标题： 哈密顿表述和最近扩展的克鲁斯卡尔时空的环量化 显示英文标题

标题： Hamiltonian formulation and loop quantization of a recent extension of the Kruskal spacetime

摘要： 我们研究了Ashtekar-Olmedo-Singh模型的哈密顿形式，用于描述非旋转、不带电黑洞的内部几何结构。 该模型通过引入两个正则化参数来包含环量子效应。 我们考虑了该模型创建者提出的扩展相空间形式，其中包含这些参数作为配置变量，并被限制为黑洞质量的函数。 我们对该限制进行了推广，允许非壳上相空间依赖性。 然后我们引入一个规范固定程序并简化系统，证明了约化辛结构无法在密度三重矢量和Ashtekar-Barbero连接的范围内再现标准相对论结构。 实际上，约化结构精确补偿了当正则化参数被视为相空间函数而非数值时在哈密顿方程中出现的修改，从而实现了动力学的一致哈密顿推导。 随后，我们选择扩展相空间形式作为起点，以处理该模型的环量子化。 以某些几何算子的定义作为唯一基本要素，并采用在环量子宇宙学中已被证明成功的规定，我们构建了所有约束的聚合物表示，并假设约束算子具有合理的谱性质，推导出物理态的形式表达式。 物理态被证明由黑洞质量的波函数表征，其支持在一个非常特定的集合上。 最后，我们讨论了保证大黑洞质量区域存在物理态的条件。 这是开发新的黑洞环量子理论的第一步。 显示英文摘要

摘要： We study the Hamiltonian formulation of the Ashtekar-Olmedo-Singh model for the description of the interior geometry of non-rotating, uncharged black holes. This model incorporates loop quantum effects through the introduction of two regularization parameters. We consider an extended phase space formalism proposed by the creators of the model that includes such parameters as configuration variables, constrained to be functions of the black hole mass. We generalize this restriction, allowing for an off-shell phase space dependence. We then introduce a gauge fixing procedure and reduce the system, proving that the reduced symplectic structure cannot reproduce the standard relativistic one in terms of the densitized triad and the Ashtekar-Barbero connection. Actually, the reduced structure precisely compensates the modifications that arise in the Hamilton equations when the regularization parameters are treated as phase space functions, rather than as numbers, attaining a consistent Hamiltonian derivation of the dynamics. We then choose the extended phase space formalism as starting point to address the loop quantization of the model. Taking the definition of certain geometric operators as the only basic ingredient and adopting prescriptions that have proven successful in loop quantum cosmology, we construct a polymer representation of all the constraints and deduce the formal expression of the physical states, assuming reasonable spectral properties for the constraint operators. The physical states turn out to be characterized by a wave function of the black hole mass with support on a very specific set. We finally discuss conditions that guarantee the existence of physical states in the region of large black hole masses. This is a first step in the development of a new loop quantum theory of black holes.