发表机构
University of the Basque Country; Centro Brasileiro de Pesquisas Físicas（巴斯克大学; 巴西物理研究中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过径向叶状结构正则量子化Schwarzschild几何，构造关系可观测量与智能态，发现视界移动、加速度和表面引力增强，并得到对数熵修正及可能的稳定残余态。
AI 中文摘要
我们考虑在极小超空间描述中对Schwarzschild几何进行正则量子化，该描述基于以径向变量标记的叶状结构。此表述在Killing视界处保持正则。由此，所得量子理论允许一个物理希尔伯特空间，其中的态满足径向约束方程，并同时描述黑洞的外部与内部区域。我们讨论了量子关系可观测量的构造，这些可观测量作为物理希尔伯特空间上的规范不变对称算子。为了分析几何上的量子效应，我们构造了一族半经典智能态，这些态对黑洞质量和渐近Killing范数同时饱和Robertson-Schrödinger不确定关系，同时展现出较小的相对涨落。这些态中关系可观测量的期望值具有清晰的几何解释，并导致一个有效的、量子修正的时空。特别地，我们发现视界的位置可能发生移动，取决于态的相关性。此外，静态观测者的固有加速度和视界表面引力均相对于具有相同视界面积的经典Schwarzschild黑洞有所增强。利用表面引力与温度的关系，我们随后获得黑洞热力学性质的修正，导致对数修正的Bekenstein-Hawking熵。最后，我们讨论了一个最小能量态的定义，该态可被解释为具有有限视界半径的稳定残余，暗示了防止黑洞完全蒸发的可能机制。
英文摘要
We consider the canonical quantization of the Schwarzschild geometry in a minisuperspace description based on a foliation with leaves labeled by the radial variable. This formulation remains regular across the Killing horizon. In this way, the resulting quantum theory admits a physical Hilbert space of states that solve the radial constraint equation and simultaneously describe the exterior and interior regions of the black hole. We discuss the construction of quantum relational observables, which act as gauge-invariant symmetric operators on the physical Hilbert space. In order to analyze quantum effects on the geometry, we construct a family of semiclassical intelligent states that saturate the Robertson-Schrödinger uncertainty relation for both the black-hole mass and the asymptotic Killing norm, while exhibiting small relative fluctuations. The expectation values of relational observables in these states admit a clear geometric interpretation, and they lead to an effective, quantum-corrected spacetime. In particular, we find that the position of the horizon may be shifted, depending on the correlation of the state. In addition, both the proper acceleration of a static observer and the horizon surface gravity are enhanced with respect to a classical Schwarzschild black hole with the same horizon area. Using the relation between surface gravity and temperature, we then obtain corrections to the thermodynamic properties of the black hole, leading to a logarithmically corrected Bekenstein-Hawking entropy. Finally, we discuss the definition of a state of minimal energy that could be interpreted as a stable remnant characterized by a finite horizon radius, suggesting a possible mechanism for preventing the complete evaporation of the black hole.
