On the algebraic types of the Bel–Robinson tensor
- 67 Downloads
The Bel–Robinson tensor is analyzed as a linear map on the space of the traceless symmetric tensors. This study leads to an algebraic classification that refines the usual Petrov–Bel classification of the Weyl tensor. The new classes correspond to degenerate type I space-times which have already been introduced in literature from another point of view. The Petrov–Bel types and the additional ones are intrinsically characterized in terms of the sole Bel–Robinson tensor, and an algorithm is proposed that enables the different classes to be distinguished. Results are presented that solve the problem of obtaining the Weyl tensor from the Bel–Robinson tensor in regular cases.
KeywordsBel–Robinson tensor Gravitational superenergy Petrov–Bel classification
Unable to display preview. Download preview PDF.
- 3.Bel, L.: Cah. de Phys. 16, 59 (1962). This article has been reprinted in Gen. Rel. Grav. 32, 2047 (2000)Google Scholar
- 8.Penrose, R., Rindler, W.: Spinors and spacetime, vol. 1, 2. Cambridge U.P., Cambridge (1984)Google Scholar
- 12.Petrov, A.Z.: Sci. Not. Kazan Univ. 114, 55 (1954). This article has been reprinted in Gen. Rel. Grav. 32, 1665 (2000)Google Scholar
- 13.Ferrando, J.J., Sáez, J.A.: (in preparation)Google Scholar
- 18.Stephani, H., Kramer, D., MacCallum, M., Hoenselaers, C., Herlt, E.: Exact solutions to Einstein’s field equations. Cambridge University Press, Cambridge (2003)Google Scholar