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

Abstract

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.

arXiv comment18 pages; v2: minor changes

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Cited by in corpus (14)

• New identities for linearized gravity on the Kerr spacetime
• An intrinsic characterization of the Kerr metric
• Geometric Invariant Measuring the Deviation from Kerr Data
• On the construction of a geometric invariant measuring the deviation from Kerr data
• Killing spinor initial data sets
• Intrinsic, deductive, explicit, and algorithmic characterization of the Szekeres-Szafron solutions
• Vacuum type D initial data
• An intrinsic characterization of 2+2 warped spacetimes
• Charges for linearized gravity
• Type D vacuum solutions: a new intrinsic approach
• Killing-Yano tensors in spaces admitting a hypersurface orthogonal Killing vector
• Spacetime characterizations of $\Lambda$-vacuum metrics with a null Killing 2-form
• Birkhoff theorem and conformal Killing-Yano tensors
• A spacetime characterization of the Kerr-NUT-(A)de Sitter and related metrics