We generalize the existing works on the way (generalized) Lemaître-Tolman-Bondi (LTB) models can be embedded into polymerized spherically symmetric models in several aspects. We reexamine such an embedding at the classical level and show that a suitable LTB condition can only be treated as a gauge fixing in the nonmarginally bound case, while in the marginally bound case, it must be considered as an additional first class constraint. A novel aspect of our formalism, based on the effective equations of motion, is to derive compatible dynamics LTB conditions for polymerized models by using holonomy and inverse triad corrections simultaneously, whereas in earlier work, these were only considered separately. Further, our formalism allows one to derive compatible LTB conditions for a vast of class of polymerized models available in the current literature. Within this broader class of polymerizations, there are effective models contained for which the classical LTB condition is a compatible one. Our results show that there exist a class of effective models for which the dynamics decouples completely along the radial direction. It turns out that this subsector is strongly linked to the property that in the temporally gauge fixed model, the algebra of the geometric contribution to the Hamiltonian constraint and the spatial diffeomorphism constraint is closed. We finally apply the formalism to existing models from the literature and compare our results to the existing ones.

中文翻译：

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将广义 Lemaître-Tolman-Bondi 模型嵌入到聚合球对称时空中


我们概括了现有工作，即（广义的）Lemaître-Tolman-Bondi （LTB） 模型可以从几个方面嵌入到聚合球对称模型中。我们在经典级别重新检查了这种嵌入，并表明合适的 LTB 条件只能在非边际束缚情况下被视为规范固定，而在边际束缚情况下，它必须被视为额外的一等约束。基于有效运动方程，我们形式主义的一个新颖方面是通过同时使用全息和逆三元校正来推导出聚合模型的兼容动力学 LTB 条件，而在早期的工作中，这些只是单独考虑的。此外，我们的形式主义允许人们为当前文献中可用的大量聚合模型推导出兼容的 LTB 条件。在这一更广泛的聚合类别中，包含一些有效的模型，这些模型与经典的 LTB 条件是兼容的。我们的结果表明，存在一类有效的模型，其动力学沿径向完全解耦。事实证明，这个子扇区与在时间规范固定模型中，对哈密顿约束和空间微分同构约束的几何贡献的代数是闭合的特性密切相关。最后，我们将形式主义应用于文献中的现有模型，并将我们的结果与现有模型进行比较。