On the problem of algebraic completeness for the invariants of the Riemann tensor: I

Journal of Mathematical Physics

Volumn 42, Issue 3, 2001, Pages 1474-1485

  Zakhary, E ^a   Carminati, J ^a  

^a DEAKIN UNIVERSITY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035530276     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1348027     Document Type: Article

References (23)

1. J. Ehlers and W. Kundt, "Exact solutions of the gravitational field equations," in Gravitation: An Introduction to Current Research, edited by L. Witten (Wiley, New York).
2. D. Kramer, H. Stephani, M. MacCallum, and E. Herlt, Exact Solutions of Einstein's Field Equations (Cambridge University Press, Cambridge, 1980).
3. E. Zakhary and C. B. G. McIntosh, Gen. Relativ. Gravit. 5, 539 (1997).
4. S. Bonanos, J. Math. Phys. 40, 2064 (1999).
5. G. E. Sneddon, J. Math. Phys. 37, 1059 (1996).
6. G. E. Sneddon, J. Math. Phys. 39, 1659 (1998).
7. G. E. Sneddon, J. Math. Phys. 40, 5905 (1999).
8. J. Géhéniau and R. Debever, Helv. Phys. Acta 4, 101 (1956).
9. J. Géhéniau and R. Debever, Bull. Acad. R. Belg. Cl. Sci. 42, 114 (1956).
10. J. Géhéniau, Bull. Acad. R. Belg. Cl. Sci. 42, 525 (1956).
11. P. J. Greenberg, Stud. Appl. Math. 51, 277 (1972).
12. V. V. Narlikar and K. R. Karmarkar, Proc. Ind. Acad. Sci. A 29, 91 (1948).
13. A. Z. Petrov, Einstein Spaces (Pergamon, New York, 1969).
14. G. E. Sneddon, Class. Quantum Grav. 3, 1031 (1986).
15. G. Sobczyk, J. Math. Phys. 22, 333 (1981).
16. L. Witten, Phys. Rev. 113, 357 (1959).
17. J. Carminati and R. G. McLenaghan, J. Math. Phys. 32, 3135 (1991).
18. Most of the calculations were carried out using the MAPLE computer algebra system and use was made of the NP spinor package (Ref. 19).
19. S. R. Czapor, R. G. McLenaghan, and J. Carminati, Gen. Relativ. Gravit. 24, 911 (1992).
20. G. C. Joly and M. A. H. MacCallum, Class. Quantum Grav. 7, 541 (1990).
21. J. Carminati and R. G. McLenaghan, unpublished work.
22. G. S. Hall, J. Phys. A 9, 541 (1976).
23. The indicated conditions on the NP curvature components are valid in the canonical Segre frame.