Pseudo-Riemannian VSI spaces

Understand

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.