On the invariant symmetries of the $\mathcal{D}$-metrics

Details On the invariant symmetries of the $\mathcal{D}$-metrics On the invariant symmetries of the $\mathcal{D}$-metrics

2007-06-22

arxiv.org/abs/0706.3301v2

J.Math.Phys.48:102504,2007

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

18 pages; v2: minor changes

Scientific paper

10.1063/1.2799264

We analyze the symmetries and other invariant qualities of the $\mathcal{D}$-metrics (type D aligned Einstein Maxwell solutions with cosmological constant whose Debever null principal directions determine shear-free geodesic null congruences). We recover some properties and deduce new ones about their isometry group and about their quadratic first integrals of the geodesic equation, and we analyze when these invariant symmetries characterize the family of metrics. We show that the subfamily of the Kerr-NUT solutions are those admitting a Papapetrou field aligned with the Weyl tensor.

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