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arXiv · 1109.2551

A spacetime not characterised by its invariants is of aligned type II

Sigbjorn Hervik
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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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Sigbjorn Hervik. 2011-09-12. A spacetime not characterised by its invariants is of aligned type II. https://doi.org/10.1088/0264-9381%2F28%2F21%2F215009

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