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.
A spacetime not characterised by its invariants is of aligned type II
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abstract
By using invariant theory we show that a (higher-dimensional) Lorentzian metric that is not characterised by its invariants must be of aligned type II; i.e., there exists a frame such that all the curvature tensors are simultaneously of type II. This implies, using the boost-weight decomposition, that for such a metric there exists a frame such that all positive boost-weight components are zero. Indeed, we show a more general result, namely that any set of tensors which is not characterised by its invariants, must be of aligned type II. This result enables us to prove a number of related results, among them the algebraic VSI conjecture.
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gr-qc 1years
2019 1verdicts
UNVERDICTED 1representative citing papers
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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.