Resolution of strong singularities and geodesic completeness in loop quantum Bianchi-II spacetimes
Resolution of strong singularities and geodesic completeness in loop quantum Bianchi-II spacetimes
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DOI：
10.1088/1361-6382/aa91f6
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发表时间：
2017-07
影响因子：
3.5
通讯作者：
Sahil Saini;Parampreet Singh
中科院分区：
文献类型：
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作者：
Sahil Saini;Parampreet Singh
研究了含有任意最小耦合物质的Bianchi-II时空圈量子化中奇异性和测地完备性的通有解决。使用有效的哈密顿方法，我们研究了两个可用的量子化：一个是基于连接算子，第二个是通过规范固定将外部曲率作为连接。结果表明，对于基于连接的量子化，无论是逆三元组修改或施加弱能量条件是必要的，以获得所有强奇异性和测地完备性的解决方案。相比之下，基于非本征曲率的量子化一般解决了所有强曲率奇异性，并产生测地线完整的有效时空，无需逆三重态修改或能量条件。在这两种量子化中，由于压力及其导数在有限密度下的发散，会出现弱曲率奇异性。这些都是无害的事件，测地线可以扩展到这些事件之外。我们的工作推广了以前的结果上的通用决议的强奇异性的环量子化的各向同性，Bianchi-I和Kantowski-Sachs时空。
Generic resolution of singularities and geodesic completeness in the loop quantization of Bianchi-II spacetimes with arbitrary minimally coupled matter is investigated. Using the effective Hamiltonian approach, we examine two available quantizations: one based on the connection operator and second by treating extrinsic curvature as connection via gauge fixing. It turns out that for the connection based quantization, either the inverse triad modifications or imposition of weak energy condition is necessary to obtain a resolution of all strong singularities and geodesic completeness. In contrast, the extrinsic curvature based quantization generically resolves all strong curvature singularities and results in a geodesically complete effective spacetime without inverse triad modifications or energy conditions. In both the quantizations, weak curvature singularities can occur resulting from divergences in pressure and its derivatives at finite densities. These are harmless events beyond which geodesics can be extended. Our work generalizes previous results on the generic resolution of strong singularities in the loop quantization of isotropic, Bianchi-I and Kantowski–Sachs spacetimes.