Weyl collineations that are not curvature collineations

Details Weyl collineations that are not curvature collineations Weyl collineations that are not curvature collineations

2008-12-28

arxiv.org/abs/0812.4810v1

Int.J.Mod.Phys.D14:1431-1437,2005

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

9 pages

Scientific paper

10.1142/S021827180500695X

Though the Weyl tensor is a linear combination of the curvature tensor, Ricci tensor and Ricci scalar, it does not have all and only the Lie symmetries of these tensors since it is possible, in principle, that "asymmetries cancel". Here we investigate if, when and how the symmetries can be different. It is found that we can obtain a metric with a finite dimensional Lie algebra of Weyl symmetries that properly contains the Lie algebra of curvature symmetries. There is no example found for the converse requirement. It is speculated that there may be a fundamental reason for this lack of "duality".

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