论文标题
黑洞内部和奇异性正则化的对称性
Symmetries of the Black Hole Interior and Singularity Regularization
论文作者
论文摘要
我们揭示了$ \ mathfrak {iso}（2,1）$poincaré代数，该代数与黑洞内部动态有关。这些Noether电荷的作用集成到庞加莱集团ISO $（2,1）$下的引力系统的对称性，该$ $（2,1）$，可以描述黑洞内部几何形状的演变，该几何形状在地球孔和ADS $ {} _ 2 $的地球孔和肉眼方面。在拉格朗日层面，这种对称性对应于适当时间的莫比乌斯转换以及翻译。值得注意的是，这是一种物理对称性，改变了系统的状态，它也自然地形成了更大的$ \ textrm {bms} _ {3} = \ textrm {diff}（s^1）\ ltimes \ textrm \ textrm {vect}（vect}（s^1）$组，其中$ s^1 $ s compactified时间量表。发现黑洞内部的这种结构很有趣，这暗示了BMS对称性对黑洞物理学的基本作用。这种对称的存在提供了一个有力的标准，可以区分不同的正则化和量化方案。遵循循环量子宇宙学，我们确定了黑洞内部的一组正规化变量和哈密顿量，该变量可以解决黑白洞过渡中的奇异性，同时保留相位空间上的庞加莱对称性。这揭开了黑洞对称性的新方面，并为严格的内部量化打开了道路。
We reveal an $\mathfrak{iso}(2,1)$ Poincaré algebra of conserved charges associated with the dynamics of the interior of black holes. The action of these Noether charges integrates to a symmetry of the gravitational system under the Poincaré group ISO$(2,1)$, which allows to describe the evolution of the geometry inside the black hole in terms of geodesics and horocycles of AdS${}_2$. At the Lagrangian level, this symmetry corresponds to Möbius transformations of the proper time together with translations. Remarkably, this is a physical symmetry changing the state of the system, which also naturally forms a subgroup of the much larger $\textrm{BMS}_{3}=\textrm{Diff}(S^1)\ltimes\textrm{Vect}(S^1)$ group, where $S^1$ is the compactified time axis. It is intriguing to discover this structure for the black hole interior, and this hints at a fundamental role of BMS symmetry for black hole physics. The existence of this symmetry provides a powerful criterion to discriminate between different regularization and quantization schemes. Following loop quantum cosmology, we identify a regularized set of variables and Hamiltonian for the black hole interior, which allows to resolve the singularity in a black-to-white hole transition while preserving the Poincaré symmetry on phase space. This unravels new aspects of symmetry for black holes, and opens the way towards a rigorous group quantization of the interior.
