A complete set of Riemann invariants

General Relativity and Gravitation

Volumn 29, Issue 5, 1997, Pages 539-581

  Zakhary, E ^a   McIntosh, C B G ^a  

^a MONASH UNIVERSITY   (Australia)

Author keywords

Curvature invariants; Petrov types

Indexed keywords

EID: 0031286870     PISSN: 00017701     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1018851201784     Document Type: Article

References (40)

1. Buchdahl, H. A. (1966). J. Aust. Math. Soc. 6, 402.
2. Buchdahl, H. A. (1966). J. Aust. Math. Soc. 6, 424.
3. Cahen, M., Debever, R., and Defrise, L. (1967). J. Math. Mech. 16, 761.
4. Campbell, J. S., and Wainwright, J. (1977). Gen. Rel. Grav. 8, 987.
5. Carminati, J. and McLenaghan, R. G. (1991). J. Math. Phys. 32, 3135.
6. Dautcourt, G., Jann, K.-P., Riemer, E., and Riemer M. (1981). Astron. Nach. 302, 1.
7. Ehlers, J., and Kundt, W. (1962). In Gravitation: An Introduction to Current Research, L. Witten, ed. (Wiley, New York).
8. Ellis, G. F. R., and Schmidt, B. G. (1979). Gen. Rel. Grav. 10, 989.
9. Gautreau, R. and Anderson, J. L. (1967). Phys. Lett. A25, 291.
10. Géhéniau, J., and Debever, R. (1956). Helv. Phys. Acta Suppl. 4, 101.
11. Géhéniau, J., and Debever, R. (1956). Bull. Acad. R. Belg. Cl. Sci. 42, 114.
12. Géhéniau, J. (1956). Bull. Acad. R. Belg. Cl. Sci. 42, 525.
13. Greenberg, P. J., Stud. Appl. Math. 51 (1972) 277.
14. Gurevich, G. B. (1964). Foundations of the Theory of Algebraic Invariants (P. Noordhoff Ltd., Groningen).
15. Haddow, B. M. (1996). Gen. Rel. Grav. 28, 481.
16. Harvey, A. (1990). Class. Quantum Grav. 7, 715.
17. Haskins, C. N. (1902). Trans. Amer. Math. Soc. 3, 71.
18. Israel, W. (1967). Phys. Rev. 164, 1776.
19. Joly, G. C., and MacCallum, M. A. H. (1990). Class. Quantum Grav. 7, 541.
20. Karlhede, A. (1980). Gen. Rel. Grav. 12, 693.
21. Kramer, D., Stephani, H., MacCallum, M. A. H., and Herlt, E. (1980). Exact Solutions of Einstein's Field Equations (Cambridge University Press, Cambridge).
22. Lake, K. (1993). J. Math. Phys. 34, 5900.
23. Letniowski, F. W., and McLenaghan, R. G. (1988). Gen. Rel. Grav. 20, 463.
24. McIntosh, C. B. G., and Hickman, M. S. (1985). Gen. Rel. Grav. 17, 111.
25. McIntosh, C. B. G., and Zakhary, E. (1994). In Relativity Today. Proc. Fourth Hungarian Workshop, R. P. Kerr and Z. Perjés, eds. (Akadémiai Kiadó, Budapest), p. 3-12.
26. Narlikar, V. V., and Karmarkar, K. R. (1948). Proc. Ind. Acad. Sci. A29, 91.
27. Newman, E. T., and Penrose, R. (1962). J. Math. Phys. 3, 156.
28. Penrose, R. (1960). Ann. Phys. (NY) 10, 171.
29. Penrose, R., and Rindler, W. (1990). Spinors and Space-time (Cambridge University Press, Cambridge), vol. 2.
30. Petrov, A. Z. (1955). Dokl. Akad. Nauk SSSR 105, 905.
31. Petrov, A. Z. (1969). Einstein Spaces (Pergamon, Oxford).
32. Schmidt, H.-J. (1996). In New frontiers in Gravitation, G. Sardanashvily, ed. (Hadronic Press Harbor), p. 337.
33. Sneddon, G. E. (1986). Class. Quantum Grav. 3, 1031.
34. Sneddon, G. E. (1996). J. Math. Phys. 37, 1059.
35. Sobczyk, G. (1981). J. Math. Phys. 22, 333.
36. Stehney, A. (1976). J. Math. Phys. 17, 1793.
37. Thorpe, J. A. (1969). J. Math. Phys. 10, 1.
38. Witten, L. (1959). Phys. Rev. 113, 357.
39. Zakhary, E., and McIntosh, C. B. G. (1994). "Classification of the Riemann Tensor: (I) Classification of the Weyl Tensor." Preprint.
40. Zakhary, E., and McIntosh, C. B. G. (1994). "Classification of the Riemann Tensor: (II) Classification of the Trace-Free Ricci Tensor." Preprint.