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Pseudo-Riemannian VSI spaces

Hervik, Sigbjørn; Coley, Alan
Journal article, Peer reviewed
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URI
http://hdl.handle.net/11250/182387
Date
2011
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  • Vitenskapelige publikasjoner (TN-IMN) [72]
Original version
Hervik, S and Coley, A. (2011). Pseudo-Riemannian VSI spaces. Classical and Quantum Gravity, 28(1)   doi:10.1088/0264-9381/28/1/015008
Abstract
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.
Description
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
Publisher
IOP publishing
Journal
Classical and Quantum Gravity

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