On the problem of algebraic completeness for the invariants of the Riemann tensor. II

Journal of Mathematical Physics

Volumn 43, Issue 1, 2002, Pages 492-507

  Carminati, J ^a   Zakhary, E ^a   McLenaghan, R G ^b  

^a DEAKIN UNIVERSITY   (Australia)

^b UNIVERSITY OF WATERLOO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035981965     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1418427     Document Type: Article

References (13)

1. E. Zakhary and J. Carminati, J. Math. Phys. 42, 1474 (2001).
2. J. Carminati and R.G. McLenaghan, unpublished work.
3. E. Zakhary, Ph.D. thesis, Monash University, 1995.
4. Equivalent real.
5. Number (equivalent real) of curvature unknowns solved for in terms of the invariants and remaining, if any, curvature components.
6. However, if further information like the additional structure of the Weyl tensor is supplied, then a NCB case might become a CB one.
7. G.C. Joly and M.A.H. MacCallum, Class. Quantum Grav. 7, 541 (1990).
8. E. Zakhary and C.B.G. McIntosh, Gen. Relativ. Gravit. 5, 539 (1997).
9. J. Carminati and R.G. McLenaghan, J. Math. Phys. 32, 3135 (1991).
10. G.S. Hall, J. Phys. A 9, 541 (1976).
11. R.V. Churchill, Trans. Am. Math. Soc. 34, 784 (1932).
12. C.B.G. McIntosh, J.M. Foyster, and A.W.C. Lun, J. Math. Phys. 22, 2620 (1981).
13. Special cases do exist which allow complete backsolving. Thus an alignment between an eigenvector of the Ricci tensor with a repeated principal null vector of the Weyl tensor is a necessary but not sufficient condition to prevent complete backsolving. More details on this aspect will be provided in a sequel paper.