Dynamics of compact homogeneous universes

Journal of Mathematical Physics

Volumn 38, Issue 1, 1997, Pages 350-368

  Tanimoto, Masayuki ^a,c   Koike, Tatsuhiko ^b,c   Hosoya, Akio ^c  

^a KYOTO UNIVERSITY   (Japan)

^b KEIO UNIVERSITY   (Japan)

^c TOKYO INSTITUTE OF TECHNOLOGY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031282780     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.531853     Document Type: Article

References (28)

1. See, e.g., S. Weinberg, Gravitation and Cosmology (Wiley, New York, 1972).
2. L. D. Landau and E. M. Lifshitz, Classical Theory of Fields (MIT, Reading, 1971).
3. M. P. Ryan and L. C. Shepley, Homogeneous Relativistic Cosmologies. Princeton Series in Physics (Princeton U. P., Princeton, 1975).
4. R. M. Wald, General Relativity (University of Chicago, Chicago, 1984).
5. V. A. Belinski, I. M. Khalatnikov, and E. M. Lifshitz, Adv. Phys. 19, 525 (1970).
6. See, e.g., J. J. Halliwell, in Quantum cosmology and baby universes, edited by S. Coleman, J. B. Hartle, T. Piram, and S. Weinberg (World Scientific, Singapore, 1991), pp. 159-243 and references therein.
7. A. Hosoya and K. Nakao, Class. Quant. Gravit. 7, 163 (1990). For recent status of (2+1 -gravity and more references, see, e.g., S. Carlip, "Lectures on (2+1)-Dimensional Gravity," gr-qc/9503024, (1995).
8. A. Hosoya and K. Nakao, Class. Quant. Gravit. 7, 163 (1990). For recent status of (2+1 -gravity and more references, see, e.g., S. Carlip, "Lectures on (2+1)-Dimensional Gravity," gr-qc/9503024, (1995).
9. T. Koike, M. Tanimoto, and A. Hosoya, J. Math. Phys. 35, 4855 (1994).
10. W. P. Thurston, The Geometry and Topology of 3-manifolds (to be published by Princeton University Press).
11. P. Scott, Bull. London Math. Soc. 15, 401 (1983).
12. For type d (which correspond to Bianchi VIII), the representative metric (or standard metric, see Sec. II B) is incorrect, due to incorrectness of the appendix. For detail, see the erratum, which will appear in the journal.
13. I. M. Singer and J. A. Thorpe, Lecture Notes on Elementary Topology and Geometry (Scott, Foresman and Co., Glenview, 1967).
14. L. Bianchi, Mem. Soc. Ital. Sci. Ser. 3a, 11, 267 (1897).
15. H. Nariai, Sci. Rep. Tohoku Univ., I, 34, 160 (1950); 35, 62 (1951).
16. H. Nariai, Sci. Rep. Tohoku Univ., I, 34, 160 (1950); 35, 62 (1951).
17. R. Kantowski and R. K. Sachs, J. Math. Phys. 7, 443 (1967).
18. H. V. Fagundes, Phys. Rev. Lett. 54, 1200 (1985).
19. J. A. Wolf, Spaces of constant curvature, 5th ed. (Publish or Perish, Wilmington, 1984).
20. K. Ohshika, Topol. Appl. 27, 75 (1987).
21. R. Kulkami, K. B. Lee, and F. Raymond, Geometry and Topology, Lect. Notes Math. 1167, 180 (1985).
22. Here, Eq. (9) is understood. The extrinsic curvature therefore has the same homogeneity as the spatial metric.
23. For simplicity, we identify the set U with a set of representatives. Similar identifications are understood also for the sets of equivalence classes defined subsequently.
24. G. F. R. Ellis and M. A. H. MacCallum, Commun. Math. Phys. 12, 108 (1969).
25. A. Ashtekar and J. Samuel, Class. Quant. Gravit. 8, 2191 (1991).
26. See, e.g., D. Kramer, H. Stephani, M. MacCallum, and E. Herlt, Exact Solutions of Einstein's Field Equations (Cambridge U. P., Cambridge, 1980).
27. 33 as a function of other Teichmüller parameters and the three-volume.
28. P. T. Chruściel and A. D. Rendall, Ann. Phys. 242, 349 (1995).