Pseudo-Riemannian VSI spaces

Details Pseudo-Riemannian VSI spaces Pseudo-Riemannian VSI spaces

2010-08-17

arxiv.org/abs/1008.2838v1

Class.Quant.Grav.28:015008,2011

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

14 pages

Scientific paper

10.1088/0264-9381/28/1/015008

In this paper we consider pseudo-Riemannian spaces of arbitrary signature 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 ${\bf S}_i$- and ${\bf N}$-properties, and show that if the curvature tensors of the space possess the ${\bf N}$-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.

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