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

Details A spacetime not characterized by its invariants is of aligned type II A spacetime not characterized by its invariants is of aligned type II

Nov 2011

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2011cqgra..28u5009h&link_type=abstract

Classical and Quantum Gravity, Volume 28, Issue 21, pp. 215009 (2011).

Computer Science

1

Scientific paper

By using invariant theory we show that a (higher-dimensional) Lorentzian metric that is not characterized 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 characterized by its invariants, must be of aligned type II. This result enables us to prove a number of related results, among which is the algebraic vanishing curvature invariant conjecture.

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