Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2006-01-26
J.Math.Phys. 47 (2006) 062503
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
18 pages; v-3: minor changes
Scientific paper
10.1063/1.2207717
The second order Killing and conformal tensors are analyzed in terms of their spectral decomposition, and some properties of the eigenvalues and the eigenspaces are shown. When the tensor is of type I with only two different eigenvalues, the condition to be a Killing or a conformal tensor is characterized in terms of its underlying almost-product structure. A canonical expression for the metrics admitting these kinds of symmetries is also presented. The space-time cases 1+3 and 2+2 are analyzed in more detail. Starting from this approach to Killing and conformal tensors a geometric interpretation of some results on quadratic first integrals of the geodesic equation in vacuum Petrov-Bel type D solutions is offered. A generalization of these results to a wider family of type D space-times is also obtained. A generalization of these results to a wider family of type D space-times is also obtained.
Coll Bartolomé
Ferrando Joan Josep
Sáez Juan Antonio
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