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

Journal of Mathematical Physics

Volumn 43, Issue 8, 2002, Pages 4020-4034

  Carminati, J ^a   Zakhary, E ^a  

^a DEAKIN UNIVERSITY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035981745     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1478803     Document Type: Article

References (10)

1. E. Zakhary and J. Carminati, J. Math. Phys. 42, 1474 (2001).
2. J. Carminati, E. Zakhary, and R. McLenaghan, J. Math. Phys. 43, 492 (2002).
3. 4 = 0 and the case would become completely backsolvable. This comment would obviously also apply to other not completely backsolvable cases. 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.
4. A complete analysis of the necessary and/or sufficient conditions for all the not completely backsolvable cases to occur will be done in future work.
5. C.B.G. McIntosh, J.M. Foyster, and A.W.C. Lun, J. Math. Phys. 22, 2620 (1981).
6. G.C. Joly and M.A.H. MacCallum, Class. Quantum Gray. 7, 541 (1990).
7. Equivalent real.
8. Number (equivalent real) of curvature unknowns solved for in terms of the invariants and remaining, if any, curvature components.
9. E. Zakhary, Ph.D thesis, Monash University, 1995.
10. a for Petrov type D, backsolving in this case is, understandably, complete.