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Locally Homogeneous Kundt Triples and CSI Metrics
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Locally Homogeneous Kundt Triples and CSI Metrics
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A pseudo-Riemannian manifold is called CSI if all scalar polynomial invariants constructed from the curvature tensor and its covariant derivatives are constant. In the Lorentzian case, the CSI spacetimes have been studied extensively due to their application to gravity theories. It is conjectured that a CSI spacetime is either locally homogeneous or belongs to the subclass of degenerate Kundt metrics. Independent of this conjecture, any CSI spacetime can be related to a particular locally homogeneous degenerate Kundt metric sharing the same scalar polynomial curvature invariants. In this paper we will invariantly classify the entire subclass of locally homogeneous CSI Kundt spacetimes which are of alignment type {\bf D} to all orders and show that any other CSI Kundt metric can be constructed from them.
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Cited by 1 Pith paper
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Locally Boost Isotropic Spacetimes and the Type ${\bf D}^k$ Condition
All type D^k spacetimes are identified as degenerate Kundt metrics obeying precise conditions on their metric functions, and any two can be distinguished by their scalar polynomial curvature invariants.
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