Title: A generalized uncertainty-inspired quantum black hole Show Chinese title

Title: 广义不确定性启发的量子黑洞

Abstract: We derive the full spacetime metric of a generalized uncertainty-inspired quantum black hole. We examine a previous model of the interior in this approach and show that extending its metric to the full spacetime leads to serious issues in the asymptotic region. To remedy this, we introduce an ``improved scheme'' mimicking a similar prescription used in loop quantum gravity, where the quantum parameters are made momentum-dependent. Under this scheme, we rework the interior of the black hole and extend it to the full spacetime. We find that the resulting metric is asymptotically flat and its associated Kretschmann scalar is regular everywhere. We also show that the null expansion and Raychaudhuri equation are regular everywhere in this spacetime, implying that the classical singularity is resolved. Show Chinese abstract

Abstract: 我们推导了广义不确定性启发的量子黑洞的完整时空度规。 我们用这种方法检查了之前模型中的内部区域，并表明将其度规扩展到完整时空会在渐近区域引发严重问题。 为了解决这个问题，我们引入了一个“改进方案”，模仿了环圈量子引力中使用的类似方法，其中量子参数被设为动量相关的。 在这种方案下，我们重新构建了黑洞的内部区域并将其扩展到完整时空。 我们发现得到的度规是渐近平坦的，其相关的克雷斯曼标量在任何地方都是规则的。 我们还证明了在这个时空中，零膨胀和瑞奇豪尔方程在任何地方都是规则的，这意味着经典奇点已被解决。