Spherically symmetric loop quantum gravity: analysis of improved dynamics
Spherically symmetric loop quantum gravity: analysis of improved dynamics
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DOI：
10.1088/1361-6382/aba842
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发表时间：
2020-06
影响因子：
3.5
通讯作者：
R. Gambini;J. Olmedo;J. Pullin
中科院分区：
文献类型：
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作者：
R. Gambini;J. Olmedo;J. Pullin
我们研究了 Chiou 等人引入的圈量子引力中处理球对称时空的“改进动力学”，与 Ashtekar、Pawlowski 和 Singh 为均匀时空构建的动力学类似。在这种动力学中，聚合参数是动力学变量的良好驱动函数，反映了面积量子取决于它们的事实。与同质情况相反，其实施不会触发不良的物理特性。我们识别量子理论中的半经典物理状态并推导相应的有效半经典度量。然后我们讨论它们的一些属性。具体而言，时空在低曲率下足够快地接近史瓦西几何。此外，无论黑洞的质量如何，经典理论中奇点所在的区域都会被具有有限和普朗克阶曲率的规则但离散的有效几何结构所取代。这规避了量化方案中天体物理黑洞出现的跨普朗克曲率，而没有改进。它使奇点的分辨率更符合使用史瓦西黑洞内部等距和康托夫斯基-萨克斯环量子宇宙学的模型中观察到的分辨率。人们可以观察到黑洞内部零能量条件的有效违反的出现，作为消除奇点机制的一部分。
We study the ‘improved dynamics’ for the treatment of spherically symmetric space-times in loop quantum gravity introduced by Chiou et al in analogy with the one that has been constructed by Ashtekar, Pawlowski and Singh for the homogeneous space-times. In this dynamics the polymerization parameter is a well motivated function of the dynamical variables, reflecting the fact that the quantum of area depends on them. Contrary to the homogeneous case, its implementation does not trigger undesirable physical properties. We identify semiclassical physical states in the quantum theory and derive the corresponding effective semiclassical metrics. We then discuss some of their properties. Concretely, the space-time approaches sufficiently fast the Schwarzschild geometry at low curvatures. Besides, regions where the singularity is in the classical theory get replaced by a regular but discrete effective geometry with finite and Planck order curvature, regardless of the mass of the black hole. This circumvents trans-Planckian curvatures that appeared for astrophysical black holes in the quantization scheme without the improvement. It makes the resolution of the singularity more in line with the one observed in models that use the isometry of the interior of a Schwarzschild black hole with the Kantowski–Sachs loop quantum cosmologies. One can observe the emergence of effective violations of the null energy condition in the interior of the black hole as part of the mechanism of the elimination of the singularity.