In the past years, black holes and the fate of their singularity have been heavily studied within loop quantum gravity. Effective spacetime descriptions incorporating quantum geometry corrections are provided by the so-called polymer models. Despite the technical differences, the main common feature shared by these models is that the classical singularity is resolved by a black-to-white hole transition. In a recent paper (Bodendorfer etal 2019 Class. Quantum Grav. 36 195015), we discussed the existence of two Dirac observables in the effective quantum theory respectively corresponding to the black and white hole mass. Physical requirements about the onset of quantum effects then fix the relation between these observables after the bounce, which in turn corresponds to a restriction on the admissible initial conditions for the model. In the present paper, we discuss in detail the role of such observables in black hole polymer models. First, we revisit previous models and analyse the existence of the Dirac observables there. Observables for the horizons or the masses are explicitly constructed. In the classical theory, only one Dirac observable has physical relevance. In the quantum theory, we find a relation between the existence of two physically relevant observables and the scaling behaviour of the polymerisation scales under fiducial cell rescaling. We present then a new model based on polymerisation of new variables which allows to overcome previous restrictions on initial conditions. Quantum effects cause a bound of a unique Kretschmann curvature scale, independently of the relation between the two masses.

在过去的几年里，黑洞及其奇点的命运在圈量子引力中得到了大量研究。所谓的聚合物模型提供了包含量子几何校正的有效时空描述。尽管存在技术差异，但这些模型共有的主要共同特征是经典奇点由黑到白的空穴过渡解决。在最近的一篇论文中 (Bodendorfer et al 2019 Class. Quantum Grav. 36195015），我们讨论了有效量子理论中两个狄拉克可观测量的存在，分别对应于黑洞和白洞质量。然后，关于量子效应开始的物理要求固定了反弹后这些可观察量之间的关系，这反过来又对应于对模型可容许初始条件的限制。在本论文中，我们详细讨论了此类可观测值在黑洞聚合物模型中的作用。首先，我们重新审视以前的模型并分析那里的狄拉克观测值的存在。视界或质量的可观察量是明确构建的。在经典理论中，只有一个狄拉克可观测值具有物理相关性。在量子理论中，我们发现了两个物理相关的可观察量的存在与基准单元重新缩放下聚合尺度的缩放行为之间的关系。然后，我们提出了一个基于新变量聚合的新模型，该模型可以克服先前对初始条件的限制。量子效应导致一个独特的 Kretschmann 曲率尺度的界限，与两个质量之间的关系无关。