Pseudo-Riemannian VSI spaces
Journal article, Peer reviewed
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Original versionHervik, S and Coley, A. (2011). Pseudo-Riemannian VSI spaces. Classical and Quantum Gravity, 28(1) doi:10.1088/0264-9381/28/1/015008
In this paper we consider pseudo-Riemannian spaces of arbitrary sig- nature for which all of their polynomial curvature invariants vanish (VSI spaces). We discuss an algebraic classification of pseudo-Riemannian spaces in terms of the boost weight decomposition and define the Si- and N-properties, and show that if the curvature tensors of the space possess the N-property then it is a VSI space. We then use this result to construct a set of metrics that are VSI. All of the VSI spaces constructed possess a geodesic, expansion-free, shear-free, and twist-free null-congruence. We also discuss the related Walker metrics.
This is an author-created, un-copyedited version of an article accepted for publication in Classical and quantum gravity. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at doi: doi:10.1088/0264-9381/28/1/015008