No-go result for covariance in models of loop quantum gravity
No-go result for covariance in models of loop quantum gravity
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DOI：
10.1103/physrevd.102.046006
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发表时间：
2020-07
影响因子：
5
通讯作者：
M. Bojowald
中科院分区：
文献类型：
--
作者：
M. Bojowald
基于Schwarzschild型解的外部时空允许两个对称切片，一个静态球对称切片和一个类时均匀切片的观察，量子宇宙学的简化模型所建议的引力动力学的修改可以用来导出相应的修改的球对称方程。一般来说，与均匀切片相比，协变理论在球对称性方面受到更多的限制，如果它们是局部的，则由$1+1$-维双光子模型给出。如图所示，在圈量子宇宙学中使用的修正并没有相应的协变球对称理论。因此，圈量子宇宙学的模型以切片独立的形式违反了一般协变性。在圈量子引力模型中，只有具有非黎曼几何的广义协方差形式才能一致地描述时空。
Based on the observation that the exterior space-times of Schwarzschild-type solutions allow two symmetric slicings, a static spherically symmetric one and a timelike homogeneous one, modifications of gravitational dynamics suggested by symmetry-reduced models of quantum cosmology can be used to derive corresponding modified spherically symmetric equations. Generally covariant theories are much more restricted in spherical symmetry compared with homogeneous slicings, given by $1+1$-dimensional dilaton models if they are local. As shown here, modifications used in loop quantum cosmology do not have a corresponding covariant spherically symmetric theory. Models of loop quantum cosmology therefore violate general covariance in the form of slicing independence. Only a generalized form of covariance with a non-Riemannian geometry could consistently describe space-time in models of loop quantum gravity.