Effective quantum extended spacetime of polymer Schwarzschild black hole
Effective quantum extended spacetime of polymer Schwarzschild black hole
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DOI：
10.1088/1361-6382/ab3f16
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发表时间：
2019-02
影响因子：
3.5
通讯作者：
N. Bodendorfer;Fabio M. Mele;Johannes Münch
中科院分区：
文献类型：
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作者：
N. Bodendorfer;Fabio M. Mele;Johannes Münch
超越经典广义相对论的理论中引力奇点的物理解释和最终命运是令人费解的问题，在各种量子引力方法中引起了极大的兴趣。圈量子引力（LQG）是广义相对论非微扰背景无关量子化的主要候选者之一，在它的背景下，人们投入了大量的精力来构建可以研究这些问题的有效模型。在这些模型中，经典奇点被量子几何校正引起的“反弹”所取代。然而，根据模型的细节，可能会出现不需要的特征。在本文中，我们重点关注史瓦西黑洞，并提出了一种新的有效量子理论，该理论基于新规范相空间变量的聚合，其灵感来自那些成功的环量子宇宙学。由有效动力学解产生的量子校正时空的特征是无限多对捕获和反捕获区域通过取代中心奇点的类空间过渡表面连接。量子效应在独特的质量独立曲率尺度上变得相关，而在地平线附近的低曲率区域中它们变得可以忽略不计。有效量子度量还描述了外部区域，并恢复了渐近经典史瓦西几何。然而，我们发现物理上可接受的解决方案要求我们选择初始条件的某个子集，对应于反弹后的特定质量（去）放大。我们还勾勒出相应的量子理论并显式计算哈密顿约束算子的内核。
The physical interpretation and eventual fate of gravitational singularities in a theory surpassing classical general relativity are puzzling questions that have generated a great deal of interest among various quantum gravity approaches. In the context of loop quantum gravity (LQG), one of the major candidates for a non-perturbative background-independent quantisation of general relativity, considerable effort has been devoted to construct effective models in which these questions can be studied. In these models, classical singularities are replaced by a ‘bounce’ induced by quantum geometry corrections. Undesirable features may arise however depending on the details of the model. In this paper, we focus on Schwarzschild black holes and propose a new effective quantum theory based on polymerisation of new canonical phase space variables inspired by those successful in loop quantum cosmology. The quantum corrected spacetime resulting from the solutions of the effective dynamics is characterised by infinitely many pairs of trapped and anti-trapped regions connected via a space-like transition surface replacing the central singularity. Quantum effects become relevant at a unique mass independent curvature scale, while they become negligible in the low curvature region near the horizon. The effective quantum metric describes also the exterior regions and asymptotically classical Schwarzschild geometry is recovered. We however find that physically acceptable solutions require us to select a certain subset of initial conditions, corresponding to a specific mass (de-)amplification after the bounce. We also sketch the corresponding quantum theory and explicitly compute the kernel of the Hamiltonian constraint operator.