Compact Homogeneous Universes
摘要
A thorough classification of the topologies of compact homogeneous universes is given except for the hyperbolic spaces, and their global degrees of freedom are completely worked out. To obtain compact universes, spatial points are identified by discrete subgroups of the isometry group of the generalized Thurston geometries, which are related to the Bianchi and the Kantowski-Sachs-Nariai universes. Corresponding to this procedure their total degrees of freedom are shown to be categorised into those of the universal covering space and the Teichm\"uller parameters. The former are given by constructing homogeneous metrics on simply connected manifold. The Teichm\"uller spaces are also given by explicitly constructing expressions for the discrete subgroups of the isometry group.
引用
@article{arxiv.gr-qc/9405052,
title = {Compact Homogeneous Universes},
author = {Tatsuhiko Koike and Masayuki Tanimoto and Akio Hosoya},
journal= {arXiv preprint arXiv:gr-qc/9405052},
year = {2015}
}
备注
50 pages with 3 tables (assembly of 3 LaTeX files), TIT/HEP-208/COSMO-26