cosmological and LTB sector. We provide a systematic procedure to construct effective spherically symmetric models encoding LQG modifications as a 1+1 field theory models encoding these properties following the analysis in our companion paper [K. Giesel et al., Embedding generalized LTB models in polymerized spherically symmetric spacetimes, Phys. Rev. D 110, 104017 (2024)]. As concrete examples of our generalized strategy, we obtain and compare with different phenomenological models, which have been investigated recently and demonstrate resolution of singularity by quantum geometry effects via a bounce. These include models with areal gauge fixing, a polymerized vacuum solution, polymerized junction conditions, and an Oppenheimer-Snyder dust collapse model. An important insight from our approach is that the dynamical equations care about the det⁡(𝑒) part rather than the square root of the determinant of the spatial metric. As a result, shock solutions that have been argued to exist in some models are found to be absent even if one considers coordinate transformations.

中文翻译：

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有效回路量子引力中尘埃坍缩的广义分析：激波和协方差的命运


基于受环量子引力 （LQG） 启发的修改，最近探索了球对称模型，以了解经典奇点的分辨率和更远时空的命运。虽然这些现象学研究提供了有用的见解，但关于这些模型是否表现出一些所需的特性仍然存在问题，例如一致的 LTB 条件、协方差以及与宇宙学和 LTB 领域中循环量子宇宙学改进的动力学的兼容性。我们提供了一个系统的程序来构建有效的球对称模型，将 LQG 修改编码为编码这些特性的 1+1 场论模型，遵循我们的姊妹论文 [K. Giesel et al.， Embedding generalized LTB models in polymerized spherically symmetric spacetimes， Phys. Rev. D110, 104017 (2024)].作为我们广义策略的具体示例，我们获得并比较了不同的现象学模型，这些模型最近进行了研究，并通过反弹证明了量子几何效应对奇点的解析。这些模型包括具有面规固定、聚合真空溶液、聚合结条件和 Oppenheimer-Snyder 尘埃坍缩模型的模型。从我们的方法中得出的一个重要见解是，动力学方程关心 det（e） 部分，而不是空间度量行列式的平方根。因此，即使考虑坐标变换，也发现某些模型中存在一直存在的冲击解是不存在的。