We use factorisations of the local isometry groups arising in 3d gravity for Lorentzian and Euclidean signatures and any value of the cosmological constant to construct associated bicrossproduct quantum groups via semidualisation. In this way we obtain quantum doubles of the Lorentz and rotation groups in 3d, as well as kappa-Poincare algebras whose associated r-matrices have spacelike, timelike and lightlike deformation parameters. We confirm and elaborate the interpretation of semiduality proposed in [13] as the exchange of the cosmological length scale and the Planck mass in the context of 3d quantum gravity. In particular, semiduality gives a simple understanding of why the quantum double of the Lorentz group and the kappa-Poincare algebra with spacelike deformation parameter are both associated to 3d gravity with vanishing cosmological constant, while the kappa-Poincare algebra with a timelike deformation parameter can only be associated to 3d gravity if one takes the Planck mass to be imaginary.
Linearised gravity as edge modes & manifest duality and Lorentz covariance
Max Planck–IAS–NTU Center for Particle Physics, Cosmology and Geometry（国立台湾大学物理系暨理论物理中心；梁林宇宙学与粒子天体物理中心；马克斯·普朗克研究所-国际学术访问学者-台湾大学粒子物理、宇宙学与几何中心）；Leung Center for Cosmology and Particle Astrophysics（伦敦帝国理工学院阿卜杜斯·萨拉姆理论物理中心）；Department of Physics and Center for Theoretical Physics, National Taiwan University；Abdus Salam Centre for Theoretical Physics, Imperial College London
Spherically symmetric loop quantum gravity: analysis of improved dynamics
本文研究了Chiou { \em et al.}提出的圈量子引力中球对称时空的“改进动力学”。类似于Ashtekar，Pawlowski和Singh为均匀时空构建的模型。在这种动力学中，聚合参数是动力学变量的良好动机函数，反映了面积量子依赖于它们的事实。与均匀情况相反，其实施不会触发不期望的物理性质。我们在量子理论中识别了半经典物理态，并导出了相应的有效半经典度规。然后我们讨论了它们的一些性质。具体地说，时空在低曲率下足够快地接近史瓦西几何。此外，在经典理论中的奇异性区域被一个规则的但离散的有效几何所取代，该有效几何具有有限的普朗克阶曲率，而与黑洞的质量无关。这避免了在量子化方案中出现的天体物理学黑洞的反普朗克曲率，而没有改进。它使得奇点的分辨率更符合在模型中观察到的一个，该模型使用史瓦西黑洞内部的等距与Kantowski-Sachs圈量子宇宙学。人们可以观察到，在黑洞内部出现了对零能量条件的有效违反，这是奇点消除机制的一部分。
